Some days ago some members have explained very well the principle of radial velocity to discover exoplanets.
Now a follow-up question. Can this technique be used to discover the total mass of planets and other satellites
orbiting the sun, or proving that there are more than nine planets ?
For our own solar system, measuring the orbits of other planets is a more sensitive method than measuring the motion of the sun. But it’s very unlikely that a new planet will be discovered through its gravitational influence. It’d have to be pretty massive to have any observable effect on the sun or other planets, and it’s highly unlikely that such a planet remains undiscovered.
Indeed, looking at deviations from the observed to theoretical orbit of Uranus is what led to the discovery of Neptune and looking at the orbit of Neptune is what led to (accidentally, the calculations were actually off) the discovery of Pluto.
Fortunately there is at least one astronomer who visits here occasionally so any boners I pull will be corrected.
The mass of other planets can most easily be found by analyzing the orbits of their satellites, if they have any. The period and distance of a satellite from the primary are related by a constant multiplied by the mass of the primary. So if the period and distance of the satellite are measured, the mass of the primary can be computed.
Doppler shifts of sunlight could, I suppose, be used to get the mass of those planets orbiting the sun, but I suspect it would be pretty difficult to distinguish the shift resulting from, say, Mercury from the much greater shift resulting from Jupiter.
To piggyback David, basically there are two things in our Solar System: Jupiter and flotsam. Jupiter is more than twice as massive as all the other planets combined (318 times Earth).