What is the speed of a communications satellite orbiting the Moon at an altitude of 290 km above the Moon’s surface?
I know that G=6.67e-11 and h=290. I plugged inthese values, 7.35e24 for the mass and 1.738e6 for the radius into
v=sqrtGM/R=h but I didn't get the right answer.
there's a typo. it should be R+h not R=h. my bad.
The mass is 7.35x10^22 kg.
The radius is 1738 km.
To calculate the speed of a communications satellite orbiting the Moon, we can use the formula for the orbital speed of an object in circular motion.
The formula for the orbital speed v of an object is given by:
v = sqrt(G * M / R)
Where:
- G is the universal gravitational constant (6.67e-11 N m^2/kg^2)
- M is the mass of the celestial body (in this case, the Moon) which is approximately 7.35e24 kg
- R is the distance from the center of the celestial body to the satellite (in this case, 290 km above the Moon's surface)
First, we need to convert the altitude of the satellite from km to meters:
290 km = 290,000 meters
Now, we can substitute the values into the formula:
v = sqrt((6.67e-11 N m^2/kg^2) * (7.35e24 kg) / (1.738e6 meters))
Calculating this value gives us the correct speed of the communications satellite orbiting the Moon.