# What would be different about satellite orbits if Earth were prolate? Would we have Sun-synchronous and Molniya orbits?

It's hard to imagine how it could happen naturally since on geological timescales the Earth would either be spherical if it didn't rotate, or oblate if it did, but from an orbital mechanical perspective, how would artificial satellite orbits differ if Earth's J2 had the opposite sign?

Could we still have Sun-synchronous orbits or Molniya orbits? If not, would there be alternatives to these? What else might be different?

Physically, you can think of a sun-synchronous orbit as having its orbital plane precessing once a year. Like a toy gyroscope’s plane of rotation precesses under the torque due to gravity, so does the satellite’s plane due to the torque of being attracted to the tidal bulge.

Now think of a prolate Earth as having a “negative tidal bulge” (to first order, this is ok). The torque, hence precession, is linear in this, so the precession is the other way!

Or, if you prefer, imagine the gravitational force due to the prolate poles as pulling away from the equator, reversing the effect.

Precessing the other way means that orbit is no longer sun synchronous.

To get back a sun synchronous orbit, you need another minus sign, so you make the orbit go the other way around the Earth’s equator. That sounds prohibitive, but it’s not really: this is a near polar orbit, and the “going around the equator” comes from about an 8 degree retrograde tilt (I.e. a 98 degree inclination). Flipping that to an 8 degree prograde, 82 degree inclination should do it.

The situation with Molniya orbits is even a bit easier. Their angle of inclination is set to cancel out the J2 component, regardless of what J2 is. So they would exist unchanged, at least to first order.

• Very nice answer, thanks! – uhoh Oct 6 '19 at 13:18