Solving for the Mass of Cyg X-1 Using Newton's Law of Universal Gravitation
Realizing that the gravitational attraction of Cygnus X-1 provides the centripetal force that is responsible for the circular motion of an orbiting satellite allows us to equate the two forces, as follows.
Look again at the equations equating the force of gravity and the force of centripetal motion above. Because the orbital radius is the same as the distance between Cygnus X-1 and the satellite, the equations can now be rewritten :
Because m, the mass of the satellite, appears on both sides of the equation, it can be eliminated. Rearranging to solve for M, the mass of Cygnus X-1, we get an exprssion with the measurable values of the probe's speed and distance from Cyg X-1 and the known value of Newton's constant of universal gravitation, G: