Determining Orbital Period of a Planet

[polskamafia]

Using the equation P² = (4 * pi² * a³)/(G(M+m)) to find the orbital period of Earth where:

P = orbital period
a = semi-major axis = 1.50e11 m
G = 6.67e-11 m³ kg^-1 s^-2
M = mass of sun (in this case) = 1.989e30 kg
m = mass of Earth = 5.972e24 kg

I have been trying to find the orbital period of the Earth but the answers I've been getting make no sense.

P² = (4 * pi² * (1.50e11)³) / (G(1.989e30 + 5.972e24))

P = 31690989.27

What are the units on P? I tried following the units as they canceled each other and I ended up with s kg^-2. Any advice would be helpful.

Thanks!

- Marcin

 

[lewando]

P has units of seconds.

 

[Bandersnatch]

Hello Marcin

Try calculating how many seconds there are in a year. And compare with your answer.

 

[polskamafia]

Ah yes. Well that was embarrassing. Thank you Bandersnatch!