Sun-Earth-Moon Gravity

Good answers. I will add one more thing: think of the sun's gravity keeping the earth in its orbit and the sun's gravity keeping the moon in its orbit. These happen to be essentially the same orbit. The earth and moon's gravity then keeps these two bodies close together while they both are orbiting the sun.

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"The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one." -- George Bernard Shaw

No. How do you derive your conclusion from the quoted sentence?

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I've done everything the Bible says, even the stuff that contradicts the other stuff! -- Ned Flanders

I'm not sure how you're coming to these conclusions. Something can interact with a "system" as a whole and still have individual effects on the individual pieces that make up the system. In fact, the effect something has on a "system" is usually the sum of the individual effects on the parts.But I can see how this might be confusing. I wouldn't explain this as the sun interacting with the earth/moon as a system. I would just say that when one does the calculations for the motions of the earth and moon due to their mutual gravitational attraction, one finds that the earth and moon both orbit their common center of mass.And when one does the calculations of the sun interacting with the eartha and with the moon, one sees that the earth and the moon orbit their common center of mass as this center of mass orbits the sun in a Keplerian orbit.

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I've done everything the Bible says, even the stuff that contradicts the other stuff! -- Ned Flanders

No. Newton only stated that bodies attract one another, and he gave a formula for this attraction. The formula very accurately describes the motions of objects in real life, so there is something to it, but he never made a guess as to why bodies attract one another.Einstein only stated that space-time is curved, and he gave some equations to describe this curvature. The equations very accurately (more accurately than Newton, even) describes the motions of objects in real life, so there is something to it, but he never made a guess as to why space-time is curved.In the language of Newton, it is simply the nature of material bodies to attract one another. Mass is simply the measure of how much a particular body attracts others, but no one has come up with a reason why this attraction exists.In the language of Einstein, it is simply the nature of space-time to be curved. Mass is simply the measure of how curved a region of space-time is, but as far as I know no one has come up with a reason why space-time should be curved.

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I've done everything the Bible says, even the stuff that contradicts the other stuff! -- Ned Flanders

Um, okay, thanks for sharing.

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I've done everything the Bible says, even the stuff that contradicts the other stuff! -- Ned Flanders

No. Both are just strings of words without any meaning until the terms are rigorously defined enough to make testable predictions.That is what Einstein's Theory of Relativity does -- it provides rigorous mathematic definitions so that we can predict phenomena that should be observed. In fact, the bent starlight was one such prediction. So Relatitivity is no longer a meaningless string of words. It is now a well-tested theory.

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I've done everything the Bible says, even the stuff that contradicts the other stuff! -- Ned Flanders

Except that the observer looking out the window may as well conclude that it is the ground that is moving past at a velocity v. The point of relativity is that there is no preferred frame of reference in which to determine absolute velocities. It is indeed not possible to determine whether the two lightning strikes occurred simultaneously or whether one occurred before the other until one decides on a frame of reference in which to make the time/position measurements.It is impossible to determine whether it is the train that is moving, or the world outside that is moving.

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I've done everything the Bible says, even the stuff that contradicts the other stuff! -- Ned Flanders

No. It depends on the frame of reference one chooses to determine the times and locations of the lightning strikes.

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I've done everything the Bible says, even the stuff that contradicts the other stuff! -- Ned Flanders

Indeed.- A better way to say this is that there are different choices for a frame of reference, each of which will provide a different timing (and distance) between the lightning strikes.- That is a choice that needs to be made by the observer. Usually the observer chooses her frame of reference -- that is the most natural one to use -- but she may decide to use a different one if it is more convenient for the problem at hand.

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I've done everything the Bible says, even the stuff that contradicts the other stuff! -- Ned Flanders

Unless the train was passing by when the lightning strikes. Then she would be right outside the train window.- I don't like the word "appear" -- it makes it sound like this is some sort of optical illusion when in fact the different observers really do measure time and distance differently.Why do different observers measure time and distance differently? Well, that's the way the universe is. Why should different observers measure time and distance the same? The reason that latter question doesn't get asked is because, being unfamiliar with relativistic speeds, we are just used to it -- it seems normal to us.

