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?
To calculate the time taken for the command module to complete one orbit around the Moon, we need to know the orbital period. The orbital period is the time it takes for an object to complete one full orbit.
The formula for orbital period is:
T = 2 * π * √(r³ / GM)
Where:
T is the orbital period,
π is a mathematical constant (approximately 3.14159),
r is the distance from the center of the Moon to the orbiting object (in this case, the altitude of the command module plus the radius of the Moon),
G is the gravitational constant (approximately 6.67430 × 10^-11 N m²/kg²),
M is the mass of the Moon.
Given that the altitude of the command module is 150 km above the lunar surface, we need to add this to the radius of the Moon. The radius of the Moon is approximately 1,737 km.
r = altitude + radius = 150 km + 1,737 km.
Plugging in the values into the formula:
T = 2 * π * √((150 km + 1,737 km)³ / (6.67430 × 10^-11 N m²/kg²) * (mass of the Moon))
Please note that the specific mass of the Moon needs to be known for an accurate calculation, which may vary. You can search for the current estimate of the Moon's mass. Once you have the accurate mass, you can substitute it into the equation to calculate the orbital period.