Wondering if anyone has experienced walking into the same room, say a bathroom, that has no natural light and finding that the shade of the light from same light globe appears different at different times of the day? Eg i find towards the end of the day, the same light in my bathroom seems whiter than it does earlier in the day when it seems more yellow.

Can the pyramids really generate energy from the sand?

Could it be possible if a mass amount of people died in the desert near the pyramids the last spark in their nervous system could cause a reaction in the pyramids?

I heard there was electricity in sand and the pyramids, just don’t know if it’s true.

You never see a picture of a lion with no teeth or missing teeth due to rotting. Why is this? What do animals do to keep their teeth clean to avoid decay?

If it were possible to create a 100% efficient light bulb (0 entropy, all power converted to light) how much light would it emit per watt?

As far as I understand it, the Alcubierre drive allows you to contract space-time in front of the ship and expand it from behind. This allows you to close the distance between two points of space, but once you decide to exit the warp bubble wouldn't space-time return to its non-contracted state and leave you in the same position as you left of?

Sightings include: 1, 2, 3, 3, 4, 5, 6

Detailed Discussion

From the Stanford Encyclopedia of Philosophy

Accessible Answer

Heisenberg's Uncertainty Principle states that certain properties of quantum mechanical systems can't be precisely known simultaneously (why this is the case doesn't matter too much for an ELI5-level understanding of the EPR argument). Among such properties are position and momentum: the more precisely you know one, the less certain you can be about the other. Quantum mechanics also (usually) purports to be a "complete" theory of quantum systems: it tells you everything there is to know about the system, with nothing left out. EPR tried to show that these two assumptions are incompatible with one another, generating a paradox.

Here's the original setup. Suppose, EPR said, we have two particles A and B that are allowed to become entangled with one another so that their positions and momentums are correlated, then the particles are separated. We can imagine this as something like allowing two billiard balls to roll down a track toward each other, strike together, and then bounce off in opposite directions along the track. We let the particles drift apart for a while without disturbing them until they're separated by a substantial distance.

Now, Heisenberg states that we can't know both the position and momentum of either particle with perfect precision. But suppose, EPR said, we do the following. We first measure the position of Particle A. Since we know how particle A is correlated with Particle B, this lets us deduce the position of Particle B as well. But we could equally well have chosen to measure the momentum of Particle A. Again, because we know how the two are correlated, this would have let us deduce the momentum of Particle B. Since Particles A and B are far apart from one another, there's no way for Particle A to "tell" Particle B whether we've chosen to measure position or momentum, and since we could make either a measurement that would let us know Particle B's position or Particle B's momentum with certainty, Particle B must have had both a particular position and particular momentum all along. This violates Heisenberg's Uncertainty Principle, generating a paradox. EPR concludes, then, that the starting assumption that quantum mechanics was complete must be false. There must be properties about Particle B that have real values, but which quantum mechanics doesn't cover. Einstein suggested that this paradox was best resolved by positing what's called "local hidden variables:" features of quantum mechanical systems that are concrete, real, and spatially localized but which are inaccessible to measurement.

Of course, there are a number of problematic assumptions in their setup that eventually turned out to be false. Most significantly, they assumed that given sufficient spatial separation, Particle A and Particle B could be prevented from interacting with one another, despite being part of an entangled pair. They justified this assumption by pointing out that otherwise, Particle A would have to exert an influence on Particle B instantaneously, which seems to violate Special Relativity's prohibition on faster-than-light information exchange. This was what Einstein called "spooky action at a distance." If you assume that Particle A and B can interact even when spatially separated, the EPR argument falls apart.

Eventually (in 1964), John Bell proved that the experimentally observed statistical behavior of entangled particles could not be explained by such local hidden variables; the numbers just failed to add up. His result, Bell's Theorem, is a proof (in the strongest possible sense) that any theory of quantum mechanics that reproduces the observed behavior of quantum systems has to be non-local in at least some sense (either by permitting action at a distance or by positing global hidden variables that aren't unique to individual particles). The EPR paradox was thus resolved by showing that one of their assumptions--locality--was false.

Instances include: 1, 2, 3, 4, and many others.

tl;dr answer:

Quantum computers aren't faster at solving all problems, only some of them. They work by replacing standard computing's "bits" (which can have two values, 1 or 0) with "qbits," which can have values that are linear combinations of 1 and 0. This allows the computer to simultaneously explore many different potential solutions at the same time, leading to much better performance at solving problems that rely on something like a "guess-and-check" approach. Examples include cryptographic analysis, and some NP-complete problems like the traveling salesman.

Extremely detailed discussion on /r/askscience here.

Layperson-Accessible Answer:

It's not necessarily faster than classical computing; it's only faster on a very specific subset of problems.

Standard (classical) computers are, as I'm sure you know, do their computation with binary digits (bits). Each bit can have two values, usually represented by 1 and 0. We can think of a classical computer as something like a device for storing and manipulating strings of bits. Imagine a system consisting of a long strip of paper with a string of 1s and 0s printed on it, and a read/write head (a scanner/printer) that can move along the tape, read what's on the tape at a particular position, erase what's on the tape at a particular position, and print either a 0 or 1 at a particular position. Any possible classical computer can be emulated on a system like that; the execution of a program is just represented as a long series of movements and read/write operations on the tape.