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I've done everything the Bible says, even the stuff that contradicts the other stuff! -- Ned Flanders

Huh? This doesn't make sense. What does the distance light travels have to do with a person's height?- I can't make any sense out of this paragraph either.Don't worry about things like "past" and "present". We assume that we can tell where an event occurred and when it occurred. How we measure these things aren't important, just that we do.We have something that occurred. Say lightning strikes a point on the ground, since that is the example you choose. A person standing on the train platform sees the lightning strike. She can presumably tell where it struck the ground and when. Maybe you're worried that it took some time for the light signals to travel from that point so that she could see it -- don't worry about that -- the observer is smart enough to take the speed of light into account so that she can figure out precisely when the lightning struck.Now say that two bolts of lightning strike the ground at different places, A and B to use your labeling. Suppose that the person on the platform (after taking into account the time it takes to reach her form each of these points, of course) determines that each of these lightning strikes occurred at exactly the same time in her frame of reference.Now there is someone sitting on a very high speed train, and this train happens to be travelling along a path that is parallel to the line between A and B. In fact, suppose that this train is travelling in the direction that goes from A toward B. This person also sees the two lightning strikes, and can tell where they occurred, and can also take into account the speed of light to tell exactly when they occurred. When he does so, he discovers that (in his frame of reference), B occurred before A did.Who's right? They are both right. We have no way of determining locations except by marking a special point as "location=0" and using a ruler to measure the distances from that special point to other points. We have no way of determining times of events except to designate some time as "time=0" and using a watch to determine how long afterwards other events occur.However, different observers in different frames of references will measure lengths and times very differently from one another. The observer on the train platform may have a measure stick that is exactly (to her) one meter long. However, the observer on the train will notice, if the measure stick is lying parallel to the path of the train) to be shorter than one meter. The observer on the platform will have a watch -- she will notice that it takes one minute for the second hand to go all the way around. However, the observer on the train will notice that it takes more than a minute for this second hand to go all the way around.Of course, this is all relative. The person on the train may also have a measuring stick that is exactly (to him) one meter long. However, if it's lying on the floor parallel to the direction the train is traveling, the the observer on the platform will notice that it is shorter than a meter. Likewise, the observer on the platform will notice the second hand on the person on the train's watch takes more than a minute to go all the way around.This isn't merely an optical illusion, but a fundamental fact of the universe that time/space coordinates "rotate" and mix together when we jump from one frame of reference to another.

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I've done everything the Bible says, even the stuff that contradicts the other stuff! -- Ned Flanders

Hmm. Now we're talking about cosmological distances where General Relativity becomes important. I'm not sure whether my answers here are going to make any sense, so don't take them too seriously.As far as I know, if an object is billions of light years away, then we are estimating the distance between the point at which the light was emitted (billions of years ago) and our position here, now. After all, we don't really have any idea where that object is now anyway, since we won't see the present time object for another billion years or so.

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I've done everything the Bible says, even the stuff that contradicts the other stuff! -- Ned Flanders

That's what they do.Say that a lightning bolt strikes the ground about a mile in front of the train. To the person standing on the platform, the train will then pass directly over the point where the event happened. However, to the person in the train, if he's using his frame of reference, the spot at which the event happened remains the less-than-a-mile* in front of the train, even as the black spot on the ground travels toward him and passes directly under him.Added by edit:
*Taking into account length contraction.Edited by Chiroptera, : No reason given.

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I've done everything the Bible says, even the stuff that contradicts the other stuff! -- Ned Flanders

Suppose that you are standing on the sidewalk, and you see a car approaching you. You see the tire blow out. The car doesn't stop, but continues by you. How do you describe the incident? You say, "The tire blew out at the corner over there," even though the flat tire is passing you right at that moment. Because you are describing the time and the position of the incident according to your reference frame.Now consider the man on the train. He notices the lightning strike the ground in front of the train. Now he notices the ground and the storm clouds are moving toward him, and knowing how far away he saw the lightning strike, how fast the ground-and-storm is traveling, and how fast light travels, he does some calculations and figures that the lightning struck a point about half a mile in front of the train. He continues to say, "The lightning struck the ground at a point about half a mile in front of the train, over there," even as the black spot on the ground in passing him.Now the lady on the platform sees that black spot isn't moving, and it is the train that is passing by the spot. In the same way, the driver in the car insists that the blow-out occurred in the tire five feet behind him, and it is you, on the sidewalk, who is passing by the tire.

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I've done everything the Bible says, even the stuff that contradicts the other stuff! -- Ned Flanders

Suppose that a murder occurs on the train. The person on the platform (somehow) notices it. The sheriff asks her, "Where did the murder occur?" She replies, "Three miles down the track." The sheriff is relieved because that is a different county and, even though the train, murderer and murder victim are passing him right that instant, the murder itself occurred in a different jurisdiction and isn't his responsibility.But, of course, the person on the train will answer, "The murder occurred in that compartment, 100 feet away." And he will continue to say this, because the murder occurred only 100 feet away from him on the train. This causes no contradiction because the person on the platform is discussing an event that occurred on a moving train when it was at a specific point in her reference frame.In the same way, the man on the train, seeing the lightning strike, will say that the lightning struck at a point half a mile in front of the train, even thought the incident occurred on a moving ground-and-storm and the moving ground carried the actual storm clouds and the black spot passed him.

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I've done everything the Bible says, even the stuff that contradicts the other stuff! -- Ned Flanders