Upon its return voyage from a space mission, the spacecraft has a velocity of 25000 km/h at point A, which is 7130 km from the center of the earth. Determine the velocity of the spacecraft when it reaches point B, which is 6625 km from the center of the earth. The trajectory between these two points is outside the effect of the earth’s atmosphere. The radius of the earth is 6371 km, and g = 9.825 m/s2 on the surface of the earth.

May someone explain how to do this question?

Space-time metric ds2= -dt2+at2dx2+bt2dy2+ct2dz2 (a)how does the area of a rectangle with vertices at ( x=0, y=0, z=0 ), (1,0,0 ), ( 0,1,0 ) and (1,1,0 ) changes with time? (b) if a photon moving in the x direction starts from the origin at t=1, when does it reach x=l? (ds=0 for the trajectory of a photon.) (c) the proper time for a particle is defined by cd=ds. what is the proper time for a particle to move along the trajectory ( x(t)=t, y(t)=0, z(t)=0 ) from t=0 to 1 ? what is the condition on the parameter a so that the velocity of the particle never exceeds the speed of light ?

What color would an object that reflects green and blue light appear to be in white light? a. blue b. cyan c. magenta d. black