Whenever two apollo astronauts were on the surface of the moon, a third astronaut orbited the moon. assume the orbit to be circular and 270 km above the surface of the moon, where the acceleration due to gravity is 1.27 m/s2. the radius of the moon is 1.70 ✕ 106 m. determine the astronaut's orbital speed.

Explanation:

We know that for circular motion the centripetal acceleration is:

where v is the speed and r is the radius.

The centripetal acceleration for the astronaut must be the gravitational acceleration due to the gravity, as there are no other force. So

.

The radius of the orbit must be the radius of the Moon, plus the 270 km above the surface

We can obtain the speed as:

And this is the orbital speed.