Quantum computers are different in that rather than using bits, they use what are called "qbits" (quantum bits) for their operation. Unlike standard bits, which always have a definite value of either 0 or 1, qbits can taken on values that are superpositions (linear combinations) of 0 and 1. Imagine that a 0 bit is represented by an arrow pointing down, and 1 is represented by an arrow pointing up. A qbit's state can be straight up (1), straight down (0), but also any angle in between. The precise angle between 0 and 1 represents the relative probability that, on measurement, the qbit will "collapse" into a 0 or a 1. For example, imagine that the 12:00 position is a 1, and the 6:00 position is a 0. A qbit with a value corresponding to 3:00 is an evenly weighted superposition of a 1 and a 0, representing a 50% chance that it will collapse to a 1 and a 50% chance that it will collapse to a 0 on measurement. A qbit with a value corresponding to 1:00 represents a superposition that's "weighted" much more toward 12:00 than 6:00, yielding an 80% probability of getting a 1 on measurement and a 20% probability of getting a 0 on measurement.

The reason this is useful is that it drastically expands the space of possible states that the computer can be in given a particular number of bits. A classical computer with two bits can be in any of four different states: (0,0); (0,1); (1,0); or (1,1). A classical computer with three bits can be in any of eight different states (1,1,1); (1,1,0), and so on. In general, a classical computer with n bits can be in any of 2^n possible states.

In contrast, a quantum computer with two bits can be in any of the same states as a classical computer, plus any possible superposition of those states. Instead of being confined to any one of 2^n possible states, a quantum computer with n qubits can be in any superposition of 2^n possible states, creating a much greater computational capacity and information density.

Moreover, the fact that qbits can be entangled with one another--that is, they can be prepared so that the value of one qbit is correlated to the value of another one in a reliable way--means that a quantum computer can extract more "work" from any given qbit manipulation than a classical computer could from an analogous bit manipulation. If two qbits are entangled, then what's done to one of them affects the state of the other one in a predictable way, so manipulating one qbit also (in some sense) allows you to manipulate its entangled partner without performing a second operation--without moving the "read/write head" of the computer.

The upshot of this is that quantum computers are very good at certain kinds of tasks that classical computers aren't good with. Specifically, quantum computers excel in tasks that involve doing things like making repeated guesses and checking those guesses against a known value, or randomly exploring a large space of possible options. Because each qbit has so many possible values and can be entangled in so many ways with each other qbit, a quantum computer can explore many different "guesses" (or many different paths through a space) at once. This has hugely significant applications in fields like cryptography, where breaking some encryption scheme is a matter of making many different random guesses at what the original algorithm might be, then checking to see if that guess produces a result that matches the original. Since a classical computer has to make each guess in succession--one after another--it isn't very good at this task. The amount of time that it will take a classical computer to hit on the right answer to a problem like that grows exponentially as the problem gets longer; for every additional "step" in difficulty, the time to a solution doubles (or more), so guessing a 4-bit encryption is twice as guessing a 3-bit encryption, and guessing a 5-bit encryption is four times as hard as guessing a 2-bit encryption. For a quantum computer, on the other hand, the time to a solution grows arithmetically rather than exponentially: the time difference between a 2-bit and 3-bit encryption scheme is about the same as the time difference between a 3-bit and 4-bit scheme, or between a 500-bit and 501-bit scheme. This lets quantum computers solve these problems in what's called "polynomial time" rather than "non-polynomial time. You probably recognize those terms from discussions of "P vs. NP."

The downside to quantum computers is that quantum states are extremely fragile. Any environmental perturbation (even something like a photon strike) can destroy a superposition, so operating qbits have to be kept very isolated, very cold, and very still while they're computing. Any disturbance will result in the quantum state collapsing via a process called decoherence and the computation will be lost. They also have to be kept rather small, as systems with large numbers of particles have an unfortunate tendency to perturb themselves, which is why we rarely see quantum mechanical behavior in the macroscopic world. That's the big limiting factor in terms of building a quantum computer: it's hard to put together a system with more than a couple of qbits and still have something stable enough to do useful computations before it decoheres.

Computation:

• Answer 1 from /u/EricPostpischil

• Answer 2 from /u/EricPostpischil

Overview of root finding methods:

• Answer from /u/DarylHannahMontana

FAQ post.

• Answer from /u/adamsolomon

• Answer from /u/fishify

FAQ Post.

A combination of the high pressure, high temperature, and corrosive atmosphere. In isolation these problems could be dealt with, but together they make it very hard to build a spacecraft that can operate on the Venusian surface. In particular, designing electronics that will not overheat is a massive challenge. Mission lifetimes are essentially limited by how much coolant they can carry.

However, there have been a number of successful Venus missions. The Roscosmos have deployed 10 landers on the surface, NASA have had a number of flyby and orbiter missions, and ESA's Venus Express has been operating continuously in orbit for nearly 8 years.

http://www.reddit.com/r/askscience/comments/17xvlj/could_we_build_a_better_venus_probe_with_modern/ http://www.reddit.com/r/askscience/comments/1f96l4/how_did_the_soviets_get_a_probe_onto_the_surface/ http://www.reddit.com/r/askscience/comments/mr2pa/why_are_we_sending_rovers_to_mars_and_not_venus/ http://www.reddit.com/r/askscience/comments/xxam8/weve_explored_mars_with_at_least_3_rovers_and_ive/ http://www.reddit.com/r/askscience/comments/myy84/why_do_we_send_rovers_to_mars_but_not_to_venus/

This question is a little unscientific (what is 'terraforming'?), is moving into the realms of science fiction, and has any number of different opinions on the answer.

