Is there any gravitational lensing for Earth bound telescopes,due to Earth's gravity?

[Frog march]

Has there ever been detected a lensing effect for the night's sky, due to Earth gravity?

I would have thought that that might mean that as stars rise in the east they start by moving faster, and as they become more over head that they slow down, and as they head to the horizon again they would speed up again.



ETA: or is the lensing effect the other way around, ie like a convex lens?

[StupendousMan]

Has there ever been detected a lensing effect for the night's sky, due to Earth gravity?

I would have thought that that might mean that as stars rise in the east they start by moving faster, and as they become more over head that they slow down, and as they head to the horizon again they would speed up again.



ETA: or is the lensing effect the other way around, ie like a convex lens?

As a general rule, the size of the gravitational lensing effect is largest when the lensing object is halfway between the source of light and the observer.

Since the Earth is so close to us, and the stars are so far from us, the gravitational lensing effect due to the Earth is miniscule. It has no discernible effect on starlight.

(Yes, yes, the gravitational redshift of starlight may be large enough to be detected by a very careful, dedicated experiment. But that's not what the original question was asking)

[Frog march]

But I suppose that it is like a convex lens effect, if the light is being curved towards the Earth; this should increase the arcs per second rate for the movement of stars directly above the viewer, shouldn't it?

[ngc3314]

The maximum effect should be seen for stars near the horizon, where the rays just graze the Earth's surface (analogous to the 1.75-arcsecond deflection for starlight grazing the solar surface). The deflection in angle in this case should be GM/2 r c^2 (half the usual deflection since we are looking at rays coming in but not going back out). That amounts to about 0.25 milliarcsecond. This might be just measurable by very-long-baseline radio interferometry except that the antennae wold have to be so far apart that the effect would be different at each site. In the optical, atmospheric refraction amounts to over a degree at the geometric horizon, and varies not only with wavelength but with weather conditions by many arcminutes. I don't see how to make the effect observable from the Earth's surface - the closest I can think of is that deflection has been observed for radiation passing near Jupiter in both radio and optical (which gave rise to claims about the speed of gravity, a different can of worms).