Frequency of small oscillations

[gpran]

Two bodies of mass m each are attached by a spring. This two body system rotates around a large mass M under gravity. Will there be any relation between frequency of oscillation of the two body system and frequency of rotation?
Frequency of small oscillations of a single body rotating in an orbit is same as frequency of rotation.

 

[gpran]

There can be a similar situation. A body of small mass- m1 is rotating around another mass- m2 with frequency f1. This two body system is rotating around a large mass M with frequency f2. What should be relation between f1 and f2 if we consider forces of gravity?

 

[drvrm]

A body of small mass- m1 is rotating around another mass- m2 with frequency f1. This two body system is rotating around a large mass M with frequency f2. What should be relation between f1 and f2 if we consider forces of gravity?

above situation is available as an example in planetary motion so you can get an answer if you see/observe say Earth moon system or saturn and its satellites and the Sun ...i think you can get a tested result.