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# Suddenly, you live in the dark!

Imagine that you lived in this world:

• The planet has a diameter of 5000 km.
• The rotation time is the same as the orbital period.
• And here it comes: the orbital period is 1027 years.
• The planet's orbit is similar to Pluto's, only much more elliptical.
• For just over 30 days, the planet is in the inner solar system, and then runs away to the distant darkness for 1026 years.

I wonder if this would be possible, and whether the planet could get so far from the sun without escaping it entirely?

And here comes the predictable question: Could there be life on such a planet?

I don't ask life like on Earth, of course: It would be adapted to darkness, and able to survive in very low temperatures. Still:

• In outer space, over so many centuries, the temperature gets really low.
• Could a species accustomed to the darkness possibly adapt to the light and heat of the sun for a few days?
• Could they have somehow developed a technology that "captured" the heat from the brief time near the sun, and would store and release it over 1026 years?

I know, it probably sounds very unrealistic, but I'd really like to see if something like this could be plausible.

• Check out A Deepness in the Sky by Verner Vinge. Their sun turned off for 200 years and was on for a 30 years, or something like that. – JDługosz Dec 27 '14 at 1:43
• The planet reaches 5000 km : is this the radius ? – Vincent Dec 27 '14 at 2:07
• Just a tangential note, but there's no reason to expect a planet with such a hugely eccentric orbit to have synchronous rotation. Even if its rotation did become resonantly locked, it would almost surely fall into a higher resonance than 1:1. Even Mercury's orbit is eccentric enough to keep it in a 3:2 resonance, and its orbit is nearly circular compared to you planet's. – Ilmari Karonen Dec 27 '14 at 13:14
• Similar idea to Nightfall, but different. – Shokhet Dec 28 '14 at 19:49
• There's another issue with the tidal locking of an eccentric orbit (beyond the fact that it's not likely to occur). Unlike a regular tidal locking, the star wouldn't actually appear stationary in the sky. This is because the rotational velocity would be constant, but the orbital velocity would not be. As seen from the "prime meridian", the sun would start directly overhead from its furthest point, then slowly approach one horizon, then get larger as the planet gets closer, then swiftly pass the zenith to the opposite horizon, then retreat smaller again, then slowly go back to center. – Caleb Hines Dec 28 '14 at 23:19

## 7 Answers

Life growing on such an unusual planet would certainly reflect its orbit. There would be virtually no movement during the cold period. During the summer "month," life would have to reap all of the energy it can, and then lie dormant again.

There are shorter term examples of this extreme seasonal behavior on Earth. There are plants growing in the Australian Outback which leave their seeds dormant for years, waiting for the rains. They don't respond to the first rain in a year, they respond to the second. This indicates an unusually "wet" year and signals a good time to grow.

During the summer, the flora would be extravagant, using all of the energy they can to further their existence.

Interesting things could form near cracks if you have a warm core, but I'm guessing you're interested in a cold core.

I would not be surprised if you saw life find an alternative method of evolution besides simple sexual and asexual reproduction. The long periods in the cold would be rough and creatures waking up would need to "inventory" their genetic code for mistakes over the years. Creatures which can identify and spread genetic material faster stand a better chance of survival.

I would also expect species which defy categorization along Earth lines. In the cold, spores would fare the best, an isolated multitude of genetic copies. As the spring arrives, plant-like life would flourish, getting a head start on the rest of the ecosystem. As summer arrives, animal life would flourish (especially short lived creations like Mayflies). In the fall, the plants would gather energy for one last hurrah, showering spores across the planet.

Given how strong such evolutionary forces would be, I would not be surprised to see species which rely on all three forms of life: ten centuries waiting as spores, just to wake up in the spring and attempt to gather all of the energy they can. In the summer, they would go under a transformation to get a head-start on evolution: they would spawn a multitude of Mayfly like animals whose entire purpose in life is to "discuss" the genetic viability of the plants that spawned them and identify what the next "crop" will contain genetically. They would then "polinate" their host plants and ceremoniously die by walking into a honeypot trap to be turned into the raw materials needed to spew billions of spores across the sky. The plants would then die off as the next winter begins, and the planet would lie in wait.

Of course this is just one exotic answer. The joy of inventing a planet like your is that you have limitless options as to how things can evolve. Your imagination is the limit.

The orbit you describe is typical for (moderately) long-period comets.

Given the desired orbital period, we can calculate the semi-major axis of the orbit (which, for a highly elliptical orbit like this, is approximately half its maximum distance from the star) using the formula $$T^2 = \frac{4\pi^2}{GM}a^3,$$ where $T$ is the orbital period, $a$ is the semi-major axis, $M$ is the mass of the star (the mass of the planet is assumed to be negligible in comparison) and $G$ is the universal gravitational constant. However, if we assume that the planet is orbiting a star of about the same mass as our Sun, and if we measure time in years and distance in AUs, we can take a shortcut: we know the Earth orbits the Sun in one year, with a semi-major axis of one AU, so we must have $a=1$ when $T=1$. The constant of proportionality thus simply becomes $1$, and we're left with $a = T^{2/3}$. For $T=1027$ (years), this works out to $a\approx 101.8$ (AU), so our hypothetical planet gets no further than $2a\approx203.6$ AU from the Sun.

This is beyond the classical Kuiper belt, but much closer to the Sun than the Oort cloud, which is believed to be the source of most long-period comets. It is also closer to the Sun than several recently discovered "detached objects" such as 90377 Sedna, which are believed to have relatively stable orbits. Your planet thus remains well within the Sun's gravitational well, and is at little risk of being scattered by passing stars. (Well, at least as long as they don't pass too close, in which case we could all be in trouble anyway.)

There is a problem, though.

Your planet might be safe and stable as long as it's far away from the Sun, but as soon as its orbit takes it into the inner solar system, it's going to occasionally pass close to to the planets already there, and thus be affected by their gravity. Such interactions could have many possible outcomes, but the statistically most likely one (at least in a solar system similar to ours) is a close pass with a large gas planet like Jupiter, which will either fling the "comet planet" straight out of the system, or, more likely, kick it into a shorter-period orbit that will keep it interacting with the other planets in the system until it gets ejected from the solar system, collides with the Sun or one of the planets, or (least likely) get captured into a stable near-circular orbit.

So, to keep our hypothetical planet safe, we really should clear the solar system of any inner planets that might disturb its orbit. Fortunately, that might not be so implausible — something obviously caused our planet to end up in that highly elliptical orbit in the first place, and it's not altogether implausible that the same something (which could've been, say, another star passing through the inner solar system) might have also conveniently swept the system clean of any inner planets in more conventional orbits. (Indeed, our planet might well have been one of those, before it was scattered into its new eccentric orbit.)

OK, so we've got the orbit stabilized. What about the climate?

First of all, let me note that there's absolutely no reason to expect a planet with an orbit like this to be tidally locked, and certainly not to a 1:1 resonance like you suggest. On such an eccentric orbit, the planet would feel almost no tides at all for most of the time, and would only experience a single tidal nudge every time it passed close to the Sun. If anything, if it locked at all, it should therefore lock to a rotational speed approximately matching its orbital angular velocity near perihelion. But I suspect it just wouldn't lock at all, but would simply retain whatever rotational period it originally started with.

So what's the weather like? Well, for most of its orbit, this planet is going to be so far from the Sun that it might as well be in interstellar space — the Sun will just be the brightest star among many in the sky. Without any significant heat from the Sun, any seas the planet may have will all but freeze solid, and even the atmosphere will freeze and snow down. In general, the surface of such a planet seems pretty inhospitable for life, or at least any kind of life as we know it.

That said, if the planet is large enough, and possesses a massive rocky core, it's possible that the bottom layers of the oceans might stay liquid due to geothermal heat (from trapped primordial heat, and from decay of radioactive elements in the core). Such a subglacial ocean could potentially support life, even if the available free energy would likely be orders of magnitude less than that on Earth's surface.

Thus, we might expect any life on such a planet to be aquatic, and likely to cluster around hydrothermal vents at the bottom of the ocean, like some deep-sea ecosystems do on Earth. Generally, I would not expect life under such conditions to evolve very fast, but in science fiction, even unlikely events are still possible, and so of you want to postulate advanced, even intelligent life to have evolved under such conditions, I'd be happy to suspend my disbelief.

