How Long Does It Take to Orbit the Moon at an Altitude of 100km?

[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

Homework Equations

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...

 

[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]

Continuing your work:

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

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

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!