Strange

You have just agreed that the moon's orbit is not a perfect ellipse. And yet we can still use it to calculate the mass of the sun. The case of S2 is slightly more complex, as Janus says, because the orbit does not average out to an ellipse (as the moon's does). But it is still possible to determine how much it deviates from an ellipse and use that to calculate the extra mass that is affecting the orbit at various points (as the paper your referenced has done). Unless you can show a flaw in their mathematics, I think you will just have to accept their results (even if you are not able to understand it).

This is rich, coming from someone who clearly doesn't understand it. NO ONE IS DENYING THAT. You are just being very very dense. Or maybe you are trolling. Either way it is not longer productive trying to communicate with you. On the Ignore list you go. My irony meter just broke.

No. Space is, well, space. It isn't time. How would it age? Is yesterday's mile different from today's? There is no such thing. Well, it expands. If you consider that changing. There is (currently) no evidence that time or space are quantised (although many theorists expect it to be). In relativity (especially general relativity) it has to be continuous. No.

This isn't really anything to do with relativity. Just the finite speed of light. So if light takes a year to get from somewhere else to here then we see it as it was 1 year (not hour) ago. So we are seeing its past. I'm not sure why you think this is connected to predetermination? We are seeing the past, not the future. And we can never see anything more recent than a year ago on that distant planet.

And can arrive hundreds of milliseconds after the visual signal. The brain does a great job of tricking you into thinking it all happens "now".

But from the perspective of the moon, for example, the ground is moving at roughly 1000km/h (at the equator). But from the point of view of someone on the ground, the ground is stationary and it is the moon that is moving. You can't treat the ground as an absolute frame of reference. Either twin can consider themselves stationary and the other moving relative to them. They will both see the other's clock run slow. I though you said you understood relativity. It seems not, after all.

That is pretty meaningless. What is "the length of constant rate"? What is the "ground state"? Why is it invariant? Even Galileo knew that either could consider themselves stationary (when they are not accelerating). https://en.wikipedia.org/wiki/Galilean_invariance

Wrong. They are in relative motion. They will each see the other's clock run slow. They can both consider themselves in the "ground state" (it doesn't help that you are inventing terminology - that just adds to the confusion).

His clock falls behind. (And note that twin 1's clock falls behind twin 2 as well.) "Falls into the past" has no meaning.

Here are three simple questions requiring very little mathematical ability. You should be able to answer all three. 1. What is the orbital period of the moon around the sun? 2. What is the relationship between orbital period and mass? 3. From 1 and 2 (and nothing else) what is the mass of the sun? After that, we can look into how to determine the mass of the Earth...

No one is saying that (apart from madmac and he is a crank opposed to relativity theory). No one is saying that. Clearly wrong. You can end up at the place by taking paths that are different length.

What is the formula for orbital period? Clue: https://en.wikipedia.org/wiki/Orbital_period#Small_body_orbiting_a_central_body

True. http://www.math.nus.edu.sg/aslaksen/teaching/convex.html Not sure what you mean by this. If we could (somehow) only see the moon and not the Earth then we would know three things: 1. From the orbital period we would know the mass of the Sun. 2. From the shape of the moon's orbit (not exactly an ellipse) we would know that there was another mass present. 3. By measuring the departure of the moon's orbit from a perfect ellipse, we could work out the relative mass of the moon and its invisible partner. (Edit: or, at least, work out the mass of the Earth) This is basically how planets like Neptune and some extra-solar planets were found. Can you explain why that is? If the deviation is too small to measure, then can it have a significant effect? Please show your working. And, as far as I can tell, this is what has been done to estimate the extra mass of other matter that it passes through.

Yes. That is a more accurate statement.

Only in the special case that one accelerates away and then returns.

Janus's explanations are always a pleasure to read. Or, in other words, time dilation. Citation needed. As seen by them; i.e. proper time. However, it doesn't [necessarily] pass at the same rate as seen by someone else. Why would that make any difference?

It is an interpretation and so it as "true" as any other interpretation. Evidence or experiment cannot distinguish between interpretations (otherwise they would be different theories).

It is relevant because it shows you can take a longer path but still arrive at the same place. Similarly, you can take a longer path through space-time and still end up in the present. This "Twin Paradox" experiment has been done, you know. It didn't end up with one of the aircraft in the past. But he still not travelling into the past.

The light from the Sun is affected by the mass of the Sun, but by an immeasurably small amount. It will make the Sun look very slightly larger than it would otherwise. However, this effect is (a) very small and (b) undetectable because the Sun does not have a solid edge. It becomes significant for black holes, for example, where the apparent size is about twice what would be expected. You seem to be confusing two different things here. The light from the Sun is radiated in all directions away from the Sun. The light from the star is also radiated in all directions away from the star. Any given ray of light light (from either the Sun or the star) will continue in a straight line unless something else affects it. In this case it passes through the gravitational field of the Sun. Or, for example it could pass through a lens. Exactly the same sort of diagram is used to show the change in position in that case. The only reason complicated words (and mathematics) are used is because the world is basically pretty complicated.

Let's look at distance rather than time. It may be less confusing for you. Two cars set off on different routes from X to Y, but they leave and arrive together. One car (A) drives a straight line between X and Y. The other (B) takes a longer circular route. A watches B's odometer and sees that it is incrementing miles more slowly than his (it is "dilated" with respect to his). When they both arrive at Y they compare "clocks" (odometers) and B's odometer is reading more miles travelled. Lets say 10 miles more. This doesn't mean that he is 10 miles ahead of A. They are at the same place. It just means he took a different journey through space-time. But they still end up in the same place at the same time. No. It only appears contradictory because you don't understand.

Or, at least, they can be. No. No.

Are you deliberately missing the point? One of the twins clock reads a different time and she has aged less. BUT IS NOT IN THE PAST. Yes.

But they are not "in the past". The two twins can still talk to each other. There isn't a 5 minute delay before twin 1 hears twin 2.

Nope.

That is the same thing. For example, in the Twin Paradox, the two twins get together at the end. One has aged less (experienced less time). But they are together at the same time - one is not in the past.