However, in theory, yes, we could terraform other planets, with several large caveats:

• It would take an immense amount of money, energy, time, infrastructure, and knowledge that we don't necessarily have yet.

• We would have to have the capability to move immense amounts of material (carbon dioxide, water, nitrogen, etc. all of which are very abundant in other places) across the solar system. If this were true, we wouldn't necessarily need to terraform anywhere.

• It might not last long. For example, if we were to create a thicker atmosphere on Mars, the solar wind would eventually strip it away.

http://www.reddit.com/r/askscience/comments/rclyb/what_is_stopping_us_from_terraforming_venus_or/ http://www.reddit.com/r/askscience/comments/fbrk7/questions_on_terraforming_venus/ http://www.reddit.com/r/askscience/comments/mkrrz/what_would_it_take_to_make_venus_habitable/ http://www.reddit.com/r/askscience/comments/1hvvuz/how_far_away_from_the_sun_would_venus_need_to_be/ http://www.reddit.com/r/askscience/comments/kldxc/would_it_be_easier_to_terraform_mars_or_venus/ http://www.reddit.com/r/askscience/comments/zdlav/what_would_the_climate_on_venus_be_like_if_its/ http://www.reddit.com/r/askscience/comments/1a8qpa/could_venus_one_day_become_what_earth_is_now/ http://www.reddit.com/r/askscience/comments/14svbj/venus_has_been_described_as_an_example_of_runaway/ http://www.reddit.com/r/askscience/comments/xcn2h/ignoring_the_difficulty_of_capturing_a_comet_or/ http://www.reddit.com/r/askscience/comments/1acw1v/is_it_possible_to_create_an_artificial_atmosphere/ http://www.reddit.com/r/askscience/comments/zeobl/any_hypotheses_as_to_how_to_give_mars_a_magnetic/ http://www.reddit.com/r/askscience/comments/y096p/how_long_would_it_take_an_earthstandard/ http://www.reddit.com/r/askscience/comments/19il14/is_terraforming_a_real_possibility/ http://www.reddit.com/r/askscience/comments/ywxto/how_would_water_behave_on_a_terraformed_mars/ http://www.reddit.com/r/askscience/comments/g8o3i/is_it_actually_possible_to_terraform_mars_to/ http://www.reddit.com/r/askscience/comments/10sggp/what_would_it_take_to_bring_the_atmosphere_on/ http://www.reddit.com/r/askscience/comments/gmsom/would_it_be_possible_to_terraform_the_moon/ http://www.reddit.com/r/askscience/comments/dt2m5/if_we_were_to_successfully_terraform_it_what/ http://www.reddit.com/r/AskScienceDiscussion/comments/1kj2t4/terraforming_mars/

Magnetized Target Fusion is one of the leading technologies to harbor fusion energy. My point here is not to argue this. My point is to get a good description that regular people can understand. I want some constructive criticisms. So here is the description I'm starting with:

So basically, this is the current prototype of a machine that is used to harbor the process of Magnetized Target Fusion. It makes a whirlpool of hot molten lead inside that vessel in the middle. Imagine water flushing down a toilet. The molten lead spins around the edge like the water and produces a magnetic field (because it is metal). This is somewhat similar to the way the earth's core produces a magnetic field. This is key because the magnetic field is needed to contain the plasma and keep it hot enough for the fusion reaction to occur. You can't hold something so hot and keep it that hot without not touching it.

After the machine gets the molten lead spinning really fast and makes a magnetic field, water and hydrogen plasma are injected into middle of the vortex (kind of like the funnel cloud part of a tornado). So imagine hot lead spinning around, with a fiery tornado in the middle. To get the reaction going, all of those giant pistons on the outside are slammed into the sphere at precisely the same time. This quickly pushes the molten lead inward and compresses the fiery tornado of plasma in the middle. When that happens the vortex in the middle (hole within the world pool, eye of the storm, whatever you want to call it) is rapidly reduced in size and the magnetic field compresses the plasma. At that point the water and hydrogen nuclei in the plasma run into each other with enough energy, and with too little free space to overcome the electromagnetic force that pushes them apart. The strong force then takes over and pulls the water nuclei together and they form helium nuclei with significantly less mass than the nuclei they started with. That mass is converted into energy in the form of light, which is then absorbed by the molten lead in the surrounding whirlpool.

The lead can continuously be pumped in and out of the whirlpool, circulating through a heat exchanger where the heat it got from fusion is given to steam which can then power a turbine generator. Using this method a single bathtub of water could power an entire city for years. General fusion, the leading company in this effort is building the first prototype to produce power on the commercial scale. The latest news is that proof of concept has been confirmed. They expect to have a working reactor by 2020. This is truly a remarkable development. Energy that is this clean and cheap could power the earth, desalinate our oceans and keep us from dumping carbon dioxide into our atmosphere. It could do this for millions of years.

Short answer: Speed & velocity are completely relative terms. There is no absolute reference-frame for the universe, and there is no such thing as "absolutely" stationary, you can only say you're stationary relative to some particular object or observer.

This means there is no one universal age to the universe - although because most things more at less than 1000 km/s relative to each other, we still all agree fairly well. But when we want to be consistent, we use the cosmic microwave background frame of reference, which sort of gives an average velocity for the observable universe - this isn't universally constant, but it's constant enough for our purposes. We are moving at about 400 km/s in this frame.

For more info, see previous posts:

http://www.reddit.com/r/askscience/comments/1jvjr9/how_fast_am_i_going/

http://www.reddit.com/r/askscience/comments/immxl/how_fast_is_the_earth_moving_relative_to/

http://www.reddit.com/r/askscience/comments/ez4ac/do_we_know_how_fast_were_moving_through_space/

http://www.reddit.com/r/askscience/comments/obch6/how_do_you_calculate_velocity_in_space/

http://www.reddit.com/r/askscience/comments/dp4vt/how_fast_are_we_really_moving_through_the_universe/

http://www.reddit.com/r/askscience/comments/1ypzbd/how_fast_are_we_actually_going_through_space/

http://www.reddit.com/r/askscience/comments/sfoac/how_fast_am_i_moving/

http://www.reddit.com/r/askscience/comments/24y2ev/how_can_a_stationary_point_zero_velocity_in_the/

http://www.reddit.com/r/askscience/comments/j7hnv/how_fast_are_we_moving_from_a_single_solitary/

For a related question, see where is the centre of the universe?

We know from relativity that how one measures lengths and times is, well... relative. Special relativity, the easy case, tells us these measures are related to relative velocity. But what happens when my velocity now is different than my velocity before. I have a change in measure with respect to my previous measurement.

I mean, I'm moving, right? So over time, I occupy a new position in space. So for each of these locations in space and time, how I'm measuring space and time keeps changing.

Well when we take all those measures of space-and-time and how they change with location, we can most easily describe it as a curvature of space-and-time. (To be more specific, we need to start using non-Euclidean geometries to describe space-time. Geometries where parallel lines maybe converge or diverge.)

So point 1: Acceleration means space-time is described as a curvature field

Now let's step back a second to the principles of special relativity. Einstein notes in special relativity, he asserts that no local experiment can distinguish between rest and motion. When you wake up at a train station and you look out the window and see a train passing you by... are you moving or is that other train moving? And if there were no windows, how would you ever know at all?

Now suppose you are in an elevator car, a "vertical" train if you will. You find yourself floating around in the elevator car. But we know if the elevator car was in free fall, you'd be floating around inside of it. And we know that if the elevator car was in "deep" space away from any other mass, you'd also be floating. Similarly, if you're standing on the floor of the car, is it "at rest" on the "ground" of a planet, or does it have a rocket firing exactly 1g of thrust somewhere again in "deep space"?

Einstein asserts again, No local experiment* can distinguish between deep space and free-fall. (* though due to the size of planets, there can be secondary effects unrelated to what we're talking about that could distinguish. But we're ignoring those, since they're a different question, much like looking outside a window would answer your question too)

point 2: The equivalence principle asserts that gravitation is indistinguishable from accelerated motion.

point 1 + point 2: So if gravitation is indistinguishable acceleration, and acceleration is best described using curved geometries, then gravitation is related to curved geometries. Specifically, Einstein discovers the Einstein Field Equations that say "thing representing how space is curved" is equal to "thing representing mass and energy and momentum and other stuff" (the Stress-Energy Tensor.)

So, now we have some massive body curving space... what happens nearby? Well we take a body, a "test mass" that we'll simply assume doesn't change space-time itself. And we give it some initial location and motion. But no forces. Well as it moves a bit forward, it moves to a location where how one measures "forward in time" and how one measures "forward in space" change slightly from where it just was. The result means that to conserve its momentum, it turns a little bit. Remember it doesn't feel any forces. It just... must change direction (as observed from some outside observer) in order to keep going "straight" through this curved space.

More specifically, we can mathematically describe all of this using more complicated mathematics than Newton did, called a Lagrangian, or a Hamiltonian. We place a free-body (feeling no forces) particle in motion in curved space time. But now our derivatives (rates of change) of space and time start producing terms that describe how space and time change with respect to location in space and time.

What's amazingly remarkable is that these new terms describing changes of space and time appear almost exactly as if they were a force of gravitation. Remember we haven't put a force on the particle. Just passed it through curved space-time, where an "inertial" path no longer looks "straight." Gravitation is not a force at all, it looks like.

"But wait!" you say, "When I stand still at rest on the ground and throw a ball... it certainly looks like gravity pulls that ball back down."

Well let's look at this famous xkcd. He speaks of "coordinate transformations." What that means is that from my "god's eye" perspective, while you're in a car making a sharp turn... there's no force "pushing" you against the outside door. There's no "centrifugal" force. Your body wants to go in a straight line, but the car door wants to turn, being pulled by the rest of the car. From my outside perspective, you're the one pushing the door. But from inside the car, you feel a centrifugal force. What's the deal?

