Question

A newly discovered planet follows a circular orbit around a star in a distant part of the galaxy. The orbital speed of the planet is determined to be 43,400 m/s. The slower planet's orbital period is 2.40x10^8 s.

a. What is the radius of the orbit of the planet?

b. What is the mass of the star? (hint: is there a centripetal force? If so, what force i causing the centripetal force?)

Answer 1

a)
The orbital period is given by
   
where, v is the orbital speed, and R is the radius of the orbit. So,
  
Now, using the given values, we get
   


b)

According to the Newton's equation of motion in this case,
  centripetal force = gravitational attraction force



So, putting the given values and the value of the gravitational constant G, we get