[time-nuts] Re: gravity fields affect time keeping?

[Marek Doršic]

Anybody studied the influence of the Sun's gravity on clocks in GNSS satellites? The field might change slightly by 40,000 km distance when the sat is closer to the Sun than later on the opossite side of Earth. Is this measurable on the clocks?

   .md

> On 31 Jan 2023, at 14:40, alan bain via time-nuts <time-nuts at lists.febo.com> wrote:
> 
> It's a consequence of general relativity.
> 
> The simplest way I can think to answer this question is to think of a
> point mass in a spherically symmetric situation  (as one would expect
> around a point mass in a vacuum) and solve Einstein's equation which
> in this case (point mass is handy) is just
> 
> G_{\mu\nu}=0
> 
> After some boring algebra with tensors in spherical co-ordinates which
> some examiners seem to think it is interesting to see if you can
> reproduce, you arrive at a metric
> 
> ds^2 = - (1-r_s/r) c^2 dt + dr^2/ (1-r_s/r) + r^2 (dtheta^2 + sin^2
> theta dphi^2)
> 
> r,theta,phi are usual spherical co-ordinates, c is the speed of light
> in vacuum and the Schwartzchild radious r_s = 2 G M /c^2 (which is
> found by comparing with Newtonian Gravitation, G is Newtonian
> coefficient, M is mass of point mass). So if we stay in the same place
> and compare time
> 
> ds^2 = - (1-r_s/r) c^2 dt
> 
> And ds^2 = -c^2 d (tau)  where tau is time measured at a stationary
> point arbitrarily far from the mass.
> 
> So
> 
> \delta t_{on planet} = \delta t_{clock infinitely far away} sqrt ( 1-r_s/r).
> 
> So the closer one gets to the point mass the slower time goes.
> 
> I don't really know any maths-free explanation of this (unlike for say
> special relativity when there are good no-maths explanations). Would
> like to know one if someone does...
> 
> Alan
> 
> On Tue, 31 Jan 2023 at 13:00, Kevin Rowett via time-nuts
> <time-nuts at lists.febo.com> wrote:
>> 
>> From an article about moon time keeping:https://www.nature.com/articles/d41586-023-00185-z <https://www.nature.com/articles/d41586-023-00185-z>
>> 
>> The author says
>> 
>> 
>> “...Clocks on Earth and the Moon naturally tick at different speeds, because of the differing gravitational fields of the two bodies. …”
>> 
>> I’m curious about what type of clocks are affected by local gravity, and how much.
>> 
>> Anyone familiar enough to go into detail?
>> 
>> KR
>> 
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