To such an ecosystem, living under a kilometers-thick blanket of ice, safe from to freezing cold of space, would be the norm. The rare and brief passes close to the Sun, if felt at all beneath the thick ice blanket, would be abnormal and catastrophic events: suddenly, scorching rays of heat blast down from what's normally the coldest part of the world, melting the ice and upsetting the ocean circulation.

Of course, any life that did survive such events would eventually adapt to them, but they couldn't possibly be easy on any hypothetical subglacial civilization on your world. Then again, that could make for an excellent story...

• You know, +1 for having the guts to drag the relevant math into it, and for an answer after my own heart. Excellent climate analysis; do you think that there would be any tidal forces at work on the planet, as there is between Jupiter and some of its moons (I'm guessing nothing of any importance because of the enormous distances we're talking about here). – HDE 226868 Dec 28 '14 at 0:18
• @HDE226868: Most of the time, I'd say no, unless the planet happens to have a massive moon of its own (and I have no idea how stable that could be, with such an eccentric orbit) and isn't tide-locked to it (like Pluto and Charon are). There would be solar tides at perihelion, which could well make things even more interesting -- not only is the solid ice crust suddely melting, but it's flexing and buckling too! Depending on stuff like the rotation rate, the perihelion distance and the thickness of the ice, it might seem like the mother of all earthquakes. – Ilmari Karonen Dec 28 '14 at 0:24
• One way to reduce the chance of being ejected would be to give it an orbit inclined well above the plane of the ecliptic. Eris, for example, is 44° above. – Schwern Dec 29 '14 at 7:16
• The idea of a relatively normal star system that gets disrupted might also explain more complex life. If life originally evolved in a more normal orbit and then had to adapt to the radically changed orbit that might work. – Tim B Dec 29 '14 at 9:57

There would be a big problem with life on such a world. As Cort Ammon says it's quite possible for life to survive in such an environment. Evolving is another matter, though. Single cell life will survive it as it generally can take being frozen. Multi-cellular life is another matter--I don't think there's anything that can survive that kind of cold other than in a totally dormant state (seeds, spores etc.) and multi-cellular life isn't going to start out that way. Thus you have an uncrossable evolutionary chasm.

The only way I see to have non-microbial life on such a world is if it started out as a terrestrial world and it's orbit slowly got stretched--enough time for plants (and conceivably even egg-laying animals) to adapt.

Note, also, that such an orbit (and it's months of sun, not days) means life spends almost all it's time in the dormant state, it can only evolve during the warm periods. It's going to evolve VERY slowly. While it has billions of years of orbiting it's star it will only evolve like it's been millions--you will not see any major changes from whatever life looked like before the orbit got stretched.

• Exactly. Life surviving somehow: possible, very low life forms. Evolving? Very unlikely. – Peter M. Dec 29 '14 at 15:53

Could there be life on such a planet? Yes, of course. Something worth researching, if you're ever looking for inspiration, are Extremophiles and Tardigrades.

Extremophiles are species which are adapted to extreme environments, whereas Tardigrades are capable of surviving in extreme environments, but are not adapted to them.

There are a lot of options here; you could have a species which freezes itself for the 1026 years, only to reanimate shortly before the sun cycle. There are many species of insects which appear only shortly (a few days) during a season to breed and reproduce; you could have something similar where they use the coldness of space to hibernate or suspend animation until the warmth comes back around.

On the flip side, what if the species are adapted to the cold, surviving off of minerals on rocks and good ol' natural selection, but are unable to withstand the 30 days of warmth? Every 1026 years they would either have to burrow closer to the cold core (assuming a cold core) to hide from the heat / UV of the sun.

>> Could they have somehow developed a technology that "captured" the heat from the brief time near the sun, and would store and release it over 1026 years?

The first thing this makes me think about is how the warmth of the 30 days would react with a normally cold planet.... Let's say the surface is dry; only rocks and minerals. But let's say there's water beneath the surface, but frozen (obviously). During 30 days of warmth, depending on how sudden the warmth comes on, it could cause cracking / shifting on the surface, releasing springs of water or pressure from beneath the surface to crack open.

And that's essentially how we generate electricity (take coal, pound it into talcum powder, ignite it in an enclosed space, filled with water pipes. When the water turns to steam, the pressure triggers a valve which pushes the steam through a turbine, inside of which is a magnet and copper wires - hence, electricity). A planet with plenty of minerals (copper, magnets, chemicals, etc), but lacking water, could use released pressure from inside the surface to "capture" the energy as electricity, storing it in fuel cells.

If electricity generation is a bit straight-forward; if you're looking for something more "magical", then what about capturing light? Definitely a bit beyond what's currently considered "plausible", but perhaps they found a way to trap the visible light (or UV) from the 30 days in containers (think an orb which is a one-way mirror; after the light gets in it cannot get out). As such, they could "release" the energy / light over 1026 years, but it would be a treasured resource.

In any case, I don't think you're outside the realm of what's plausible. Half the fun in making planets is making things beyond what we would normally think.

Note: I used the software Universe sandbox2 to get the numbers used in my answer.

Suopposing a planet about the size of Earth having an orbital period of more or less 1027 years around a sunlike star, it would be at 15 billion kilometres or 102 AU from the star. That is very far. You are still considered in the star system but it's too cold to have liquid water. In this test I used an orbit that was almost a perfect circle, but it gives a good idea of the situation. With an ellipse, the planet would be further away. How close and how far can it go, I don't know for sure but the coldest is too cold for life as we know it.

Other form of life could sustain the cold temperatures but if there is a large temperature difference between the hottest and coldest points, life might not be possible.

More about exotic form of life: Is it possible for life to evolve on planets without water?

• The orbital period depends on the semi-major axis, which equals the orbital radius for a circular orbit, and approximately half the maximum distance for a very highly elliptical orbit. So a highly elliptic orbit with a period of 1027 years around the sun would get about 204 AU from the sun. – Ilmari Karonen Dec 27 '14 at 22:34

Look at the orbit of comets. You can plot the exact path and timing. You'll find it spends several months in the vicinity of the sun. You're nowhere near losing the sun's grip: look up Sedna.

I think the planet's surface will always become ridiculously cold, but if the planet has a molten core, that might allow some warm enough underground areas. If the crust has an extensive cave system that can remain stable enough for life to move in and out as needed, that might present a possibility.

A different planet with a very long day cycle but more consistent heat in the lighted region, might be able to support animals which can migrate around the planet, staying in the light.

If you are looking for different values for your orbit, consider that the star's size and brightness can also vary.


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## Engage NY Eureka Math 8th Grade Module 6 Lesson 4 Answer Key

### Eureka Math Grade 8 Module 6 Lesson 4 Exercise Answer Key

Exercise 1.
Read through each of the scenarios, and choose the graph of the function that best matches the situation. Explain the reason behind each choice.
a. A bathtub is filled at a constant rate of 1.75 gallons per minute.
b. A bathtub is drained at a constant rate of 2.5 gallons per minute.
c. A bathtub contains 2.5 gallons of water.
d. A bathtub is filled at a constant rate of 2.5 gallons per minute.

Scenario:
Explanation:
Scenario: c

Explanation: The amount of water in the tub does not change over time; it remains constant at 2.5 gallons.

Scenario:
Explanation:
Scenario: b

Explanation: The bathtub is being drained at a constant rate of 2.5 gallons per minute. So, the amount of water is decreasing, which means that the slope of the line is negative. The graph of the function also shows that there are initially 20 gallons of water in the tub.

Scenario:
Explanation:
Scenario: d

Explanation: The tub is being filled at a constant rate of 2.5 gallons per minute, which implies that the amount of water in the tub is increasing, so the line has a positive slope. Based on the graph, the amount of water is also increasing at a faster rate than in choice (a).

Scenario:
Explanation:
Scenario: d

Explanation: The tub is being filled at a constant rate of 2.5 gallons per minute, which implies that the amount of water in the tub is increasing, so the line has a positive slope. Based on the graph, the amount of water is also increasing at a faster rate than in choice (a).