Well again, let's go back to our basic relativity, special relativity. We said rest was indistinguishable from uniform motion, right? We call such observers, ones that are at rest or in uniform motion, "Inertial Frames of Reference." They're observers for which inertia is a good way of describing the world. Objects at rest stay at rest, objects in motion stay in motion.

But there are non-inertial frames of reference too. A non-inertial frame of reference is one that's being accelerated. You can always tell if you're being accelerated (or by point 2, that you're near some massive body). When your car is turning, you're inside of it, being accelerated, so you're in a non-inertial frame of reference. The centrifugal force that comes from this frame of reference is a fictitious force. It's a force that doesn't exist in inertial frames, but a force that makes doing physics in a non-inertial reference frame easier. If you toss a ball in your sharply turning car, that ball will act (from your perspective) as if there's a force pushing it towards the center of the turn, just like the door pushing you. It's a fictitious force, since that outside observer will just see the ball travelling in a straight, inertial line (ignoring gravitation for the moment, we're about to get there).

So now we come to you standing still on the ground. And hopefully there are enough hints to see where I'm going with this. You're not being "accelerated" in the conventional sense. But you're not in an inertial reference frame because you're not free-falling towards the center of the mass. You're being pushed upwards by all the ground beneath you, all the same as a rocket would be pushing you upwards in our conventional way of thinking of acceleration. So since your reference frame is non-inertial... guess what fictitious force now exists to describe physics around you? gravitation. All the basic Newtonian ballistics and stuff works because there's this fictitious force from your reference frame that looks as if it's a standard kind of force.

Corollary 1 Gravitation, as seen from a point stationary with respect to the center of mass of an object, appears as a fictitious force, and is useful as such in standard kinds of gravitational equations.

More at this thread: http://www.reddit.com/r/askscience/comments/20woji/could_someone_explain_the_relationship_between/

Short answer: The galaxies are further than 13.7 billion light-years away now, but were closer in the past when they emitted their light. Because the universe is expanding, the galaxy was still getting further and further away while the light was travelling. So the light travelled less than 13.7 billion light-years, but the galaxy it came from could now be more than 13.7 billion light-years away.

For a mental picture, imagine someone kicking a soccer ball at you and then turning around and running away. When the soccer ball hits your face, he is further away than he was when he kicked the ball. The distance from you to the guy is bigger than the distance the ball travelled.

Some sightings:

http://www.reddit.com/r/askscience/comments/nttrk/question_about_the_age_vs_the_size_of_the_universe/

http://www.reddit.com/r/askscience/comments/m1mdc/how_can_the_universe_be_150_billion_lightyears/

http://www.reddit.com/r/askscience/comments/il3yc/how_is_it_that_the_radius_of_the_universe_is/

http://www.reddit.com/r/askscience/comments/hkfff/if_the_diameter_of_the_observable_universe_is_93/

http://www.reddit.com/r/askscience/comments/14pmb0/ive_read_that_the_observable_universe_has_a_45/

http://www.reddit.com/r/askscience/comments/elzmc/til_that_the_observable_universe_has_a_diameter/

http://www.reddit.com/r/askscience/comments/1s22mo/can_we_only_see_things_that_are_137_billion_light/

tl;dr: Yes.

Fundamental limit: Under higher pressure materials will compress more. One can use this to predict what a planet's size (radius) will be versus its mass for a given composition. Here is an example (from S. Seager et al. 2007, Ap.J. 669, 1279). As can be seen on that figure, planets that have a 'rocky' composition (the red lines, MgSiO2: rock, Fe/MgSio3: rocky with an iron core) have a maximum radius of ~3.5 Earth radii. Planets composed of hydrogen have a maximum radius of about 1 Jupiter radius (~11 Earth radii). (Note: the linked figure assumes the body in question has no internal heat source, so this figure is not applicable to stars that are undergoing fusion.)

Practical limit: When planets form there is typically a lot of hydrogen and helium gas around. If a rocky proto-planet gains enough mass then it will start gravitationally capturing this gas. This mass limit is about ~10 Earth masses, which equates to a radius of ~2 Earth radii.

Sightings:

• Questions about a Jupiter sized Earth

• Is there a limit to the size of rocky planets?

• What is the maximum size of a rocky planet, and what happens when a rocky planet is "too large"?

• Is it possible for an earth-like planet to be the size of our sun?

• A question about the size of planets.

• Is there a limit for the size of moons and planets?

• Is there a size limit for terrestrial planets?

• Would it be possible to find a Jupiter-sized rocky planet /Is there a limit to the size of rocky planets?

• Is it possible for a terrestrial planet to be the size of a gas giant?

• Is it possible for there to be terrestrial planets bigger then some stars? If so, can they have their own solar system?

• So we've all seen the .gif of .jpg of the known sizes of stars and how they dwarf us-- but are there planets that achieve that scale?

Tides tl;dr: Tidal forces are the difference in force felt on one side of a body versus the opposite side. In the context of astronomy, tidal forces arise from the fact that gravity depends on the distance to the (other) massive object and that objects (like planets and moons) have non-zero size.

