# Time to go around the Moon

balletgirl

## Homework Statement

During an Apollo lunar landing mission, the command module continued to orbit the Moon at an altitude of about 100km. How long did it take to go around the Moon once?

Rm= 1.74x10^6 m
Mm= 7.35x10^22 kg
G= 6.67x10^-11
r= Rm + 100,000 m

v= sqrt(Gm/r)

V=2pi*r/t

## The Attempt at a Solution

after using the first equation, i got v= 1,679 m/s

i plugged this into the second equation to solve for T, and got
T= 2.9x10^9 s

This seems way too high to be the answer...

## Answers and Replies

shallgren
It would appear you forgot to consider "r= Rm + 100,000 m"

balletgirl
You're right I didn't, but this time got 1.89x10^10.

Here is my work:
v=sqrt(6.67x10^-11)(7.35x10^22)/[(1.74x10^6)+100,000]
v= sqrt(2.66x10^6)
v= 1,631 m/s

1,631= 2(3.14)(1.74x10^6 + 100,000)/T
1631= 1.16x10^7/T

T=1.89x10^10 s

shallgren

$$1631 = \frac{1.16 \times 10^7}{T}$$

$$T = \frac{1.16 \times 10^7}{1631} \neq 1.89 \times 10^{10} s$$

You have a simple arithmetic error in there somewhere.

balletgirl
Okay I believe I figured it out, and got 7,112 s instead, which seems much more reasonable. Thank you!