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

  • Thread starter balletgirl
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In summary, during an Apollo lunar landing mission, the command module orbited the Moon at an altitude of 100km. Using the equations v= sqrt(Gm/r) and V=2pi*r/t, the time it took for the module to go around the Moon once was calculated to be approximately 7,112 seconds. This is a more reasonable answer compared to the initial calculation of 2.9x10^9 seconds.
  • #1
balletgirl
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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...
 
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  • #2
It would appear you forgot to consider "r= Rm + 100,000 m"
 
  • #3
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
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
Okay I believe I figured it out, and got 7,112 s instead, which seems much more reasonable. Thank you!
 

What is "Time to go around the Moon"?

"Time to go around the Moon" refers to the amount of time it takes for an object to complete one full orbit around the Moon.

How long does it take for the Moon to orbit the Earth?

The Moon takes approximately 27.3 days to orbit the Earth once.

What factors affect the time it takes to go around the Moon?

The main factors that affect the time it takes to go around the Moon include the mass of the Moon and the distance between the Moon and the object orbiting it.

Can the time it takes to go around the Moon change?

Yes, the time it takes to go around the Moon can change due to various factors such as gravitational pull from other celestial bodies and changes in the Moon's orbit.

Why is it important to study the "Time to go around the Moon"?

Studying the "Time to go around the Moon" can provide valuable insights into the Moon's orbit and gravitational forces, which can help us better understand our solar system and the universe as a whole.

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