Exercise 2.
Read through each of the scenarios, and sketch a graph of a function that models the situation.
a. A messenger service charges a flat rate of $4.95 to deliver a package regardless of the distance to the destination. Answer: Answer: The delivery charge remains constant regardless of the distance to the destination. b. At sea level, the air that surrounds us presses down on our bodies at 14.7 pounds per square inch (psi). For every 10 meters that you dive under water, the pressure increases by 14.7 psi. Answer: The initial value is 14.7 psi. The function increases at a rate of 14.7 psi for every 10 meters, or 1.47 psi per meter. c. The range (driving distance per charge) of an electric car varies based on the average speed the car is driven. The initial range of the electric car after a full charge is 400 miles. However, the range is reduced by 20 miles for every 10 mph increase in average speed the car is driven. Answer: The initial value of the function is 400. The function is decreasing by 20 miles for every 10 mph increase in speed. In other words, the function decreases by 2 miles for every 1 mph increase in speed. Exercise 3. The graph below represents the total number of smartphones that are shipped to a retail store over the course of 50 days. Match each part of the graph (A, B, and C) to its verbal description. Explain the reasoning behind your choice. i. Half of the factory workers went on strike, and not enough smartphones were produced for normal shipments. Answer: C; if half of the workers went on strike, then the number of smartphones produced would be less than normal. The rate of change for C is less than the rate of change for A. ii. The production schedule was normal, and smartphones were shipped to the retail store at a constant rate. Answer: A; if the production schedule is normal, the rate of change of interval A is greater than the rate of change of interval C. iii. A defective electronic chip was found, and the factory had to shut down, so no smartphones were shipped. Answer: B; if no smartphones are shipped to the store, the total number remains constant during that time. Exercise 4. The relationship between Jameson’s account balance and time is modeled by the graph below. a. Write a story that models the situation represented by the graph. Answer: Answers will vary. Jameson was sick and did not work for almost a whole week. Then, he mowed several lawns over the next few days and deposited the money into his account after each job. It rained several days, so instead of working, Jameson withdrew money from his account each day to go to the movies and out to lunch with friends. b. When is the function represented by the graph increasing? How does this relate to your story? Answer: It is increasing between 6 and 9 days. Jameson earned money mowing lawns and made a deposit to his account each day. The money earned for each day was constant for these days. This is represented by a straight line. c. When is the function represented by the graph decreasing? How does this relate to your story? Answer: It is decreasing between 9 and 14 days. Since Days 9–14 are represented by a straight line, this means that Jameson spent the money constantly over these days. Jameson cannot work because it is raining. Perhaps he withdraws money from his account to spend on different activities each day because he cannot work. ### Eureka Math Grade 8 Module 6 Lesson 4 Problem Set Answer Key Question 1. Read through each of the scenarios, and choose the graph of the function that best matches the situation. Explain the reason behind each choice. a. The tire pressure on Regina’s car remains at 30 psi. b. Carlita inflates her tire at a constant rate for 4 minutes. c. Air is leaking from Courtney’s tire at a constant rate. Scenario: Explanation: Answer: Scenario: c Explanation: The tire pressure decreases each minute at a constant rate. Scenario: Explanation: Answer: Scenario: a Explanation: The tire pressure remains at 30 psi. Scenario: Explanation: Answer: Scenario: b Explanation: The tire pressure is increasing each minute at a constant rate for 4 minutes. Question 2. A home was purchased for$275,000. Due to a recession, the value of the home fell at a constant rate over the next 5 years.
a. Sketch a graph of a function that models the situation.

Graphs will vary; a sample graph is provided.

b. Based on your graph, how is the home value changing with respect to time?
The value is decreasing by $25,000 over 5 years or at a constant rate of$5,000 per year.

Question 3.
The graph below displays the first hour of Sam’s bike ride.

Match each part of the graph (A, B, and C) to its verbal description. Explain the reasoning behind your choice.
i. Sam rides his bike to his friend’s house at a constant rate.
A; the distance from home should be increasing as Sam is riding toward his friend’s house.

ii. Sam and his friend bike together to an ice cream shop that is between their houses.
C; Sam was at his friend’s house, but as they start biking to the ice cream shop, the distance from Sam’s home begins to decrease.

iii. Sam plays at his friend’s house.
B; Sam remains at the same distance from home while he is at his friend’s house.

Question 4.
Using the axes below, create a story about the relationship between two quantities.
a. Write a story about the relationship between two quantities. Any quantities can be used (e.g., distance and time, money and hours, age and growth). Be creative. Include keywords in your story such as increase and decrease to describe the relationship.
Answers will vary. Give students the freedom to write a basic linear story or a piecewise story.
A rock climber begins her descent from a height of 50 feet. She slowly descends at a constant rate for 4 minutes. She takes a break for 1 minute; she then realizes she left some of her gear on top of the rock and climbs more quickly back to the top at a constant rate.

b. Label each axis with the quantities of your choice, and sketch a graph of the function that models the relationship described in the story.

Answers will vary based on the story from part (a).

### Eureka Math Grade 8 Module 6 Lesson 4 Exit Ticket Answer Key

Question 1.
The graph below shows the relationship between a car’s value and time.

Match each part of the graph (A, B, and C) to its verbal description. Explain the reasoning behind your choice.
i. The value of the car holds steady due to a positive consumer report on the same model.
B; if the value is holding steady, there is no change in the car’s value between years.

ii. There is a shortage of used cars on the market, and the value of the car rises at a constant rate.
C; if the value of the car is rising, it represents an increasing function.

iii. The value of the car depreciates at a constant rate.
A; if the value depreciates, it represents a decreasing function.

Question 2.
Henry and Roxy both drive electric cars that need to be recharged before use. Henry uses a standard charger at his home to recharge his car. The graph below represents the relationship between the battery charge and the amount of time it has been connected to the power source for Henry’s car.

a. Describe how Henry’s car battery is being recharged with respect to time.

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# Easy question about convergence in mean

Let $(a_n)$ be a sequence of real numbers and $g\in \mathbb{R}$. Assume that $$\frac{a_1+\cdots+a_n}{n}\rightarrow g$$ as $n \rightarrow \infty$. Now let $k \in \mathbb{N}$. Is it then $$\frac{a_{k+1}+\cdots+a_{k+n}}{n} \rightarrow g$$

Thanks.

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Yes: $$\frac{a_{k+1}+\cdots+a_{k+n}}n=\frac{k+n}n\left(\frac{a_1+\cdots+a_{k+n}}{k+n}-\frac{a_1+\cdots+a_k}{k+n}\right)\;,$$ which clearly approaches $g$ as $n\to\infty$.
Yes this is true since $$\lim_{n\rightarrow\infty}\frac{a_1+a_2+\cdots +a_k}{n}=0,$$ as the numerator is a fixed constant since $k$ is fixed. This means we can remove the first $k$ terms without affecting the limit.
May I ask you what happened to $a_{k+n}$ in your limit above? – Babak S. Jan 18 '12 at 19:04


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# get_corvars: Generate normal, correlated variables In metan: Multi Environment Trials Analysis

## Description

Given the mean and desired correlations, generate normal, correlated variables.

## Usage

 1 get_corvars(n = 10, mu, sigma, tol = 1e-06, seed = NULL)

## Arguments

 n The number of samples required. mu A vector with the means for the variables. sigma A symmetric, positive-definite matrix with the (co)variance or correlation matrix of the variables. tol Tolerance (relative to largest variance) for numerical lack of positive-definiteness in sigma. seed An integer value interpreted as seed.

## Value

A tibble containing the simulated data.

## Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

## Examples

 1 2 3 4 5 6 7 8 sigma <- matrix(c(1, .3, 0, .3, 1, .9, 0, .9, 1),3,3) mu <- c(6,50,5) df <- get_corvars(n = 10000, mu = mu, sigma = sigma, seed = 101010) means_by(df) cor(df)

metan documentation built on Nov. 10, 2021, 9:11 a.m.


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Get the array of _id in MongoDB?

