When the nuclear fuel in the sun is gone, the sun will collapse to a

a. black hole
b. white dwarf
c. supernova
d. neutron star

My answer: I think its a black hole.

If the mass of the Earth were suddenly doubled while the radius was unchanged, your weight would be?

My answer: increased by a factor of two.

How would the earth move if the sun were to suddenly vanish from existence?

My answer: move in a straight line tangent to its previous orbit.

A satellite is moving at a constant velocity around the Earth. The net force on it is?

My answer: It would be directed toward the Earth

The first is wrong; The mass of the Sun is not great enough, however it will shrink, and be white.
The others are ok.

I apologize for the incorrect answer to the first question. You're correct, when the nuclear fuel in the Sun is depleted, it will collapse and become a white dwarf, not a black hole. A white dwarf is a dense, hot stellar remnant composed mostly of electron-degenerate matter.

As for the other questions, your answers are correct:

- If the mass of the Earth were suddenly doubled while the radius remained unchanged, your weight would indeed be increased by a factor of two. This is because weight depends on the gravitational force exerted by an object, which is directly proportional to its mass.

- If the Sun were to suddenly vanish from existence, the Earth would continue moving in a straight line tangent to its previous orbit. This is due to Newton's first law of motion, also known as the law of inertia, which states that an object in motion will remain in motion with the same velocity unless acted upon by an external force. In this case, the external force provided by the Sun's gravitational pull would no longer be present, so the Earth would continue moving in a straight line.

- A satellite moving at a constant velocity around the Earth experiences a net force directed toward the Earth. This force is provided by gravity and is necessary to maintain the satellite's circular motion. The satellite is constantly accelerating towards the Earth but does not change its speed because the change in velocity (acceleration) is always directed perpendicular to the direction of motion.