Calculate Speed and Time to Revolve Around the Moon

In summary, to calculate the speed of the command module and the time it takes to complete one revolution around the moon, we need to use the given values of mass and radius of the moon as well as the altitude above the surface. After converting the altitude to meters, we can use the formula Vcm^2 = G * Mm/Ro to find the speed of the command module, which is 1.679 meters/sec. To calculate the time it takes to complete one revolution, we can use Kepler's third law and the values of semimajor axis and gravitational parameter.
  • #1
cowgiljl
63
1
if the command module is 60 miles above the surface of the moon it wants me to calculate the speed of the module adn the time it takes to complete one revolutionaround the mooon?
givens

mass moon = 7.35 * 10 to the 22 power
radius moon = 1.74 * 10 to the 6 power
altitude above the surface of the moon = 60 miles

converted the 60 miles to meters which was 96540 m

Ro = Rm + h
Ro = 1.74E6 + 96540
Ro = 1.74E22

Vcm is the command module

Vcm^2 = G * Mm/ro
Vcm^2 = 6.673E-11 * 7.35E22/1.74E22
Vcm = 1.679 meters/sec

and not sure if this is right and don't know what to use to figure out the time it took to make 1 revolution

thanks
 
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  • #2
on the time part of it should i use kelpters law?
 
  • #3
Period can be found by using this formula:

[tex]

P = 2\pi \sqrt{\frac{a^3}{\mu}}}

[/tex]

Where a is the semimajor axis (the radius for circular orbits, like your problem)
and mu is the gravitational parameter, or G*M
 

1. How do you calculate the speed needed to revolve around the moon?

To calculate the speed needed to revolve around the moon, you can use the formula v = √(GM/r), where G is the gravitational constant, M is the mass of the moon, and r is the distance from the center of the moon.

2. What information is needed to calculate the time it takes to revolve around the moon?

To calculate the time it takes to revolve around the moon, you need to know the distance from the center of the moon to the orbiting object, as well as the speed of the object around the moon.

3. How does the mass of the moon affect the speed and time to revolve around it?

The mass of the moon affects the speed and time to revolve around it through the gravitational force it exerts on the orbiting object. The larger the mass of the moon, the greater the gravitational force and the higher the speed and shorter the time needed to revolve around it.

4. Can you use the same formula to calculate the speed and time to revolve around other celestial bodies?

Yes, you can use the same formula to calculate the speed and time to revolve around other celestial bodies, but you will need to adjust the values for the gravitational constant and the mass of the specific celestial body.

5. How can the calculated speed and time to revolve around the moon be applied in real-life scenarios?

The calculated speed and time to revolve around the moon can be applied in various real-life scenarios, such as space exploration missions, satellite orbits, and understanding the gravitational pull of the moon on Earth.

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