Details: Take for example a planet experiencing tides as a result of its moon. The acceleration felt on the near side of the planet (near to the moon) is a_ns = GM/(r-R)^2 , where r is the distance from the planet's center of mass to the moon's center of mass, and R is the radius of the planet. On the far side: a_fs = GM/(r+R)^2 . The tidal acceleration is: a_ns - a_fs =

= GM [ 1/(r-R)^2 - 1/(r+R)^2 ]

= GM [ (r+R)^2 - (r-R)^2 ] / [ (r+R)^2 (r-R)^2 ]

= GM [ 4rR ] / [r^4 + .....]

= 4GMR / [r^3 + .....]

Thus, for tides on some object being perturbed by a massive object, the strength of tides is proportional to the mass of the perturber, the radius of the object being perturbed, and inversely proportional to the cube of the distance between the two objects.

Tidal locking tl;dr: Tidal forces raise a tidal bulge that points towards and away from the perturber. If the tidally distorted body rotates at a different rate then the perturber orbits around the body then the bulge will get rotated away from the line directly from the body in question to the perturber. Here's a diagram for the case where the body orbits faster than the perturber orbits. The perturber will torque on the tidal bulge and try to pull it back in to line. This will change the rotation rate of the body (and the orbital rate of the perturber) until the rotation rate of the body and the orbital rate of the perturber are equal. In other words, until the same side of the body is always facing the perturber. Many moons are (or are expected to be) tidally locked to their planet. Also, many extrasolar planets that orbit close to their star are expected to be tidally locked.

Tides in general:

• How would oceanic tides be affected if the moon were orbiting at an ISS altitude?

• Since the moon has an influence over the Earth's oceanic tides, would it have any effect over my ability to jump?

• Why are the times of ocean tides so different between relatively nearby areas?

• Are things lighter below the moon?

• When the tide goes out, where does the water go?

• Can someone explain why there is an antipodal high tide?

• How is the moon's gravity strong enough to affect so many millions of litres of water to create tides, yet we feel no effects?

• tides on a moon

• Why are there two spring tides per lunar month?

• Why do both sun-earth-moon syzygies cause stronger tides?

• Are tides stronger or weaker at the poles?

• How exactly does the Moon effect the tides of Earth?

• A few questions about tides

• How do I develop physical intuition for the tidal force?

Tides from multiple bodies:

• How would multiple moons affect a planet's tides?

• Pretend we have a second moon, basically identical to our current one, orbiting perfectly on the opposite side of the planet as our own. Would we still have tides?

• If Earth had a second moon, how would it affect the tides?

• What would happen to the tide on a planet with more than one moon?

• Multiple questions about having 2 moons

Tidal locking:

• Why is the same side of the moon always facing Earth? Is this common among satellites?

• Tidal Locking Earth to The Sun

• What causes tidal locking?

• Why we always look at the same side of the moon?

• Why do we only see one side of the moon?

Orbital evolution and tides:

• Why is the the Earth's Moon gradually drifting further away from us, rather than gradually spiraling in as what I would seem to consider more intuitive?

• Could we make the Earth rotate faster by bringing the Moon closer?

Relevant Wikipedia articles:

• Tides

• Tidal force

• Tidal acceleration

• Tidal locking

• Tidal heating

My favourite answer is from an old post by /u/seladore :

This is a very interesting question - there are self-consistent solutions to GR corresponding to a rotating Universe, and I wouldn't say that we have proved that it it isn't rotating. Just that it probably isn't.

If the Universe was rotating, then the light coming from the cosmic microwave background (CMB - you can think of it as the 'echo' of the big bang, if you don't know what it is) would be uneven, due to the axis of rotation. Recently, there has been a lot of interest in the idea of a rotating Universe, because an unevenness in the CMB has been found. People naturally wondered if the unevenness could be due to rotation, or whether it was from something else.

A test of this is to look at something called the Sachs–Wolfe effect. Simply put, this is a measure of how much photons from the CMB are affected by gravity, and, if found, would be a telltale signature of rotation.

Last year, two scientists measured this as part of the Cosmic Microwave Background Anisotropies experiment. Read the paper here - it gets pretty technical, but the introduction should make sense. Basically, they find that the data are consistent with a non-rotating Universe. Being good scientists, they don't say that the Universe isn't rotating - they show that the data don't support it, and put an upper limit on the rotation speed (i.e., if it is rotating we don't see it, so it must be going slower than x).

The tl;dr to the paper is (1) It's perfectly possible to construct a rotating Universe using the physics we know, (2) they find no proof of rotation using our current data, and (2) if the Universe is rotating, it is slow - they show that it has to be going slower than 1e-9 radians per year, or one full rotation every two billion years.

