1) If the earth shrinks into a black hole, what will be the radius of the earth?

Solution:

Since the minimum escape speed is v(esp)=c=3x10^8m/s

v(esp)=square root of (2GM/r)

3x10^8=square root of [2(6.67x10^-11)(5.98x10^24)/r)]

r can be found.

As we know, light CAN'T escape from a black hole. But, if we substitute the escape speed as the speed of light, that means speed can escape the black hole's gravitational field. Why can't we substitute c as the escape speed, as the solution does?

2) What is the total amount of energy needed to place a 2000kg satellite in circualr Earth orbit, at an altutide of 500km.

[Is the answer simply Et=1/2 Eg=-5.80x10^10 J or is it the change in total energy or something? I don't get what the question is asking for.]

3) The mass of the Moon is 6.7x10^22 kg, and its radius is 1.6x10^6 m. If a woman can raise her centre of gravity 2.0m vertically in a high jump at earth's sruface. How high can she jump with the same muscular effort on the Moon's surface?

[My question is, will theinitial velocityof the woman be the same on the earth and on the moon? What I am thinking is that the earth and the moon have different values of Fg, so if she applies the same muscular strength (or same applied force), wouldn't the initial speed as she leaves the ground be different?]

Thanks everyone for explaining!