Continuous thrust orbit changes

[ScramjetCCO]

Most threads about making orbit changes assume impulsive changes in velocity (short period bursts). What if one wants to increase the radius of a circular orbit with a very small constant thrust? I assume the thrust should be applied tangentially in the direction of travel, but what would be the rate of change of the orbit's radius be at any point in time given the acceleration applied and the other parameters describing the orbit at that time?

 

[Ronie Bayron]

You may look at FBD and do 3rd Law. The solution should not be far from there.

 

[anorlunda]

https://www.physicsforums.com/threads/dawns-altitude-now-1000-km.793140/page-34#post-5278365

You should read this thread, active right now. The Dawn spacecraft is using an ion engine to decrease its orbital radius around the asteroid Ceres. Fascinating.

 

[mfb]

Most threads about making orbit changes assume impulsive changes in velocity (short period bursts). What if one wants to increase the radius of a circular orbit with a very small constant thrust? I assume the thrust should be applied tangentially in the direction of travel, but what would be the rate of change of the orbit's radius be at any point in time given the acceleration applied and the other parameters describing the orbit at that time?

You can keep track of energy and angular momentum. Both are conserved in free-fall, so only thrust is changing them. If thrust is small enough the (ideal) orbit is nearly circular, so you can relate energy and angular momentum to orbital height, speed and so on, which is then needed to determine the effect of thrust.

 

[marcus]

https://www.physicsforums.com/threads/dawns-altitude-now-1000-km.793140/page-34#post-5278365

You should read this thread, active right now. The Dawn spacecraft is using an ion engine to decrease its orbital radius around the asteroid Ceres. Fascinating.

Sample simulated view of Dawn spacecraft retrothrusting so as to spiral in closer to Ceres, as anorlunda mentioned:

This is the view as of around 6:25 PM pacific time on 6 November. (UTC is 8 hours ahead of pacific time).
Dawn is in roughly polar orbit and is heading north to pass above Ceres north polar region, after which it will come south over the dayside.