Does Earth's Elliptical Orbit Affect Time Dilation Due to Gravity?

[nitsuj]

Relative some arbitrary point in Earth’s orbit around the Sun, does Earth experience varying degrees of time dilation specifically from gravity?

With Earth's orbit around the sun being elliptical I wondered if Earth experiences varying degrees of time dilation caused by the suns gravity (or moon for those cycles).

For example in January we are closest to the sun and farthest in June.

Is time slower in January relative to June.

 

[PAllen]

Generally, the answer to your question is yes, with some caveats and clarifications. First, note that speed varies along the orbit. However, this adds to the gravitational time dilation (faster when closer), so competing effects don't need to be balanced - instead they add to each other. More important, the question really has no meaning without a definition of 'slow relative to what'? Locally, you measure no changes at all.

However, if ones asks what is the total redshift of signals you send, when received by an observer at infinity (assuming asymptotic flatness), you have a well specified question. With this clarification, you could say time on Earth runs slower in January compared to June as perceived by observers at infinity (or, for practical purposes, distant radial observers).

 

[PAllen]

I'd like to add one more caveat about this. If you ask about clock time on Earth compared to a single distant clock, the situation is more complex if the distant clock is in the plane of the ecliptic - orbital motion towards and away from that clock would become significant.

So, to get a reasonably simple statement you could say: Compared to a distant clock on a line through the sun, perpendicular to the ecliptic, time on Earth would be slower in January than in June.

 

[nitsuj]

I'd like to add one more caveat about this. If you ask about clock time on Earth compared to a single distant clock, the situation is more complex if the distant clock is in the plane of the ecliptic - orbital motion towards and away from that clock would become significant.

So, to get a reasonably simple statement you could say: Compared to a distant clock on a line through the sun, perpendicular to the ecliptic, time on Earth would be slower in January than in June.

So if I get what your saying, I forgot to mention a frame of reference?

What about a ring of clocks, initiated simultaneously, all along Earth's elliptical orbit around the sun, do they all display the same time after a year? (just gravity)

 

[PAllen]

So if I get what your saying, I forgot to mention a frame of reference?

What about a ring of clocks, initiated simultaneously, all along Earth's elliptical orbit around the sun, do they all display the same time after a year? (just gravity)

Yes, that would just measure gravitational time dilation differences for 'hovering observers' (note these are a special class of non-inertial observers; the orbiting Earth is inertial - excluding its rotation). You would indeed see the clocks at perihelion fall behind the other clocks, with the one at aphelion being most in the lead.