Time to go around the Moon

  • Thread starter balletgirl
  • Start date
  • #1
balletgirl
36
0

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...
 

Answers and Replies

  • #2
shallgren
44
0
It would appear you forgot to consider "r= Rm + 100,000 m"
 
  • #3
balletgirl
36
0
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
 
  • #4
shallgren
44
0
Continuing your work:

[tex]1631 = \frac{1.16 \times 10^7}{T}[/tex]

[tex]T = \frac{1.16 \times 10^7}{1631} \neq 1.89 \times 10^{10} s[/tex]

You have a simple arithmetic error in there somewhere.
 
  • #5
balletgirl
36
0
Okay I believe I figured it out, and got 7,112 s instead, which seems much more reasonable. Thank you!
 

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