Brent Meeker <meekerdb@verizon.net> wrote:

Keith F. Lynch wrote:

...

(Copernicus, Galileo, Kepler et al believed that the celestial sphere stood still and Earth rotated. They were mostly right, but if they had kept close track, they would have noticed that the celestial sphere rotates by about 0.04 seconds of arc per year due to frame dragging.)

I don't understand that. The celestial sphere is defined as not rotating and is empirically fixed by distant galaxies.

That certainly wasn't the original definition. Before Copernicus it was generally believed that it rotated about once per day around the stationary Earth. According to relativity, with linear motion it's arbitrary which frame of reference is regarded as stationary. Not so with rotary motion. Numerous experiments can be done to determine whether the Earth turns or whether the celestial sphere, distant galaxies and all, revolve around the Earth. Or some of each. At Earth's north or south pole, set up a frictionless pendulum that's free to swing in any horizontal direction. Set it to swing towards and away from some distant galaxy that's on the horizon. If Earth is rotating, it will continue to swing towards and away from that distant galaxy as the Earth rotates under it. Anywhere on or near Earth, point a gyroscope's axis at some distant galaxy. See if it keeps pointing at that galaxy. Fire a cannonball in the northern hemisphere. See if its trajectory curves to the right, and if so by how much. On the equator, simultaneously launch two satellites into equatorial orbits, identical except that one is eastbound, the other westbound. See whether they're directly overhead when they collide. Send a radio signal in all horizontal directions at once. Measure when it returns to you from each direction. Deduce Earth's rotational rate from the magnitude of its equatorial bulge. The frame dragging effect, also known as Lense-Thirring precession, says that space in and near a rotating mass such as Earth will be dragged along with it somewhat. As such, those experiments ought to show that Earth is rotating slightly less than observations of distant galaxies would imply, and that those distant galaxies are all revolving slowly around the Earth in the opposite direction. Slowly in terms of arc seconds, quite rapidly in meters per second, given how distant those galaxies are. They're going many times faster than light. No, that doesn't contradict general relativity. GR says that that speed limit is strictly local. With the possible exception of Gravity Probe B, Earth frame dragging has never been detected, as the numbers are just too small. But it's certainly been detected around neutron stars and black holes. In _Incandescence_ by Greg Egan, a pre-technological civilization with no knowledge of astronomy (they live inside a hollow asteroid) works out general relativity from a few simple experiments and measurements and some careful reasoning. They have the advantage of being in close orbit of a massive black hole where GR effects are significant. (Well, it's an advantage in discovering GR, but a great disadvantage in all other ways, as it's a rather dangerous neighborhood.)