Elen Sila

Here's what I'm saying. (And this goes for both my original scenario, and the scenario I just posted a few minutes ago.) Upon achieving its orbit, the satellite sends a "requesting response" signal to the earth, and the satellite's clock starts counting. Upon the earth receiving this signal, a "verifying response" signal is sent back towards the satellite, and the earth's clocks start counting. Upon receiving the earth's response, the satellite's clocks stop counting, and beam their recorded time elapsed back to the earth. When the earth receives the satellite's second signal, the earth clocks stop counting, and compare their result to the result the satellite reported. In the first scenario, the one-way signal transit time for an earthbound observer should be 57.75 days, or 115.50 days for a two-way exchange; in the second scenario, the one-way signal transit time should be about 505.2 seconds, or 1010.4 seconds for a two-way exchange. My question is this: would the satellite and the earth count the same amount of time elapsed between receipt of signals?

Yeah, I was thinking about that. That's why I decided to create a revised scenario. In case you can't read my handwriting, it reads as follows. "Satellite, orbiting at 74.865 km/s [with respect to the sun], with a semi-major axis of 23685251 kilometers, or 34 solar radii, or 0.1583 AU. Satellite's orbital nodes precess at a rate of about 22.68 degrees per orbit, or one full circuit every 365.25636 days. Earth, orbiting at 29.785 km/s [with respect to the sun], with a semi-major a[x]is of 149598261 kilometers, or 215 solar radii, or 1 AU." We'll say that Mercury's orbit has somehow been altered to provide the gravitational impetus for the satellite to precess at such an outrageously rapid rate, so we don't need to fire the satellite's rockets at all once we've achieved orbit. Regardless of the details however, the satellite is moving about 2.5 times faster than the earth, with respect to the sun, completing one orbit every 23 days, and its orbit is slowly turning so that the earth is always located at the satellite's orbital north pole. The satellite is thus maintaining a constant distance from the earth, despite its outrageous orbital velocity. In this scenario, why would the satellite experience time dilation, IE not be in the same frame of reference, as an observer standing on earth's north pole?

But how close together do they have to be to be considered "in the same reference frame"? If "in the same reference frame" just means "travelling in the same direction, and maintaining the same distance from each other", then the earth and the satellite are in the same reference frame, just as two atomic clocks would be if they were in the same room together. The distance between the earth and the satellite, like the distance between the two atomic clocks, is only significant in that it creates signal delay.

I guess I just don't get time dilation. In order to say "Spacecraft A is moving faster than planet B; therefore spacecraft A is experiencing time slower than planet B," you must have an absolute point of reference from which to determine A's and B's absolute velocities. If you only base time dilation off relative velocity, then an observer onboard spacecraft A would view planet B as moving faster, and thus planet B would be the one experiencing time at a slower rate. They can't both be experiencing time slower than the other; that's a contradiction. The way I've always resolved the contradiction is by imagining that time dilation is simply an illusion, caused by the Doppler effect. If you're moving away from someone at 0.99c, you both observe each other as perceiving time very slowly, because each of your signals from each other are highly red-shifted. However, this means that if you were moving towards someone at 0.99c, then you would both observe each other as perceiving time very quickly, because your signals from each other would be highly blue-shifted; and likewise, if you were maintaining a constant distance from each other, but travelling at different velocities relative to an outside reference point (like the sun in my scenario, or the center of the earth in the GPS scenario), you would not observe time dilation from each other, except in the form of signal delay. And if you travelled very far away from the earth and then returned, the red-shifting during departure and the blue-shifting during return would cancel each other out, and you would still be the same age as your twin on earth. How can both spacecraft A and planet B observe time dilation from the other, if time dilation is NOT simply the Doppler effect?

In case you can't read my handwriting, this is what it says. "Satellite orbiting sun at a distance of 10,000 AU. Satellite completes one circuit every 365.25636 days, travelling at 99.35 percent the speed of light, but maintains a constant distance from the earth. Not counting time dilation incurred during transit to this distance, or acceleration to this speed, and reckoning only from the moment the satellite receives a confirming signal from the earth... would the satellite's clocks experience time dilation (relative to the earth)?" NOTE – I'm aware that the satellite couldn't actually be orbiting at that speed and at that distance; Kepler's laws demand that the satellite actually have an orbital period of about one million years. However, this scenario assumes that the satellite is using its engines to maintain a constant speed, and a constant distance from the earth and the sun. It's not technically "orbiting" the sun so much as it is "flying around" it in circles.

So, the other day somebody figured out how to exploit the LaTeX math script on 4chan's /sci/ board. This exploit allowed them to alter the background of the website to any tiled image they wished. I couldn't resist the temptation, and proceeded to create a Carl Sagan appreciation thread, complete with Carl Sagan background. Unfortunately, my use of the script caused my post to be automatically flagged later, and my IP address was banned for 30 days. I can't figure out how to change my global IP address, so after spending the last 48 hours or so attempting various methods of doing that, I finally gave up and decided to just find another science/math messageboard to visit. This was the first one that came up on Google. So hi! I'm Elen. I'm currently going to university, pursuing undergraduate degrees in physics and math; I intend on going to a bigger university later to pursue a graduate degree in astronomy or astrophysics, probably at the university of Minneapolis or the university of Chicago. Even though I'm really good at math and science, I also enjoy a number of right-brained subjects, like linguistics, poetry, and photography. Hopefully this forum is active and full of intelligent people and enlightening discussions.