MongoDBDatabaseBig Data Analytics

The _id in MongoDB is a field, which is mandatory. In MongoDB, each document stored in a collection requires a unique _id field that acts as a primary key. Following is the syntax to get the array of all the ids i.e. _id in MongoDB

db.yourCollectionName.find({ _id : { $in : [yourValue1,yourValue2,yourValue3,.......N] } } ); Let us first implement the following query to create a collection with documents > db.selectInWhereIdDemo.insertOne({"_id":23}); { "acknowledged" : true, "insertedId" : 23 } > db.selectInWhereIdDemo.insertOne({"_id":28}); { "acknowledged" : true, "insertedId" : 28 } > db.selectInWhereIdDemo.insertOne({"_id":45}); { "acknowledged" : true, "insertedId" : 45 } > db.selectInWhereIdDemo.insertOne({"_id":75}); { "acknowledged" : true, "insertedId" : 75 } > db.selectInWhereIdDemo.insertOne({"_id":85}); { "acknowledged" : true, "insertedId" : 85 } > db.selectInWhereIdDemo.insertOne({"_id":145}); { "acknowledged" : true, "insertedId" : 145 } Following is the query to display all the documents from the collection with the help of find() method > db.selectInWhereIdDemo.find().pretty(); This will produce the following output { "_id" : 23 } { "_id" : 28 } { "_id" : 45 } { "_id" : 75 } { "_id" : 85 } { "_id" : 145 } Following is the query to get _id i.e. all the ids in an array > db.selectInWhereIdDemo.find({ _id : {$in : [23,45,85,145] } } );

This will produce the following output

{ "_id" : 23 }
{ "_id" : 45 }
{ "_id" : 85 }
{ "_id" : 145 }
Published on 11-Apr-2019 12:00:18


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The Madelung equations are Erwin Madelung's equivalent alternative formulation of the Schrödinger equation.

## Equations

The Madelung equations[1] are quantum Euler equations:[2]

$\partial_t \rho+\nabla\cdot(\rho\bold u)=0,$
$\partial_t\bold u+\bold u\cdot\nabla\bold u=-\frac{1}{m}\nabla\left(\frac{1}{\sqrt{\rho}}\hat H\sqrt{\rho}\right)=-\frac{1}{\rho}\nabla\cdot\bold p_Q-\frac{1}{m}\nabla U,$

where $\bold u$ is the flow velocity in the quantum probability space with mass density $\bold \rho=m|\psi|^2$. The circulation of the flow velocity field along any closed path obeys the auxiliary condition $\begin{matrix}\Gamma \doteq \oint{m\mathbf{u}\cdot d\mathbf{l}}=2\pi n\hbar , & n\in \mathbb{Z} \\\end{matrix}$.[3] The term in the brackets represents a quantum chemical potential $\mu$ in vacuum. The kinetic energy operator from the Hamiltonian $\hat H$ results in a non-local quantum pressure tensor

$\bold p_Q=-(\hbar/2m)^2 \rho \nabla\otimes\nabla \ln \rho$

which is related to the Bohm quantum potential $Q$. While the latter is the icon of the de Broglie–Bohm theory, $\bold p_Q$ is the quantum symbol of the Madelung hydrodynamics.[4] The integral energy stored in the quantum pressure tensor is proportional to the Fisher information, which accounts for the quality of measurements. Thus, according to the Cramér–Rao bound, the Heisenberg Uncertainty principle is equivalent to a standard inequality for the efficiency (statistics) of measurements. The thermodynamic definition of the quantum chemical potential $\mu =Q+U$ follows from the hydrostatic force balance above $\ \nabla \mu = (m/\rho)\nabla \cdot \bold p_Q + \nabla U$. According to thermodynamics, at equilibrium the chemical potential is constant everywhere, which corresponds straightforward to the stationary Schrödinger equation. Therefore, the eigenvalues of the Schrödinger equation are free energies, which differ from the internal energies of the system. The particle internal energy is calculated via $\ \epsilon = \mu - tr(\bold p_Q)(m / \rho) = -\hbar^2(\nabla\ln \rho)^2/8m + U$ and it is related to the local Carl Friedrich von Weizsäcker correction.[5] In the case of a quantum harmonic oscillator, for instance, one can easily show that the zero point energy is the value of the oscillator chemical potential, while the oscillator internal energy is zero in the ground state, $\ \epsilon = 0$. Hence, the zero point energy represents the energy to place a static oscillator in vacuum, which shows again that the vacuum fluctuations are the reason for quantum mechanics.


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# Help on normal family

Suppose, I have a function $f(z)=\xi z$ where $|\xi|=1$ but $\xi$ is not a root of unity. Then, from the fact that the $n$-th iteration $f^{\circ n}(z)$, $z \in \mathbb{C}$, is dense on the circle around $0$ and radius $|z|$, how can I can deduce that $\{f^{\circ n}\}$ is a normal family?

Thanks for any help!

-

According to the Arzelà–Ascoli theorem (see, e.g., Ahlfors, Complex analysis, chapter 5, section 4.3) a family of continuous functions $f_\alpha: \Omega\to{\mathbb C}$ is normal iff it is equicontinuous on every compact set $E\subset\Omega$. Now given a $\xi$ on the unit circle one has
$$|f^{\circ n}(z_1)-f^{\circ n}(z_2)|=|\xi|^n\ |z_1-z_2|=|z_1-z_2|$$
for all $z_1$, $z_2\in\Omega:={\mathbb C}$, which shows that the condition of the theorem is more than fulfilled whether $\xi$ is a root of unity or not.


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# Astronomy & Astrophysics

2
Is anyone interested in the full data release of the ALHAMBRA data?
The ALHAMBRA survey (http://alhambrasurvey.com/) has just published its 1st full data release.
You can find the the data (catalogs with photo-z and synthetic F814W images) through the following links:
* web server: http://cloud.iaa.es/alhambra/
* FTP server: ftp://ftp.iaa.es/alhambra
* Spanish Virtual Observatory: http://svo2.cab.inta-csic.es/vocats/alhambra/index.php
Enjoy!!
• Source
##### Article: The ALHAMBRA Survey: Bayesian Photometric Redshifts with 23 bands for 3 squared degrees
[Hide abstract]
ABSTRACT: The ALHAMBRA (Advance Large Homogeneous Area Medium Band Redshift Astronomical) survey has observed 8 different regions of the sky, including sections of the COSMOS, DEEP2, ELAIS, GOODS-N, SDSS and Groth fields using a new photometric system with 20 contiguous ~ $300\AA$ filters covering the optical range, combining them with deep $JHKs$ imaging. The observations, carried out with the Calar Alto 3.5m telescope using the wide field (0.25 sq. deg FOV) optical camera LAICA and the NIR instrument Omega-2000, correspond to ~700hrs on-target science images. The photometric system was designed to maximize the effective depth of the survey in terms of accurate spectral-type and photo-zs estimation along with the capability of identification of relatively faint emission lines. Here we present multicolor photometry and photo-zs for ~438k galaxies, detected in synthetic F814W images, complete down to I~24.5 AB, taking into account realistic noise estimates, and correcting by PSF and aperture effects with the ColorPro software. The photometric ZP have been calibrated using stellar transformation equations and refined internally, using a new technique based on the highly robust photometric redshifts measured for emission line galaxies. We calculate photometric redshifts with the BPZ2 code, which includes new empirically calibrated templates and priors. Our photo-zs have a precision of $dz/(1+z_s)=1%$ for I<22.5 and 1.4% for 22.5<I<24.5. Precisions of less than 0.5% are reached for the brighter spectroscopic sample, showing the potential of medium-band photometric surveys. The global $P(z)$ shows a mean redshift =0.56 for I<22.5 AB and =0.86 for I<24.5 AB. The data presented here covers an effective area of 2.79 sq. deg, split into 14 strips of 58.5'x15.5' and represents ~32 hrs of on-target.
Monthly Notices of the Royal Astronomical Society 06/2013; 441(4). DOI:10.1093/mnras/stu387

Hi Somak,

the description of the data in the catalogues can be found in Molino et al.(2014) paper:

If you have doubts about the content of the catalogues, I would suggest to contact directly the first author (Dr. Alberto Molino).

Regarding the public images, you are right, they are indeed the synthetic F814W images reconstructed from the narrow band images. The way in which they have been constructed is also explained in Molino et al.(2014).

Finally, with respect to the NIR images, I'll try to find out whether they will be made public.

Cheers!

24
Why don't we consider the time before the Big Bang?
The entire universe originated from a single point after the Big Bang. Then how can we explain the time before big bang?

Model is restricting " time". The fact may be something else and time may have existed even before Big-Bang. I asked similar question posted in RG:" What was before Big-Bang?" If we accept Big-Bang theory, what has been before that? No space, no time, no mass, no energy, no momentum, no event, no sequence...??!!

6
Are there wave models of planetary orbits in the solar system?
I just found a new paper by Chaudry and Thurman, with the title "A simple planetary evolution model using the solar nebula theory." (H-SC journal, march 2014). See : http://blogs.hsc.edu/sciencejournal/files/2014/03/Chaudhry.pdf

Other papers that I know include the wave universe model by Chechelnitsky, and the fractal Schrodinger model of Laurent Nottale.

Do you know other papers discussing planetary orbits in the solar system using the wave model? Your comments are welcome.

38
Can a planet or star exist without rotating on its axis?
Do magnetic fields exist because of the rotation of planets and stars, or do magnetic fields induce rotation in the planets and stars? Can we say a planet is dead if it does not rotate about its axis?

I know that the actions of the down vote are anonymous..  However I would like to know why my last comment which is well within the excepted science of today, was voted down.

I reserve the down vote for comments that are not scientific or intellectual in nature but just stabs at others.  My concern here is that down votes should not be just because you do not like something or someone.  Have the courage to tell me I am wrong.

If I have pointed out something outside of science or incorrect in this forum I except a rebuttal from someone that knows better than I do.

The down votes can be taken back as can the up votes.  This is a scientific forum not a popularity contest.

6
What are the main astrophysical radio wave sources?
I have a project and I need to know the sources of electromagnetic radiation along with the processes by which they are emitted in space. Any help would be appreciated.

Emission from molecular electronic transitions (rotational and vibrational)

5
Scaling solution to BBGKY-hierarchy in Astrophysics
I am interested in finding closure relations for the BBGKY-equations and came across an old article On the integration of the BBGKY equations for the development of strongly nonlinear clustering in an expanding universe'' by M DAVIS, PJE PEEBLES, Astrophysical Journal Supplement Series, 1977. I am used to closures where the three-particle correlations are either neglected or are approximated by Kirkwood's superposition principle, which appears ad hoc to me and is inaccurate for certain applications.
In the article by Davis and Peebles, something I haven't seen before was used, a scaling solution where n-particle correlation functions are approximated by a simple power law. It looks like this only works if the particles are far apart from each other and if there is no characteristic length scale in the particle interactions, which is the case for gravity. This made me curious: How useful did this approach become in Astrophysics simulations, is it still used or was this a dead end? If not, has there been any recent improvements on this approach?
Has such a scaling approach to the BBGKY-hierarchy been used in other areas of physics, like plasma physics where there is also a power law (Coulomb) interaction?

Thank you for your answer. If your truth would be embarrassing for me, it would also embarrass such icons of soviet physics as Bogolubov and Landau, and I'd be totally fine with being part of that axis-of-shame :-) I agree that one has to be careful with ensemble averages when talking about inhomogeneous systems, for example, when describing soliton-like waves in active matter (see my Phys. Rev. E from 2013, and the Discussion on Ohta paper in 2014)). However, I disagree that hierarchy-equations like the BBGKY-hierarchy are useless in general. In your own papers, you also use such hierarchies of equations for multi-point correlation functions. In my opinion, for the ensemble average, one just has to imagine that only  the proper microscopic members that describe a particular inhomogeneous state are part of the ensemble. For example, for a single soliton, only those microscopic states should be  included that have the same density and momentum profile (coarse-grained over small cells in phase space) at the same time. Another argument to not dismiss BBGKY-like hierarchies is to consider the extreme case of a N-particle ensemble distribution that consists of products of delta-functions at time t. That means, all ensemble members have particles at the same positions with the same momenta and the BBGKY-equations would be equivalent to the evolution of a particular real system with those initial conditions. A more pragmatic argument: I recently used the first two BBGKY equations (adopted to my system) for self-propelled particles in a weakly-correlated limit where three-particle correlations are negligible compared to two-particle ones and I found perfect quantitative agreement with particle-based direct simulations. I didn't have to explicitly select the proper members of the ensemble, I did neither use thermodynamics nor Gibbs distributions, I just solved the time-dependent hierarchy equations until  a stationary state was reached. Thus, if you have an alternative theory, I suggest testing it quantitatively with Molecular Dynamics simulations and see how it does. In contrast to experiments, simulations can be adjusted to mirror all the approximations made in a theory and thus allow comparing apples with apples''. In my opinion, the more serious problem with kinetic theory is the closure of the hierarchy. You mentioned in your papers that you somehow close your equations at the two-particle level but I couldn't find any details. For self-propelled particles, there is parameter ranges where the three-particle correlations are stronger than the two-particle ones and the four-particle-ones are even stronger than three-particle ones and so on. Thus, in this strongly-correlated system, some type of generating function should be found that contains correlations to all orders, at least approximately, or a systematic closure for all multi-particle correlations is needed. In your papers, you mention discrepancies between experiments and theory. Could that also be due to neglecting these higher multi-particle correlations or using an inappropriate closure ?

13
Time freezes at the event of horizon therfore for observer the mass falling into it looks like it doesn't fall, so how could you get this pre and post flare?
At the center of our Milky Way Galaxy, a mere 27,000 light-years away, lies a black hole with 4 million times the mass of the Sun. Fondly known as Sagittarius A* (pronounced A-star), the Milky Way's black hole is fortunately mild-mannered compared to the central black holes in distant active galaxies, much more calmly consuming material around it. From time to time it does flare-up, though.

The flare sequence is illustrated in the panels at the far right. X-rays are generated in material heated to over 100 million degrees Celsius, accelerated to nearly the speed of light as it falls into the Miky Way's central black hole. The main inset X-ray image spans about 100 light-years. In it, the bright white region represents the hottest material closest to the black hole, while the pinkish cloud likely belongs to a nearby supernova remnant.

Credit: NuSTAR project,APOD(NASA)

The motion of a particle near a black hole is given by the geodesics corresponding to the metric describing the black hole. The motion can be described in various coordinate systems, but it is, of course, always the same motion. This motion has no particular singularity at the horizon, if we are talking of an ordinary Schwarzschild black hole. However distant observers will in fact see strange things as the paticle nears the horizon, but these are simply due to the fact that the coordinate system of the distant observer cannot be used to describe the neighbourhood of the horizon.

Saying that time freezes'' is doubtless easier than attempting to describe in detail what a particle does when it comes near a black hole. But it is not nearly as clear, nor nearly as precise. What is the time we mean? In what sense does it freeze''? I do not deny that such expressions may be used to describe what happens, but it is very easy to be led to misconceptions when abstract concepts are used without reference to their concrete use and their precise definitions....

5
How do I check the performance of the Genetic Algorithm in MATLAB ?
As every time GA gives different results but how do I know which one is best ?

