Does the clock aboard a GPS ...


by vector22
Tags: aboard, clock
harrylin
harrylin is offline
#19
Apr9-11, 05:48 AM
P: 3,178
Quote Quote by Drakkith View Post
So is using "Force" instead of "Potential" just a bad choice of words for me, or is it just pretty much wrong on all levels?
To illustrate the difference: it is possible to have the same gravitation force at different heights, for example at ground level and deep below the surface.
- http://en.wikipedia.org/wiki/File:EarthGravityPREM.jpg

The gravitational potentials at those depths are very different.
Cleonis
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#20
Apr9-11, 07:26 AM
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Quote Quote by Drakkith View Post
So is using "Force" instead of "Potential" just a bad choice of words for me, or is it just pretty much wrong on all levels?
Another way of illustrating the difference:
At each point in space the gravitational force is given by the gradient of the gravitational potential.

You can state the gravitational force for a single point in space and that is a meaningful statement. And you can measure it right there. An accelerometer positioned at some point on the Earth's surface gives you the local gravitational acceleration. There is no outside reference; a state of zero acceleration is defined by the accelerometer giving a reading of zero acceleration.

A statement of potential is by nature stating a relation, it's not about a single point.
For the two inverse square forces, gravity and the Coulomb force, the most common practice is to relate the potential at some altitude to the potential at infinity. It is convenient to designate the gravitational potential at infinity as zero. At all lower altitudes the potential is lower.

Whenever you specify a gravitational potential at a particular altitude you reference this potential to some designated zero point. Another use of potential is that you compare the potential at one altitude to the potential at another altitude. Potential is designed to provide an integral picture. (Quite literally: the mathematical definition of gravitational potential is that it's the integral of work being done by gravitational force.)
vector22
vector22 is offline
#21
Apr9-11, 12:25 PM
P: 56
Cleonis

you said:
(Quite literally: the mathematical definition of gravitational potential is that it's the integral of work being done by gravitational force.)
A sattelite in orbit does no work as energy is not consumed in free fall (conservation of energy) so how does the gravitational potential relate to time dialation for objects in orbit (free fall)?
Cleonis
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#22
Apr9-11, 05:56 PM
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Quote Quote by vector22 View Post
[...] how does the gravitational potential relate to time dialation for objects in orbit [...]?
As every introduction to general relativity describes: for an object located at some depth in a gravitational well less proper time elapses than for an object that is not subject to gravitational time dilation. The bigger the difference in gravitational potential the larger the difference in amount of proper time that elapses.

For an object on the surface of the Earth the difference is in the order of tens of microseconds per day.

See also the following 2005 physicsforums post by George Jones about Difference in lapse of proper time for satellites.


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