Question

The sun has a mass of 1.99 * 10^30 and the earth has a mass of 5.98 * 10^24kg. If the force of gravity between the sun and the earth is 3.55 * 10^22N how far is the earth from the sun? What is the tangential speed of the earth around the sun?

Answer 1

$$(3.55\cdot10^{22})=(6.67\cdot10^{-11})\frac{(1.99\cdot10^{30})(5.98\cdot10^{24})}{r^2}\\r=1.50\cdot10^{11}\ m\\v=2\pi\frac{1.50\cdot10^{11}}{365\cdot24\cdot3600}=2.99\cdot10^{4}\frac{m}{s}$$