Maybe it is possible to check the fitness error but I do not know how to check it

Thanks a lot.
19
What is the possibility of a Carrignton Type event in the recent future ?
I got pulled to the Solar Physics field by interest and now exploring it in its full depth. One major area I have found highly intersting is the Effect of Solar Flares on the technology we possess. In accordance to several anomalies put forward by different research groups, I am curious to know the possibility of a Solar Super storm in the near future. Calling in seasoned researchers to spark a discussion and also come up with ideas to counter attack such an event.
Thanks to all, this discussion has truly beefed up my current understanding. For a young researcher like me, its a gold mine :)
@yuri great work. if that's the frequency, i hope we should be ready in the next 450yrs for such an event. maybe on Mars?
42
What is the effect of microlensing and weak lensing on the stability of the International Celestial Reference Frame?
Spacetime curvature creates a space time "seeing" effect, which is analogous to astronomical seeing. This is due to microlensing and weak lensing, which becomes problematic from an ICRF stability viewpoint as astrometric VLBI and optical measurements (e.g. GAIA) moves into the tens of micro-arcsecond accuracy region. This space time seeing effect will create a noise floor, limiting ICRF stability due to apparent source position distortions and amplitude variations. This will of course have an impact on the high accuracy requirements of the Global Geodetic Observing System (GGOS), which has the objectives of 0.1 mm stability and accuracy of 1 mm for the ITRF. The distribution of dark matter complicates the problem.
Dear Matts, thank you for your useful clarifications that confirm what I think and wrote in my previous comments. You are right, cosmic muons quoted by me in the previous comment are secondary and derive from other charged primary cosmic particles. The astronomy in the twentieth century considered justly first of all neutral cosmic radiations (photons, neutrinos, etc..). Now we know the astronomy for the future will consider always more charged cosmic rays (leptonic or baryonic) that allow to have always more precise knowledges on the structure of the Universe. Thechnologies and methodologies
for this type of astronomy are today more complex but it represents certainly the way for the future astronomy.
11
Why we are interested in Astronomy and Astrophysics? Why we are interested in studying the Cosmos and solving the mysteries of our Universe?

Well... for me, I will tell why i am interested in studying the Cosmos...
"Knowing and understanding the stage on which our life is being played is crucial for any existence to have real meaning."
Astronomy has always been my passion since my childhood. I started looking at the pictures in astronomy books before I could even read. The pictures were beautiful,fascinating and intriguing. As I grew up I wanted to know all about what those pictures meant.I am still learning. Perhaps i like astronomy because we are personally a way of the Universe experiencing itself,or that we are all made of star-stuff,as Carl Sagan so elegantly put it. Astronomy is a science that seeks to explain everything that we observe in the Universe,from the comets and planets in our own solar system to distant galaxies to the echoes of the Big Bang. By studying the cosmos beyond our own planet,we can understand where we came from,where we are going,why is the universe organized as it is?Are we alone? And how physics works under conditions which are impossible to recreate on Earth. In astronomy,the Universe is our laboratory! Astronomy provides an example of an alternative approach to the scientific method- observation,simulation,and theory. It is an enjoyable,inexpensive hobby for millions of people- the naturalists of the night. But above all astronomy has shown us how insignificant the human physical existence is,and how great the human mind with an intelligence that is now embracing a dazzling range of phenomena,from the astronomically large to the infinitely small. I have very little doubt that what astronomy will still give us in the future will dwarf all of its past contributions by comparison. I am motivated by curiosity and a deep desire to understand some of the grandest and most beautiful phenomena in the universe,as well as a desire to share these wonders with others. To me, research is often a bridge to an ambitious goal - a bridge that needs to be crossed in steps..

Astrophysics strike me as one of the most exciting areas of research today. Thanks to new observations,better methods and more powerful simulations that we can now hope to answer,with reasonable confidence,some of the most profound questions ever raised.Astronomy has emerged forever from the old books of mythology to assert itself as an exact science,an unclouded crystal ball of the universe. I would like to be a part of it.. :)

For me, it is the same curiosity that human kind have since its early existence: explore the environment where we are. Nowadays, we have resources to explore even far away from our home. But, in universal terms, the universe is also our home.
10
Is there any experimental evidence for how much time a photon takes to flow from the core to the surface of the sun?
I have seen different estimations of photon diffusion time in different papers (30000 to a million years). There are many different mean free paths used. I want to know if these results are just speculations or if there is a way to verify these results?
I also want to know what the current standard time of diffusion is. It would be helpful if you could give me the links to some important research papers on this subject.
again

the original and most correct source for this kind of calculation is

17
How can one explain existence of acoustic peaks in cosmic microwave background anisotropies?
When delta T/T is plotted against angular separations between points we see several peaks in the plot. The first one is most prominent one is between l value 200-300, or in terms of angular scales at about 1 degrees. How to explain the existence of these
peaks. We know that CMBR anisotropies provide a snapshot of the surface of last scattering. How does acoustic oscillations deform that surface? What are acoustic oscillations in primordial universe?
BTW - I found a very approachable article reviewing cosmological acoustic oscillations at http://dx.doi.org/10.1063/1.2911177 - and http://aether.lbl.gov/bccp/PDFs/BAO.pdf - to be very helpful...
39
Could a supermassive black hole singularity experience amplification of quantum fluctuations similar to AQFs that Linde claims cause a big bang?
Could a singularity in a supermassive black hole experience amplification of quantum fluctuations similar to quantum fluctuations that form ever larger cycles, causing a big bang as described by Linde?

If it is reasonable to assume that an amplification of quantum fluctuations can occur spontaneously at the quantum level and continue to fluctuate in ever larger cycles until it produces a universe--forming big bang (Andrei Linde, inflationary multiverse and eternal chaotic inflation), then would it also be reasonable to assume that a singularity in a supermassive black hole could experience a similar amplification of quantum fluctuations?

(PhysOrg.com) – “In a new study by physicists Vanzella and Lima, it is proposed that gravity could trigger a runaway effect in quantum fluctuations, causing them to grow so large that the quantum field’s vacuum energy density could dominate its classical energy density. This vacuum-dominance effect, which emerges under some specific but reasonable conditions, contrasts with the widely held belief that the influence of gravity on quantum phenomena should be small and subdominant.”
“If the vacuum-dominance effect exists and is strong enough to have such consequences, scientists will still have to discover a new kind of quantum field that would react to gravity in this way, since none of the quantum fields based on known forces could induce these effects. Still, the physicists note that the possibility of vacuum dominance itself is surprising to discover within “a simple and classically well-behaved situation.” Read more at: http://phys.org/news193330592.html#jCp Daniel Vanzella and William Lima. “Gravity-Induced Vacuum Dominance.” Phys. Rev. Lett. 104, 161102 (2010).

Such an amplification of a quantum fluctuation in a supermassive black hole singularity could occur either spontaneously or possibly caused by some unusual event. The following are proposed as possible causes of cyclic amplification of quantum fluctuations: 1. Spontaneous event similar to the subatomic quantum fluctuation proposed by Linde; 2. The merging of two very large supermassive black holes; 3. The mass of the black hole exceeding the mass of the rest of the galaxy, thus causing an extreme warp of space; or 4. An usual interaction with dark matter.
THE SUN's PULSAR CORE

Today JoNova and David Evans are in the process of discovering Earth’s climate is driven by the Sun’s deep-seated magnetic fields (and the X Force) from the Sun’s compact innards (Fe-mantle and/or pulsar core).

http://joannenova.com.au/2014/06/big-news-part-iv-a-huge-leap-understanding-the-mysterious-11-year-solar-delay/

That was also the conclusion of a paper by Professors Barry Ninham, Stig Friberg and I [“Super-fluidity in the solar interior: Implications for solar eruptions and climate”, Journal of Fusion Energy 21, 193-198 (2002)].

