The space shuttle is in a 150km-high circular orbit. It needs to reach a 560km-high circular orbit to catch the Hubble Space Telescope for repairs. The shuttle's mass is 7.00×10^4kg.
How much energy is required to boost it to the new orbit?
In the original orbit, I calculated the shuttle's Ug = -(GMeMs) / r = -(6.67x10^-11 x Me x Ms) / (6370 + 150) = 4.28x10^15. I then calculated Ugfinal (when the shuttle is in the new orbit. I found this Ug = 4.029 x 10^15. I'm not sure if these Ug's are correct or what to do with them.
I don't see a change in kinetic energy for the two orbits.
Orbit1energy-orbit2energy= work done
KE1+PE1-KE2-PE2= work done
Slow down and your orbit will decrease.you need to speed up to climb to 560 km. orbit. That kinetic energy of the earth stays about the same but the shuttle needs more .so... Ov equals Amt. Needed to achieve + exististing kinetic energy ..or an unequal amount. See?
Go up then slow down .
To find out the energy required to boost the shuttle to the new orbit, you need to calculate the change in potential energy (ΔU) between the two orbits. The formula for potential energy (U) in this context is given by:
U = -(G * Me * Ms) / r
where G is the gravitational constant (6.67x10^-11 N(m/kg)^2), Me is the mass of the Earth (5.97x10^24 kg), Ms is the mass of the shuttle (7.00x10^4 kg), and r is the distance from the center of the Earth to the shuttle.
First, you correctly calculated the potential energy in the original orbit as Ug = 4.28x10^15 J. However, there seems to be a calculation error in determining the potential energy in the new orbit. The correct calculation should be:
Ug_final = -(G * Me * Ms) / r_final
where r_final is the distance from the center of the Earth to the new orbit (560 km + 6370 km).
Now, let's calculate the change in potential energy between the original and new orbit (ΔU):
ΔU = Ug_final - Ug
= [- (G * Me * Ms) / r_final] - Ug
Substituting the values:
ΔU = [- (6.67x10^-11 N(m/kg)^2 * 5.97x10^24 kg * 7.00x10^4 kg) / (560 km + 6370 km)] - 4.28x10^15 J
To get the answer, you can calculate the value of ΔU using the given values for the constants and then subtract it from the initial potential energy (Ug) to find the total energy required to boost the shuttle to the new orbit.