1. The problem statement, all variables and given/known data A spacecraft orbiting the Sun uses its jet engine for slowing down its orbital rotation and changing the direction of its velocity. At the moment when the velocity is directed away from the Sun and has a magnitude of v = 30 km/s, the jet engine is switched off. At the same moment, the mass of the spacecraft is m = 1500 kg and the distance to the Sun is R = 150 x 10^9 m. 1) Find the distance at which the velocity of the spacecraft is zero 2) Now suppose that in addition to the jet engine, the spacecraft is equipped with a solar sail, which can be opened at the moment of time when the jet engine is switched off. A solar sail is a very large mirror, that reflects photons emitted by the Sun. The reflected photons change their momenta and thus generate a force directed away from the Sun: F = C/r^2 (where C = 1.2 x 10^17 Nm^2 is a constant and r is a distance to the Sun in meters). Is the power of the solar sail sufficient for this aircraft to leave the Solar system? G = 6.67 x 10^-11, the mass of the Sun is M = 2.0 x 10^30kg 3. The attempt at a solution 1) I used F = ma the force of gravitation being GmM/r^2 = ma made a the subject of the formula integrated to find v and used the information given to find the constant. Then I integrated that v to get x, again finding a value for the constant using the relevant information. I set the velocity equation equal to zero to find a value for t (ie the moment in time when the velocity is zero) and subbed that t into my x equation I think my procedure is very coherent, at least it seems so to me, others are using the Conservation of Energy approach and now I'm getting really confused 2) I know that Power = work done/time and that work done = (Force)(distance) so I found the work done by the gravitation pull of the Sun by multiplying (GmM/x^2) by (x) where x is the distance I found previously and divided that by time (the same time I found when v = 0 previously) I did exactly the same for the work done by the photons except this time I multiplied C/x^2 by x (x, again same as before) and divided by time (same as before). I then verified the following inequality, if the power done by the gravitational pull of the sun > power done by photons then it doesn't leave the Solar System I subbed in values for G and the M's and found that it indeed stays in the Solar System. I really appreciate your comments and sorry if it's wordy!