3
Can entropic force explain dark energy properly?
Since Verlinde's proposal that gravitation is related to entropy, there have been many papers discussing or extending his hypothesis. In a recent paper, Basilakos and Sola reconsidered entropic-force dark energy (http://arxiv.org/pdf/1402.6594v3.pdf). They wrote: "We reconsider the entropic-force model in which both kind of Hubble terms appear in the effective dark energy (DE) density affecting the evolution of the main cosmological functions, namely the scale factor, deceleration parameter, matter density and growth of linear matter perturbations. However, we find that the entropic-force model is not viable at the background and perturbation levels due to the fact that the entropic formulation does not add a constant term in the Friedmann equations."
So do you think that entropic force can explain dark energy?
Dear Antonio, thank you for your answer. For your information, since 2010 there were many papers discussing entropic dark energy, including by Smoot et al. The file that i attached is one of the most recent papers. Best wishes
2
How can I perform weighted averages over mass or volume of the cell for cell count to get dark matter density?
Having count in cell for different bins provides different densities in a cell. Therefore I think I need to perform weighted averages over mass or volume of the cell. I am looking for an explanation how to do the averaging in either over cell-mass or cell volume?
Thank you very much!!
99+
How many dimensions are there in the universe?
In particular, why do we only experience three spatial dimensions in our universe, when superstring theory, for instance, claims that there are ten dimensions — nine spatial dimensions and a tenth dimension of time?
@Marshall, I don't refer to this conversation only, but to many past ones, where you couldn't even express your opinion and then... suddenly a downvote was always present at every post of you!
Probably the publicity to this process has led to an improvement... we will see.
As for the core of the problem, I agree with Bernard, since, as the 'like' process is so popular, then we don't need a 'negative vote'.
10
Can someone suggest galaxies, for which both the total baryonic mass and the mass of its central supermassive black hole have been calculated?
Of the 72 central supermassive black holes on the McConnell and Ma table in their paper “Revisiting the Scaling Relations of Black Hole Masses and Host Galaxy Properties”, I have only found six galaxies in which the baryonic mass has been estimated for the entire galaxy. McConnell and Ma have listed the mass of 41 central bulges of these galaxies; however, in this project the central bulge is not a good proxy for total mass. In addition to publications, any leads to people who or institutions that may have done these calculations would be helpful.
I also suggest a recent paper - http://arxiv.org/abs/1212.5317.
3
What verification we need on the latest BICEP2's universe inflation?
There are a few points being raised lately on the first direct evidence on the universe inflation and the detection of gravitational waves:

1. The cosmic microwave polarization patterns referred to carry a lot of information. They do not solely refer to the gravitons (the gravitational waves - the ripples in space-time amalgam)

2. The indication to gravitons were carefully disentangled from many other irrelevant things.

3. Which could refer to objects - like dust or any thing of density that would simply cause the same (more or less) type of distortions in the cosmic microwave background that indicated the existence of gravitons.

4. For one thing, most importantly, no previous indication from a different method other than the polarization in cosmic microwave background has ever been made. An independent method is needed to confirm this uniquely new result against different set of results that would lead to same findings.

5. The detection was made 3 years ago, after which tedious calculations and investigations were made. Can such a polarization pattern be detected again? Why or why not?

6. We need to know how would, at least theoretically, the cosmic microwave polarization pattern purely (without the interference from any thing, like dust) look under the effect of gravitons? Can we do gravitons in a lab?

What methods should be followed to verify the findings of this discovery?
"Now, serious flaws in the analysis have been revealed that transform the sure detection into no detection."

http://www.nature.com/news/big-bang-blunder-bursts-the-multiverse-bubble-1.15346
9
What is the Inflation model of the Big Bang?
It refers to the existence of the big bang, and it predicts the predominal energy that is universally spread out.
All,

remember that the "big bang" really means the instant at which space-time, as a geometry, came into existence.
3
In a two temperature plasma, we have the ratio of electron and ion temperature given by T_e = (m_e/m_i)^0.5 T_i. How do we arrive at this relation?
The above relation has been used in the synchrotron cooling expression in the paper "Behaviour of dissipative accretion flows around black holes" 2007MNRAS.376.1659D.

We know that the electron thermal velocity is v_e = (k T_e/m_e)^0.5 and ion thermal velocity is v_i = (k T_i/m_i)^0.5. If we say that ions and electrons have same kinetic energy then...m_e (v_e^2) = m_i (v_i^2)...and we arrive at the ralation...

T_e = (m_e/m_i)T_i

But under what assumptions can we arrive at the relation T_e = (m_e/m_i)^0.5 T_i ??
have to think -- I am not quite familiar with what's going on with T_e/T_i when you do approach black hole.. depends on heating sources of the electron, I guess.
13
Is it possible to see mercury transit the same way that I saw venus transit i.e without a telescope?
I saw venus transit in the morning 6-june-2012 at sunrise just by putting a sun glass and looking at the sun as it was rising. I calculate that mercury during transit would have
about one fifth the angular size of venus. My question : Is it possible to see mercury
transit the same way that I saw venus transit in 2012?
Yacoub, yes with binocular with 7x or more power, you should see Mercury.
2
How to calculate power spectrum from density perturbation?
What is the method for finding the power spectrum from the distribution of density? Considering I have the distribution of density over a certain volume.
https://www.researchgate.net/publication/221936046_Non-linear_power_spectra_of_dark_and_luminous_matter_in_halo_model_of_structure_formation?ev=prf_pub
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##### Article: Non-linear power spectra of dark and luminous matter in halo model of structure formation
[Hide abstract]
ABSTRACT: The late stages of large-scale structure evolution are treated semi-analytically within the framework of modified halo model. We suggest simple yet accurate approximation for relating the non-linear amplitude to linear one for spherical density perturbation. For halo concentration parameter, $c$, a new computation technique is proposed, which eliminates the need of interim evaluation of the $z_{col}$. Validity of the technique is proved for $\Lambda$CDM and $\Lambda$WDM cosmologies. Also, the parameters for Sheth-Tormen mass function are estimated. The modified and extended halo model is applied for determination of non-linear power spectrum of dark matter, as well as for galaxy power spectrum estimation. The semi-analytical techniques for dark matter power spectrum are verified by comparison with data from numerical simulations. Also, the predictions for the galaxy power spectra are confronted with 'observed' data from PSCz and SDSS galaxy catalogs, good accordance is found.
Physical Review D 03/2012; 88(10). DOI:10.1103/PhysRevD.88.103505
2
Is it possible to have some quasi-periodic solutions for the accretion disk equations?
Can the accretion disk disappear and form again for the same compact star? And If yes what is the time scale for this process?In which type of disk this quasiperiodicity can appear?
It seems the Marscher work was published in 2002 - I'm not sure that the regularity of AGN cycle has been borne out... Here's some more recent research from 2012: http://arxiv.org/abs/1205.3175. It also provides other, more recent references. As I understand, the case of galaxy 3C120 accretion is peculiar...
7
Can we build nuclear power plants on the Moon and transport energy to the Earth? Wouldn't that be very safe for all of us?
Nuclear power plants are some of the most sophisticated and complex energy systems ever designed. Any complex system, no matter how well it is designed and engineered, cannot be deemed failure-proof. Veteran anti-nuclear activist and author Stephanie Cooke has argued:
The reactors themselves were enormously complex machines with an incalculable number of things that could go wrong. When that happened at Three Mile Island in 1979, another fault line in the nuclear world was exposed. One malfunction led to another, and then to a series of others, until the core of the reactor itself began to melt, and even the world's most highly trained nuclear engineers did not know how to respond. The accident revealed serious deficiencies in a system that was meant to protect public health and safety.
The 1979 Three Mile Island accident inspired Perrow's book Normal Accidents, where a nuclear accident occurs, resulting from an unanticipated interaction of multiple failures in a complex system. TMI was an example of a normal accident because it was "unexpected, incomprehensible, uncontrollable and unavoidable".
Perrow concluded that the failure at Three Mile Island was a consequence of the system's immense complexity. Such modern high-risk systems, he realized, were prone to failures however well they were managed. It was inevitable that they would eventually suffer what he termed a 'normal accident'. Therefore, he suggested, we might do better to contemplate a radical redesign, or if that was not possible, to abandon such technology entirely..
A fundamental issue contributing to a nuclear power system's complexity is its extremely long lifetime. The timeframe from the start of construction of a commercial nuclear power station through the safe disposal of its last radioactive waste, may be 100 to 150 years.
Controversy

