Question

A distant star has a single planet circling it in
a circular orbit of radius 6.33 × 1011 m. The
period of the planet’s motion about the star
is 828 days.
What is the mass of the star? The
value of the universal gravitational constant
is 6.67259 × 10−11 N · m2/kg2.
Answer in units of kg

Answer 1

Since the planet is going on a circular orbit, A centripetal force should exist. This force is generated by the gravitational forces by the two masses.

When the circular velocity is \(\omega\), radius is \(r\) The centripetal force \(F_c\) is,
\[F_c=mr\omega^2\]
Also from Gravitational field theory,
\[F_c=\frac{GMm}{r^2}\]
Use these equations to find the appropriate answer

Answer 2

How do I solve for centripetal force if I don't have mass?

Answer 3

Just do some manipulations to the equations to the equations that i've given by combining them. as a hint all I can say is that you do not need to find \(F_c\)

Answer 4

Oh ok :)

Answer 5

Wait I have another question since I figure you may know, how do you solve for the period of an orbit?

Answer 6

Period is given. Use it to find the angular velocity - \(\omega\)
\(\text{Period}=\frac{1}{\displaystyle\text{frequency}}\)

\(2\pi(\text {frequency})=\omega\)

Answer 7

Well... I got 2.188*^-25 but that seems so wrong ._.