Can a Satellite Maintain its Angular Velocity with Continuous Low Thrust?

[dansmith170]

TL;DR Summary

Can a satellite that undergoes a low continuous thrust maintain the same angular velocity as a satellite that does not undergo said thrust?

Suppose two satellites are in a circular heliocentric orbit with radius R and with angular velocity O'. Satellite 2 then undergoes a low continuous thrust. Can Satellite 2 (the one that undergoes the continuous low thrust) maintain the same angular velocity O' about the sun?

It seems that Satellite 2 may now be in an elliptic orbit (or outward spiraling orbit) and presumably its thrust vector is perpendicular to a line connecting Satellite 2 to Satellite 1, to the Sun. (Tangential thrust).

How might one go about proving that angular velocity (O') can be maintained as Satellite 2 accelerates (if it is possible at all)?

P.S. I think I am confused about whether increasing tangential velocity increases radius in a way that would prohibit O' from being maintained by the accelerating satellite.

 

[Devin-M]

I did a quick & dirty numerical simulation... First I put a James Webb in a circular orbit around the sun at 1AU (with no planets). Next I doubled the distance to 2AU without changing the orbital velocity. The spacecraft at 2AU with enough orbital velocity for a 1AU circular orbit escapes the Sun (no orbit).

Or if you start with a circular orbit at 1AU then double the orbital speed, you also leave the solar system (no orbit)...

 

[Tom.G]

Look up (Google?) how gravity varies with distance.
Then look up how centrifugal force varies with orbital speed or distance.

Have Fun and Learn Much!
Tom