Various discussions:

http://ww.reddit.com/r/askscience/comments/dn2po/how_did_scientists_determine_that_the_universe_is/

http://www.reddit.com/r/askscience/comments/15o4lj/is_there_any_evidence_the_universe_is_rotating/

http://www.reddit.com/r/askscience/comments/feywi/is_dark_energy_just_the_universe_rotating/

http://www.reddit.com/r/askscience/comments/16ph2s/how_do_astrophysicists_know_that_the_universe_is/

http://www.reddit.com/r/askscience/comments/hqgcl/other_than_expanding_is_the_universe_moving/

You are lighter at the equator than the poles because the Earth is rotating. The difference is not very big, maybe 0.5%.

http://www.reddit.com/r/askscience/comments/hw14h/how_much_would_i_weigh_if_the_earth_was_not/

http://www.reddit.com/r/askscience/comments/j6aaa/what_would_happen_to_the_weather_if_the_earth/

http://www.reddit.com/r/askscience/comments/ln0v7/hypothetically_if_the_earth_stop_rotating_on_its/

http://www.reddit.com/r/askscience/comments/1ghx89/would_we_be_able_to_feel_if_the_earth_suddenly/

http://www.reddit.com/r/askscience/comments/ltw34/earth_stops_rotating_i_am_in_the_middle_of_a/

http://www.reddit.com/r/askscience/comments/nhw4n/could_we_survive_on_earth_if_it_stopped_rotating/

http://www.reddit.com/r/askscience/comments/sfvag/if_the_earth_was_to_stop_rotating_around_its_axes/

http://www.reddit.com/r/askscience/comments/11k8b9/is_it_true_that_due_to_the_rotation_of_earth/

http://www.reddit.com/r/askscience/comments/1elkfj/does_the_rotation_of_the_earth_impart_centripetal/

http://www.reddit.com/r/askscience/comments/rjjc6/does_earths_rotation_affect_our_weight/

http://www.reddit.com/r/askscience/comments/18fkzj/do_atmosphere_gasses_rotate_with_the_rotation_of/

http://www.reddit.com/r/askscience/comments/ksdws/how_much_would_our_climate_change_if_the_earths/

http://www.reddit.com/r/askscience/comments/tb7jg/at_what_point_after_we_die_do_our_cells_cease_to/

http://www.reddit.com/r/askscience/comments/qicr4/when_someone_dies_how_long_does_it_take_for_all/

http://www.reddit.com/r/askscience/comments/13pme9/when_people_die_are_there_any_cells_in_their_body/

http://www.reddit.com/r/askscience/comments/11kdgc/when_an_organism_ie_an_animal_or_a_human_is/

http://www.reddit.com/r/askscience/comments/1650z2/what_happens_to_the_cells_in_our_body_when_we_die/

For fruit:

http://www.reddit.com/r/askscience/comments/106cz5/in_canned_fruits_are_the_cells_still_alive/

http://www.reddit.com/r/askscience/comments/z3vdp/are_the_cells_of_say_a_fruit_still_alive_when_you/

First, let us note that F=GMm/r^2 is an approximation, not the whole story. It is useful in many cases, but not perfectly exact. In order to answer this question exactly we must look at what causes gravitation.

That answer is quite long, and perhaps worthy of its own ScienceFAQ, but let us suffice to say that General Relativity tells us that the way one measures distances and times in the presence of energy (including mass, momentum, and other factors) must change so that all observers measure c to be a constant value.

We can solve these equations for a few simple cases; first we'll consider the case of a spherical mass, the Schwarzschild Metric. The space around the mass is "curved" in a specific way described by the metric. (think of a metric as a way of describing the rules of how to measure space and time as a function of location in space and time.) Well we can set a body in motion in this curved space, and using the mathematics for a body feeling no forces (not putting in a gravitational force) we will find that its motion is described as if it feels a force of gravity. Gravitation is a consequence of this curved space, not a true force. We also find small corrections to Newton's formula that are relevant as the gravitational field gets stronger (say closer to the source of the mass).

The next case is the universe as a whole, the FLRW metric. Now in this case, we note that the universe is approximately uniformly dense in matter and energy, and particularly that the mass density is very low. The solution of the FLRW metric is nothing at all like the solution of the Schwarzschild metric (as a sidebar, this is why the big bang is nothing at all like a black hole: the big bang is an FLRW, and a black hole is a Schwarzschild). So on the largest scales of the universe, we don't see a law like Newtonian gravitation. We see metric expansion.

Now, the mass of the Sun and Earth and Milky Way all play a role in that metric expansion, but they don't create an apparent force like Newtonian gravitation on these scales. If the universe was just the sun and no dark matter and no dark energy, it would be true that GR would still result in something like Newtonian gravitation. But our universe is not just massive bodies. Dark energy, in particular, drastically changes the result we see from General Relativity to something not-like-a-force.

tl;dr: Newtonian gravitation is an effect of the solutions of General Relativity. On smallish scales (clusters of galaxies and smaller) GR produces stuff like Newtonian gravitation. On larger scales, metric expansion of the universe. So no, Newtonian gravitation does not stretch infinitely far across the universe, unless you drastically want to change what you mean by gravitation or the universe.

Also: the differences in this solution, on the short and long scales of the universe also are the reason why metric expansion only happens on long scales (in the spaces between clusters of galaxies), and gravitation happens in short scales (galaxies gravitating toward each other).

Edit/Update: in trying to answer this question more fully, I'm going to sit down with the mathematics of it today. Particularly in messing around with the de Sitter-Schwarzschild Metric

Update

Okay, so I've done the calculation, and the effective potential energy, and radial force in the universe is:

V(r) = -mbr^2 - GMm/r + L^2 /2mr^2 - GML^2 /mc^2 r^3

F(r) = GMm/r^2 -2mbr (neglecting the angular momentum terms)

The first term (in the potential, the second term in the force) is the new one that includes the cosmological constant. b is the strength of the cosmological constant (or 1/3 the cosmological constant, the wiki article on the de Sitter metric was a little vague). These two are equal when r = (GM/b)^1/3 . Now, I could really be wrong on this but b seems to be something like 10^-35 s^-2 . When you combine this with say, the mass of the sun, you get something like 2 x 10^18 meters, or just about 200 light years. So within 200 light years, the dark energy of the universe becomes a relevant factor in the gravitation from the sun. More relevant to our universe, the local group of galaxies is about 10^12 solar masses, so a factor of 10^4 times larger radius, so in about 2 million light years, the dark energy component starts to become relevant to the gravitation of the mass of the local group of galaxies.