The abandoned city of Prypiat, Ukraine, following the Chernobyl disaster. The Chernobyl nuclear power plant is in the background.
The nuclear power debate is about the controversy which has surrounded the deployment and use of nuclear fission reactors to generate electricity from nuclear fuel for civilian purposes. The debate about nuclear power peaked during the 1970s and 1980s, when it "reached an intensity unprecedented in the history of technology controversies", in some countries.
Proponents argue that nuclear power is a sustainable energy source which reduces carbon emissions and can increase energy security if its use supplants a dependence on imported fuels. Proponents advance the notion that nuclear power produces virtually no air pollution, in contrast to the chief viable alternative of fossil fuel. Proponents also believe that nuclear power is the only viable course to achieve energy independence for most Western countries. They emphasize that the risks of storing waste are small and can be further reduced by using the latest technology in newer reactors, and the operational safety record in the Western world is excellent when compared to the other major kinds of power plants.
Opponents say that nuclear power poses many threats to people and the environment. These threats include health risks and environmental damage from uranium mining, processing and transport, the risk of nuclear weapons proliferation or sabotage, and the unsolved problem of radioactive nuclear waste. They also contend that reactors themselves are enormously complex machines where many things can and do go wrong, and there have been many serious nuclear accidents.Critics do not believe that these risks can be reduced through new technology.They argue that when all the energy-intensive stages of the nuclear fuel chain are considered, from uranium mining to nuclear decommissioning, nuclear power is not a low-carbon electricity source.
It is not necessary or desirable to build nuclear plant on the moon. Nuclear power is, based on actual statistics, one of the safest ways to produce energy and also has one of the least environmental impacts. The reasons are simple:

1. There is no air pollution and no carbon dioxide. Air is not used in the process
2. The amount of fuel and waste produce is small. The fuel in a 1000 MWe reactor core can fit in a two garage.
3. Since the amount of fuel required is smaller than coal, gas, wood or any other burning fuel the mining impact of nuclear is the least of all the major energy opitons.
4. The amount of land usage for a reactor is the least compared to Wind or Solar or bio mass
5. Nuclear energy production is 24/7 except for a refueling outage which takes 3 weeks every two years. Solar and Wind have capacity factor 25 and 35% are are very intermittent.
6. Concerning accidents, even with TMI, Chernobol and Fukushima, the loss of life (none in the case of TMI and none in the case of Fukushima), is still very low and cancer rates are not significantly above the norm.

FinallyAll energy options should be assessed against one another for there pro and cons. There is a serious problem with climate change and nuclear power must be part of the energy mix.
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Can the Lambda-CDM cosmological model survive the discrepancy between galaxy cluster observations and CMB projections?
See http://www.nature.com/news/cosmic-mismatch-hints-at-the-existence-of-a-sterile-neutrino-1.14752. It states:
"… The background radiation shows the small density variations in the early universe that would eventually cause matter to clump in some places and form voids in others. We can see the end product of this clumping in the recent universe by observing the spread of galaxy clusters across space.
"The best measurements of the cosmic background radiation came from the European Space Agency’s orbiting Planck telescope in March 2013. Galaxy-cluster measurements, on the other hand, come from various methods that include mapping the spread of mass across the universe by looking for the gravitational lensing, or warping of light, it causes. The two measurements, however, are inconsistent with one another. "We compare the universe at an early time to a later time, and we have a model that extrapolates between the two," says Richard Battye of the University of Manchester, UK, co-author of the new study1 published on 7 February in Physical Review Letters (PRL). "If you stick to the model that fits the CMB data, then number of clusters you find is a factor of two lower than you expect.""

Recent reports of X-ray signals that may signify the decay of sterile neutrinos have raised hopes for a cosmological solution, as some mix of Cold Dark Matter (CDM), Warm Dark Matter (WDM) and/or Hot Dark Matter (HDM) could fit CMB projections of galaxy cluster formations to observations since WDM and HDM would prevent structure formation at increasingly larger scales. See http://arxiv.org/abs/1308.3255 http://arxiv.org/abs/1402.2301 http://arxiv.org/abs/1402.4119 http://dx.doi.org/10.1103/PhysRevLett.112.051303 and http://dx.doi.org/10.1103/PhysRevLett.112.051302.
Also see http://phys.org/news/2014-02-massive-neutrinos-cosmological-conundrum.html https://www.technology.org/2014/02/25/neutrino-replaces-higgs-boson-sought-particle/ http://news.sciencemag.org/physics/2014/02/x-rays-other-galaxies-could-emanate-particles-dark-matter and http://www.nature.com/news/physics-broaden-the-search-for-dark-matter-1.14795.

However, if the composition of universal mass-energy included HDM or WDM and less total CDM than now thought, how would that affect the enormous gravitational effects routinely attributed to CDM in the observed universe?

Adding HDM and/or WDM may help with LCDM problems such as 'the small scale structure problem', 'the missing satellite problem', the 'cuspy halo problem' and others, but it must do so while maintaining alignment with other observations. What other L-CDM results would be affected by the inclusion of HDM and/or WDM?
Dear Biswajoy,
There have been a few L-CDM anomalies identified even in the Planck CMB data - see http://www.esa.int/Our_Activities/Space_Science/Planck/Planck_reveals_an_almost_perfect_Universe
"One of the most surprising findings is that the fluctuations in the CMB temperatures at large angular scales do not match those predicted by the standard model – their signals are not as strong as expected from the smaller scale structure revealed by Planck.
"Another is an asymmetry in the average temperatures on opposite hemispheres of the sky. This runs counter to the prediction made by the standard model that the Universe should be broadly similar in any direction we look.
"Furthermore, a cold spot extends over a patch of sky that is much larger than expected."

Moreover, to this pedestrian, it seems that L-CDM power spectrum analyses may be more an exercise in parametric curve-fitting than stringent testing of model results. For example, see http://physics.aps.org/articles/v1/31.

There are also some very fundamental observations of low mass, large separation stellar binary systems in our galactic neighborhood that do not comply with Keplerian expectations for inverse-square diminishment of rotational velocity as a function of separation distance. While they do fit with the general expectations of modified gravity theories, there seems to be no configuration of dark matter that could produce the observed rotational characteristics. See http://arxiv.org/abs/1401.7063.

Dark matter's only purpose, even in the primordial universe, is to increase the effects attributed to mass-energy to fit observations. Alternatively, the analytical determination of effects produced by mass-energy, especially under widely varying conditions, could be different than currently established evaluation methods presume. If the effects of mass-energy in the early universe were different than determined by the L-CDM model, results might still fit with observations despite the absence of any dark matter.

Again, our interpretation of early, large scale conditions may be skewed by averaging methods and other scale dependent factors - see http://arxiv.org/abs/1109.2314.
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From dwarfs to giants: how were ellipticals formed ?
Updating a basic question: what are the possible ways to make elliptical galaxies with various masses? Is merging the only way for the massive ones?
I have not done any simulations in regards to monolithic collapse producing unstable rotation curves. However, it is relatively easy to conclude that if we initially have a spheroidal galaxy with mostly radial motion transitioning to a more tightly concentrated disk, then the exchange of gravitational potential to momentum along the z-axis would need to be conserved in some manner (x-y plane is aligned with the disk). There was a recent article about wavy motion in the Milky Way disk and I believe that this is a residual of collapse along the z-axis (http://www.newscientist.com/article/dn24464-milky-way-galaxy-is-fluttering-like-a-flag.html#.U1m9laIa7pc), along with the motion of UV excess stars.

The theory that seems to match observations best is an origin from dense, x-ray emitting gas. Therefore, initial star formation begins due to a prior higher density of the ISM and then is halted in early-type galaxies due to expansion of the ISM (decreased density). The next phase would be cooling of the x-ray emitting gas, which relative to the Jean's criterion would allow a new generation of stars to form (high redshift ETG in the paradigm that I am arguing for). This is the only way I can think of that would reconcile the bottom heavy IMF in massive ETGs with its correlation to metallicity, stellar dispersion and x-ray temperature. For example, a very dense hot initial state would induce significant fragmentation while producing fewer massive stars. In regards to elliptical galaxies in cluster and field environments, the field varieties have more neutral hydrogen and increased ring/disk formation. One can therefore infer that cluster environments provide a look-back as to the previous evolution and state of field galaxies. Also remember that the gas in ETG's is on the order of that contained in their stellar populations, so a lot of future star formation is still possible.
Following Dr. Eubanks, if one assume gravity as a gauge theory, there is a nice analogy with Yang-Mills theory about possible gauge fixations. For example, let $h_{\mu\nu}$ be the graviton field in a perturbative regime, then the "Coulomb" gauge must be $\partial_i h_{i\nu}=0$. Observe that this fixation is no more a general relativistic covariant constraint. So, in gravity a gauge fixation and covariance constraint go hand in hand.