On Apollo missions to the Moon, the command module orbited at an altitude of 150 above the lunar surface.
How long did it take for the command module to complete one orbit?
Try your later post, which I saw and answered first.
Sra
Just for the record, 150 WHAT?
To determine the time it takes for the command module to complete one orbit around the Moon, we need to know the orbital period of the module. The orbital period is the time it takes for an object to complete one revolution around another object.
The formula to calculate the orbital period is:
T = 2π√(r³/GM)
Where:
T is the orbital period,
π is a mathematical constant approximately equal to 3.14159,
r is the radius of the orbit (in this case, the altitude above the lunar surface),
G is the gravitational constant,
M is the mass of the Moon.
Given that the altitude above the lunar surface is 150 miles, we need to convert it to the radius of the orbit by adding the radius of the Moon (approximately 1,079 miles) to it. So, the radius of the orbit (r) would be 150 + 1,079 = 1,229 miles.
The mass of the Moon (M) is approximately 7.342 × 10^22 kilograms.
The gravitational constant (G) is approximately equal to 6.67430 × 10^(-11) m³ kg^(-1) s^(-2).
Now we can substitute the known values into the formula and calculate the orbital period (T). However, note that we need to convert the result from seconds to minutes or hours for more practical understanding.
Once we have calculated the orbital period, we will have the answer to how long it took for the command module to complete one orbit.