Orbital velocity and radius for satellite

[joemmonster]

Homework Statement

A geostationary satellite is to be placed to view the far side of the moon. How far away should it be placed from the center of the Earth and what velocity should it travel in order to maintain its orbit? (Considering the moon and Earth as one entity and solve for the center of gravity, then determine the distance the satellite should be)

Mass of Earth: 5.97x10^24kg
Mass of moon: 7.349x10^22kg
Distance of moon to earth: 384,000,000 m
Center of gravity from earth: 4,669,513.807 m

Homework Equations

http://media.wiley.com/Lux/78/331278.image0.png

http://media.wiley.com/Lux/83/331283.image5.png

The Attempt at a Solution

I calculated the orbital radius and it seems that it's not going to be on the far side of the moon (42,399,473.46 m)

 

[Delta2]

when you saying the far side of the moon you mean the so called "dark-side" of the moon? That is the side that we can't observe by no means with an observatory in the surface of the earth?

The center of the orbit of the sattelite will be the center of earth, the center of the moon, or the center of the system earth+moon?

 

[HallsofIvy]

Frankly it doesn't sound like this is possible. A satellite can stay stationary over a specific point on earth by orbiting with a specific velocity and distance from the earth, ignoring the influence of the moon. Similarly a satellite can stay stationary over a specific point on the moon with a specific velocity and distance ignoring the influence of the Earth (which would be a greater error) and a satellite can even orbit at a specific velocity and distance from the joint center of mass of the Earth and moon but such a satellite would NOT stay stationary over a point on the moon.

 

[BruceW]

yeah, the moon goes round the Earth once per month. So if we had a satellite that stayed exactly on the other side of the moon to us, the satellite would need to also go round the Earth once per month. And on the other hand, if we wanted the satellite to be geostationary, it would need to go round the Earth once per day (since the Earth takes one day to rotate). So it's not possible to have both.

 

[Filip Larsen]

If one replaces "geostationary" with "seleno-stationary", then the problem text seems to ask for a simplified solution of the Earth-Moon L2 point [1].

[1] http://en.wikipedia.org/wiki/Lagrangian_point

 

[SteamKing]

Homework Statement

A geostationary satellite is to be placed to view the far side of the moon. How far away should it be placed from the center of the Earth and what velocity should it travel in order to maintain its orbit? (Considering the moon and Earth as one entity and solve for the center of gravity, then determine the distance the satellite should be)

Mass of Earth: 5.97x10^24kg
Mass of moon: 7.349x10^22kg
Distance of moon to earth: 384,000,000 m
Center of gravity from earth: 4,669,513.807 m

Homework Equations

[PLAIN]http://media.wiley.com/Lux/83/331283.image5.png

The Attempt at a Solution

I calculated the orbital radius and it seems that it's not going to be on the far side of the moon (42,399,473.46 m)

It's not at all clear what you have done, except find the location of the c.o.m. of the earth-moon system.

Please provide all of your calculations.