How exactly, with steps and math shown, do you derive the masses of asteroids via perturbations? please, no links, because I have searched and searched for years and can't find anything.

I mean like asteroids- how are their masses determined exactly? What equations are used?

• Do you mean perturbations of heavier objects (e.e. gas giants) that have known masses? Mar 24, 2015 at 21:25
• I mean like asteroids- how are their masses determined exactly? What equations are used? Mar 25, 2015 at 16:12
• Also on Physics: physics.stackexchange.com/questions/173682/… Apr 2, 2015 at 0:07

The math involved is essentially just Newtonian mechanics. You know the positions and velocities before the encounter. There is an energy conserving encounter with a force of $$F = \frac{m_1 m_2 G}{r^2}$$ Finding the angle of perturbation allows you to find the reduced mass $$\frac{m_1 m_2}{m_1+m_2}$$