Hi, If we were to change the Earth's orbit, what force should we apply and in what direction? Shoud we go against G.(M_Earth + M_Sun) / distance^2 or against the centripetal force, M_Earth.v^2/distance? I've calculated this last one and I got the result: 3,542396634E+22 Newtons Is this correct? Regards, Kepler
The problem with mv^2/r is that you've assumed the earth is in a circular orbit. It is, in fact, somewhat elliptical. That difference drastically changes the problem.
It really depends on how you want to change the orbit.(what kind of an orbit do you want after the change?) If you want to raise it to an higher orbit, you have to push it in the same direction it is moving around the Sun. If you want to move it into a lower orbit, you push in the opposite direction. If you push directly towards or away from the Sun, you will change the shape of the orbit such that it will be closer to the Sun at part of its orbit and further at another part. If you push it at a right angle to its orbital plane, you will change the inclination or "tilt" of the orbit.