Imagine two planets orbiting a star with orbits edge-on to the Earth. The peak Doppler shift for each 90 m/s, but one has a period of 5 days and the other has a period of 500 days.
Also, what is the mass of the longer period planet?
Doppler implies same velocity
period implies different Radius and there fore different velocity
Look up Kepler's laws. Observation of our planets.
Newtons laws require Kepler observations
For both planets we have the conservation of momentum for the movement of star and planets: MV = mv, where the capitals refer to the star.
We have the following relations for each planet, (the capitals refer to the star)
- MV = mv consevation of momentum
- mv^2/r = GmM/r^2, which reduces to GM = r v^2 . balance of forces
- P^2 = 4 pi^2 r^2 /GM Kepler's third law.
We know V=90 m/s and P = 5 days or 500 days.
The equations allow us to eliminate the unknowns.