My work: http://imgur.com/a/JWIe5

• TLDR: Various physiological factors can affect "attractiveness," including blood type, sex, body size, carbon dioxide production, and heat.

• Link to most detailed answer.

• http://www.reddit.com/r/askscience/comments/nneg7/are_certain_people_more_desireable_to_mosquitos/

• http://www.reddit.com/r/askscience/comments/hv3ik/what_attracts_insects_black_fliesmosquitos_to_the/

• http://www.reddit.com/r/askscience/comments/w499f/are_mosquitos_attracted_to_certain_people_more/

• http://www.reddit.com/r/askscience/comments/voq37/can_blood_ingesting_insects_smell_blood_and_have/

• http://www.reddit.com/r/askscience/comments/tsiav/what_causes_mosquitos_to_be_super_attracted_to/

• http://www.reddit.com/r/askscience/comments/l712m/why_is_it_that_mosquitoes_tend_to_bite_some/

• http://www.reddit.com/r/askscience/comments/j5u51/why_do_mosquitoes_love_my_tasty_tasty_flesh/

• http://www.reddit.com/r/askscience/comments/k73cn/why_have_i_never_experienced_a_mosquito_bite/

• http://www.reddit.com/r/askscience/comments/l8ybr/do_mosquitoes_prefer_a_certain_blood_type_or_have/

So we can't definitively observe this one way or the other. But we can look at what the data point toward. General Relativity allows for a basic set of solutions to the overall "shape" of the universe. We observe our local universe to have a uniform and isotropic distribution of matter. Assuming that our location isn't anything special, we assume that the universe, on the whole is uniform and isotropic. We further have no evidence that the laws of physics change with location in space, so let us assume that they do not change.

Okay with these two assumptions, and General Relativity, we can solve GR for the family of solutions called the FLRW metric. This is the solution that tells us all about the expansion of space over time, and gives us the general description of the large scales of our universe.

Well we find that there is overall one parameter, a "curvature" that can be calculated from the relative mass and energy densities of the stuff making up the universe. We can also observe the curvature over the portion of our observable universe. So let's think of some 2-D analogues of these solutions. For a positive curvature, the 2-D analogue is the surface of a sphere, if you look "north/south" and "east/west" it curves "in the same direction." So it's a positive curvature. But it's also a finite surface area, and it doesn't have boundaries.

Now let's think of a pringles chip or horse saddle. It curves "up" in the forward-back direction, and "down" in the left-right direction. This is a "negative" curvature. Now for a negatively curved space we can only really imagine a portion of it at once, a single chip if you will. But without boundaries, this surface must be infinite.

Finally, we think of just a plane old sheet of paper. It doesn't "curve" at all. Again, without boundaries, this sheet would be infinite in size.

Now each of these types of curvatures are really represented by special geometry. The paper kind (no curvature) is called "Euclidean" geometry, it's the kind you learn in Elementary School. If I take 2 points, and I draw a line between them, then I draw two lines perpendicular to that line, passing through each point, this is how we construct "parallel" lines. And on a piece of paper, these parallel lines never get closer or further apart. Similarly, if we draw a triangle between three points, the sum of the angles on the inside of the triangle add up to 180^o . And if you take the ratio of the length of a string around a circle divided by the length of string crossing the circle, you get a number we call pi 3.14159.....

Now on a sphere, you can start at two points on the equator and head straight north (thus perpendicular to the equator, and thus parallel). These lines then grow closer together over time, and then intersect at the North Pole. Similarly if you add up the interior angles of this triangle, you'll find that they add up to more than 180^o , and the ratio of a circumference to diameter is less than pi.

And in a negatively curved space, we find that parallel lines grow further apart over space, that triangles have less than 180^o and that c/d >pi.

Okay so there's your crash course in non-Euclidean Geometry. So we go out and observe the large scale curvature of the universe, and measure it to be very nearly zero. This matches pretty well with our other observations of the mass and energy densities, and our overall combination of all the data available looks like this paper.

So, within error bounds, the curvature is very nearly zero, and thus the universe is very likely infinite in size. We don't really have sufficient reason to assume that the error bars prefer positive curvature, and thus the closed universe, but it could be a possibility. And there are other flat geometries more complex than the basic ones suggested by the FLRW metric that are also finite (think of like... the arcade game Asteroids, where flying through one edge of the screen lands you back on the opposite edge). Those could also be a possibility of a finite universe.

TL;DR:But the data really does seem to point heavily toward infinite. We can't prove it definitively at the moment, but it seems to lean that way.

Cosmic distance ladder is a good resource more in depth, but a great quick video on the subject is

Measuring the Universe by the Royal Observatory Greenwich