Physics
posted by Roberto .
A satellite is placed between the Earth and the Moon, along a straight line that connects their centers of mass. The satellite has an orbital period around the Earth that is the same as that of the Moon, 27.3 days. How far away from the Earth should this satellite be placed?
Physics  drwls, Saturday, May 7, 2011 at 9:04pm
What you have here is a threebody problem. You cannot use Kepler's law to solve it.
It turns out that there is a point of unstable equilbrium between the earth and the moon where the gravity forces cancel and the satellite will remain at equilbrium at that location and revolve around the earth at the same angular velocity as the moon. There are also two other points along the earthmoon line (one beyond the moon and another on the opposite side of the earth from the moon) and two others at equilateral triangle points. This set of locations is called the Lagrangian points.
Put the satellite at a point between earth and moon where distances to earth and to the moon are such that
M(moon)/d(moon)^2 = M(earth)/d(earth)^2
But to solve this equation won't I need the distance of the moon from the satllite?

No. You solve for
d(moon)/d(earth) =
sqrt[M(moon)/M(earth)] = 0.111,
and also require that
d(earth) + d(moon) = d = 3.84*10^5 km 
The point in question is called Lagrangian Point L1. At that location, the gravity forces of earth and moon do NOT cancel. Instead, they act in opposite directions such that the net force provides the centripetal force to keep it revolving at the same angular speed as the moon.
You can find the required equation here:
http://www.ottisoft.com/Activities/Lagrange%20point%20L1.htm
It is 84.9% of the way from earth to moon.
Respond to this Question
Similar Questions

Phyisics
A spy satellite is in circular orbit around Earth. It makes one revolution in 6.02 hours. How high above Earth's surface is the satellite Use keplers law, comparing the moon period and distance from Earth to the Satellite. There are … 
Physics
Given that the distance between the Earth and the Moon is d = 3.84 x 10^8 m, show that a satellite located exactly inbetween the Earth and the Moon at a distance of 90% d from the Earth experiences no net force (at least when only … 
force of gravity
A satellite orbits around the earth. The mass of the satellite is 1170 kg, and its altitude is 220 km. The mass of the earth is 5.98×1024 kg. The radius of the earth is 6.38×106 m. 1)What is the gravitational force on the satellite? 
physics
The physics of energy and Earth's moon as a satellite. The moon is an Earth satellite of mass 7.35 x 10^22 kg, whose average distance from the centre of Earth is 3.85 x 10^8 m. a) What is the gravitational potential energy of the moon … 
Physics
A satellite is placed between the Earth and the Moon, along a straight line that connects their centers of mass. The satellite has an orbital period around the Earth that is the same as that of the Moon, 27.3 days. How far away from … 
Physics
A satellite is placed between the Earth and the Moon, along a straight line that connects their centers of mass. The satellite has an orbital period around the Earth that is the same as that of the Moon, 27.3 days. How far away from … 
physics
A satellite orbits a planet at a distance of 3.80 108 m. Assume that this distance is between the centers of the planet and the satellite and that the mass of the planet is 3.90 1024 kg. Find the period for the moon's motion around … 
physics
A satellite is placed between the Earth and the Moon, along a straight line that connects their centers of mass. The satellite has an orbital period around the Earth that is the same as that of the Moon, 27.3 days. How far away from … 
Calculus Physics
Imagine a spaceship on its way to the moon from the earth. Find the point, as measured from the center of the earth, where the force of gravity due to the earth is balanced exactly by the gravity of the moon. This point lies on a line … 
physics
NASA launches a satellite into orbit at a height above the surface of the Earth equal to the Earth's mean radius. The mass of the satellite is 550 kg. (Assume the Earth's mass is 5.97 1024 kg and its radius is 6.38 106 m.) (a) How …