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.

its c i just checked it

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach