Calculate the orbital period of a spacecraft around the moon

In summary, the conversation discusses the calculation of the time it takes for the command module to orbit the Moon at an altitude of 100km during an Apollo lunar landing mission. The equation used is T= 2(pi)(r^3/2) / root (GM), where the mass of the Moon is 7.35 X 10^22 and the radius is 1.74 X 10^6. The question of whether the 100km altitude should be added to the radius of the orbit is also raised. However, the equation is confirmed to be correct and it is suggested to show the results of calculations for further clarification.
  • #1
pinkerpikachu
29
0
1. During an Apollo lunar landing mission, the command module continued to orbit the Moon at an altitude of 100km. How long did it take to go around the Moon once?

2. T= 2(pi)(r^3/2) / root (GM)
mass of moon = 7.35 X 10^22
radius of moon= 1.74 X 10^6




3. I think that is the correct equation, and I've tried plugging all the values in. I know that the radius will have the 100km (100,000m) added on to it...right?
 
Physics news on Phys.org
  • #2
pinkerpikachu said:
1. During an Apollo lunar landing mission, the command module continued to orbit the Moon at an altitude of 100km. How long did it take to go around the Moon once?

2. T= 2(pi)(r^3/2) / root (GM)
mass of moon = 7.35 X 10^22
radius of moon= 1.74 X 10^6

3. I think that is the correct equation, and I've tried plugging all the values in. I know that the radius will have the 100km (100,000m) added on to it...right?
Your equation is correct. What are you using for the radius of the orbit?

AM
 
Last edited:
  • #3
Be sure to include that the radius of the orbit is 100+ radius of the moon in km.
 
  • #4
Welcome pinkerpikachu to PF forums! You will find this is a great forum for interactive discussion on all kinds of topics.

In your question, you are off to a good start. It would be useful to show us the results of your calculations (and the steps you made to get there). This will enable us to see if you are on the right track.
 
  • #5
I'm working on the same problem, can you help me understand how you derived your initial equation?
 

What is the formula for calculating the orbital period of a spacecraft around the moon?

The formula for calculating the orbital period of a spacecraft around the moon is T = 2π√(a^3/GM), where T is the orbital period in seconds, a is the semi-major axis of the orbit in meters, G is the gravitational constant (6.67 x 10^-11 N*m^2/kg^2), and M is the mass of the moon (7.35 x 10^22 kg).

How do I find the semi-major axis of the spacecraft's orbit around the moon?

The semi-major axis can be found by taking the average of the spacecraft's closest and farthest distance from the moon during its orbit. This can be measured using data from the spacecraft's trajectory or by using images of the moon and the spacecraft's position.

Does the mass of the spacecraft affect its orbital period around the moon?

Yes, the mass of the spacecraft does affect its orbital period around the moon. The formula for calculating orbital period (T = 2π√(a^3/GM)) includes the mass of the object in orbit. Therefore, the greater the mass of the spacecraft, the longer its orbital period will be.

What is the average orbital period of a spacecraft around the moon?

The average orbital period of a spacecraft around the moon is approximately 27.3 Earth days. This is because the moon's orbital period around the Earth is 27.3 days, and a spacecraft orbiting the moon will have a similar orbital period due to the moon's gravitational pull.

Can the orbital period of a spacecraft around the moon be changed?

Yes, the orbital period of a spacecraft around the moon can be changed by adjusting its speed or distance from the moon. By increasing its speed or moving it closer to the moon, the spacecraft's orbital period will decrease, and vice versa. This can also be achieved by using a gravitational assist from another celestial body, such as Earth or Jupiter, to alter the spacecraft's trajectory and orbital period.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
760
  • Introductory Physics Homework Help
Replies
1
Views
926
  • Introductory Physics Homework Help
Replies
1
Views
771
Replies
4
Views
649
  • Introductory Physics Homework Help
Replies
21
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
3K
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
1K
Replies
2
Views
970
Back
Top