Why do black holes exist?

After the near spacecraft passed mathilde, on several occasions rocket propellant was expelled to adjust the spacecraft's momentum in order to follow a path that would approach the asteroid eros, the final destination for the mission. after getting close to eros, further small adjustments made the momentum just right to give a circular orbit of radius 45 km (45 × 10^3 m) around the asteroid. so much propellant had been used that the final mass of the spacecraft while in circular orbit around eros was only 545 kg. the spacecraft took 1.04 days to make one complete circular orbit around eros. calculate what the mass of eros must be.

Ahuge (essentially infinite) horizontal nonconducting sheet 10.0 cm thick has charge uniformly spread over both faces. the upper face carries +95.0 nc/m2 while the lower face carries -25.0 nc/ m2. what is the magnitude of the electric field at a point within the sheet 2.00 cm below the upper face? (ε0 = 8.85 × 10-12 c2/n · m2)

How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is 4.57×10−21 newtons?