Question

How would one plug the gravitational constant into an equation? To be honest, I'm having a hard time with the idea of the gravitational constant in general, but I need to solve an equation for the circular velocity of a galaxy. I know I need to multiply the gravitational constant by the mass (1.313x10^40 kg) and divide that by the radius (5.676x10^17 m) and the square root of that is somehow my answer, but I'm not sure how it all works. Any help is appreciated!

Answer 1

If the mass of the Galaxy is all at the center the angular velocity at distance R is given by
ω = sqr(M•G/R^3),
where M = central mass kg,
G = gravitational constant 6.67 x 10-11 Nm2kg-2,
R = distance from central mass m