For the purpose of this question, I'm assuming that
- The Earth is perfectly spherical
- The Earth is made of material whose density, if it varies at all, depends only on the distance from the center of the Earth
- The Earth spins, completing a rotation once every 24 hours.
- The mass of the Earth is much greater than that of the satellite my question is about
- The Earth is far away from the gravitational influence of any other celestial body.
Also assuming the absence of any atmosphere, or solar wind, or any solar radiation in the vicinity.
If we have a satellite orbiting the Earth in an circular orbit that is inclined at, say, 45° to the Earth's equatorial plane, is there any factor (however small) in Newtonian mechanics that can cause the speed (in meters per second) of the satellite at any instant to vary with its distance from the equatorial plane (and thus the latitude of the sub-satellite point) at that instant?
Or, in summary, does the spin of a planet affect the orbital speed of a satellite going around it according to Newtonian mechanics?
I ask this because I saw a web-page somewhere (which I can't find now, unfortunately) that stated that this speed is different between when the satellite is over high latitudes and when it is crossing the equator, and that this is due to conservation of angular momentum. Wanted to understand whether this is legit, and if so, how.
Edit: Ok, so the web-page I read is this one and I may have misread it. What it does actually say, unfortunately under the heading 'Inclined Orbits', is that for a satellite in circular orbit that isn't actively station-keeping
for reasons beyond the scope of this article (conservation of angular momentum), the orbit assumes a slightly elliptical shape
I'd like to understand the reason for that instead.