Find the energy necessary to put 5kg , initially at rest on Earth's surface, into geosynchronous orbit.
Do I use the formula U=GMm/r
G=6.67*10^-11
M=2.5*10^24
m=5
r=41000
Is this sort of right, any help would be greatly appreciated.
Dont you have to add the kinetic energy that the satellite will have in orbit?
Do i do this by k=1/2mv^2
If so what wll be my m and v then
To find the energy necessary to put an object into geosynchronous orbit, you can indeed use the formula U = GMm/r, where U is the gravitational potential energy, G is the gravitational constant, M is the mass of the Earth, m is the mass of the object, and r is the distance from the center of the Earth to the object's initial position.
In this case, the mass of the Earth (M) is given as 2.5*10^24 kg, the mass of the object (m) is 5 kg, and the distance (r) is 41000 km (which needs to be converted to meters by multiplying by 1000).
Let's calculate the energy necessary:
G = 6.67 * 10^-11 N(m^2/kg^2) (given)
M = 2.5 * 10^24 kg (given)
m = 5 kg (given)
r = 41000 km * 1000 = 41000000 meters
Now, substitute these values into the formula:
U = (6.67 * 10^-11 N(m^2/kg^2)) * (2.5 * 10^24 kg) * (5 kg) / (41000000 meters)
Calculating this expression will give you the potential energy (U) needed to put the object into geosynchronous orbit.