A moon orbiting a planet in the solar system has an orbital period of 5.0 x 10^4 s, and the distance between the center of the moon and the planet is 2.0 x 10^8 m. What planet is it?
a.
Mars (mass = 6.42 x 10^23 kg)
c.
Venus (mass = 4.87 x 10^24 kg)
b.
Neptune (mass = 1.02 x 10^26 kg)
d.
Jupiter (mass = 1.90 x 10^27 kg)

Question

A moon orbiting a planet in the solar system has an orbital period of 5.0 x 10^4 s, and the distance between the center of the moon and the planet is 2.0 x 10^8 m. What planet is it?
a.
Mars (mass = 6.42 x 10^23 kg)
c.
Venus (mass = 4.87 x 10^24 kg)
b.
Neptune (mass = 1.02 x 10^26 kg)
d.
Jupiter (mass = 1.90 x 10^27 kg)

compphysgeek · Answer

to solve this problem you use the expression for centripetal force $$ F_C = m \omega^2 r $$ and set it equal to the gravitational force $$F_G = G \frac{m_P m_M}{r^2}$$ with $m_P$ the mass of the planet that you're looking for, $m_M$ the mass of the moon, $r$ the distance between moon and planet, $\omega = \frac{2 \pi}{t}$ and the gravitational constant $G = 6.67 \times 10^{-11} [G]$. 

You then solve for the planet's mass. $$ m_M = \frac{\omega^2 r^3}{G}$$

compphysgeek · Answer

the last one is of course $m_P = $

anonymous · Answer

was he right

compphysgeek · Answer

I was right ;)