1221
Physics, Astronomy & Cosmology / Re: gravity and time dilation
« on: 30/11/2015 20:24:36 »
I assume that this question is about time dilation due to gravitational fields (ie general relativity), but also time dilation due to velocity (ie special relativity)?
Both effects affect the atomic clocks on the GPS satellites, and they work on opposite directions, the two effects partially canceling each other. The clocks on GPS satellites run faster in orbit because they are further out of Earth's gravitational well; but they also run slower because they are traveling at orbital speed.
A laser pulse from Earth's surface is partially reflected from the metalized surface of the balloon and the remainder is reflected back to Earth from the retroreflector at the center. Someone on Earth can measure the delay between the two light pulses.
A similar set of tools on the ground is used to measure the distance to the Moon.
Since this satellite is a big balloon, I assume that it has negligible mass, so it will effectively have no gravitational time dilation of its own (just the time dilation due to the Sun and the Galaxy, which is shared with the Earth).
Since the retroreflector is moving in a circular orbit, it is not traveling radially towards or away from the laser, so there will be no doppler shift, and no relativistic frequency shift (ie there is no laser source on the balloon).
I don't think the satellite orbital speed will have any impact on the result.
I expect that the light will travel in straight lines, for all practical purposes.
But in reality, light is very fast, and gravitational time dilation on Earth is very small. The ability to measure r accurately is very limited, since a balloon is very stretchy, it's shape will be slightly distorted by the heat of the Sun, the Solar Wind and/or any drag from Earth's outer atmosphere, and it is very hard to mount a retroreflector at the precise geometric center. The proposed experiment is trying to measure something very precisely (gravitational time dilation), using something which can be known only very approximately (r).
So I suggest that the best way to measure r is to measure the time difference between a pulse of light reflected from the surface, and one measured from the mirror at the center. Forget measuring gravitational time dilation this way. Much better measurement of relativistic effects are available from GPS satellites and Gravity Probe B.
Both effects affect the atomic clocks on the GPS satellites, and they work on opposite directions, the two effects partially canceling each other. The clocks on GPS satellites run faster in orbit because they are further out of Earth's gravitational well; but they also run slower because they are traveling at orbital speed.
Quote from: saspinski
a (huge) artificial satellite... a beam of light reaches the satellite surface (and) bounces back from a mirror at its centerFrom this description I am imagining something like a huge partially reflective balloon in a circular orbit around Earth, inflated by a low-pressure gas, with something like a retroreflector at its center?
A laser pulse from Earth's surface is partially reflected from the metalized surface of the balloon and the remainder is reflected back to Earth from the retroreflector at the center. Someone on Earth can measure the delay between the two light pulses.
A similar set of tools on the ground is used to measure the distance to the Moon.
Since this satellite is a big balloon, I assume that it has negligible mass, so it will effectively have no gravitational time dilation of its own (just the time dilation due to the Sun and the Galaxy, which is shared with the Earth).
Since the retroreflector is moving in a circular orbit, it is not traveling radially towards or away from the laser, so there will be no doppler shift, and no relativistic frequency shift (ie there is no laser source on the balloon).
Quote
For someone in the earth, the time would be bigger than 2r/c due to the satellite orbital speed.I don't expect so. There is no clock on board the satellite, so we are really just talking about the speed of light in an (almost) vacuum.
I don't think the satellite orbital speed will have any impact on the result.
Quote
The beam should be travelling a curved path from the surface to the center and back to the surface from earth perspective.I don't expect so. The photons in the laser beam travel in a straight line. Some will be reflected from the metallic surface of the balloon; others will bounce off the mirror. Because they are traveling radially out from the Earth and returning radially to the Earth, any curve will be negligible. (When Eddington was trying to test the General theory of Relativity, he used light traveling tangentially to the Sun's surface, close to the Sun's much larger mass, and was able to demonstrate a small bend in direction.)
I expect that the light will travel in straight lines, for all practical purposes.
Quote
For someone in the earth, the time would be bigger than 2r/cSince the Earth is in a gravitational well, time will pass more slowly on Earth. So I expect that the measured time will be smaller than 2r/c.
But in reality, light is very fast, and gravitational time dilation on Earth is very small. The ability to measure r accurately is very limited, since a balloon is very stretchy, it's shape will be slightly distorted by the heat of the Sun, the Solar Wind and/or any drag from Earth's outer atmosphere, and it is very hard to mount a retroreflector at the precise geometric center. The proposed experiment is trying to measure something very precisely (gravitational time dilation), using something which can be known only very approximately (r).
So I suggest that the best way to measure r is to measure the time difference between a pulse of light reflected from the surface, and one measured from the mirror at the center. Forget measuring gravitational time dilation this way. Much better measurement of relativistic effects are available from GPS satellites and Gravity Probe B.