Question

Astar has a mass of 1.74 x 1030 kg and is moving in a circular orbit about the center of its galaxy. The radius of the orbit is 1.5x 10^4light-years (1 light-year-9.5x 10¹5 m), and the angular speed of the star is 2.9 x 10-15 rad/s. (a) Determine the tangential speed of the star. (b) What is the magnitude of the net force that acts on the star to keep it moving around the center of the galaxy?

Answer 1

(a)

In order to calculate the tangential speed, we can use the formula below:

$\begin{gathered} V=r\omega\\ \\ V=15000\cdot9.5\cdot10^{15}\cdot2.9\cdot10^{-15}\\ \\ V=413250\text{ m/s} \end{gathered}$

(b)

The force that acts on the star to keep it moving around the center is the centripetal force, and it's calculated with the formula below:

$\begin{gathered} F=\frac{mv^2}{r}\\ \\ F=\frac{1.74\cdot10^{30}\cdot4132.5^2}{15000\cdot9.5\cdot10^{15}}\\ \\ F=208.526\cdot10^{15}\\ \\ F=2.085\cdot10^{17}\text{ N} \end{gathered}$