The command module orbited at an altitude of 110 km above the lunar surface. How much time did it take for the command module to complete one orbit?
I am not good at physics, hence why I came here for help and not to be put down. Thanks.
Look up the mass M of the moon and the gravitational constant G, and then just plug them into your formula
T = 2π√(r^3/(GM))
Note that r is the radius of the orbit, not its altitude above the surface.
To calculate the time it takes for the command module to complete one orbit, we need to know the period of its orbit. The period of an orbit is the time it takes for an object to complete one full revolution around another object.
The formula to calculate the period of an orbit is:
Period = 2 * pi * (Radius / Velocity)
Where:
- Period is the time it takes for one complete orbit (in seconds)
- pi is a mathematical constant approximately equal to 3.14159
- Radius is the distance between the center of the Earth and the object in orbit (in meters)
- Velocity is the speed at which the object is moving in its orbit (in meters per second)
In this case, the command module is orbiting the Moon, not the Earth. So, we need to adjust the formula accordingly.
The radius of the moon is approximately 1,737 kilometers (1,737,000 meters). The altitude of the orbit is given as 110 kilometers (110,000 meters). Therefore, the radius of the orbit (distance from the center of the Moon to the command module) is the sum of the radius of the Moon and the altitude:
Radius = Moon's radius + Altitude
Radius = 1,737,000 meters + 110,000 meters
Next, we need to determine the velocity of the command module in its orbit. This can be calculated using the formula:
Velocity = sqrt(G * M / Radius)
Where:
- G is the gravitational constant (approximately 6.67430 × 10^(-11) m^3 kg^(-1) s^(-2))
- M is the mass of the Moon (approximately 7.348 × 10^22 kg)
Now, we can plug in the values we have into the equation to calculate the period:
Period = 2 * pi * (Radius / Velocity)
This will give us the time it takes for the command module to complete one orbit around the Moon.
How do I find the radius of the orbit?
come on, come on.
It's the radius of the moon + 110 km