1. Two satellites A and B of the same mass are going around Earth in concentric orbits. The distance of satellite B from Earth’s center is twice that of satellite A. What is the ratio of the centripetal force acting on B to that acting on A?
1. 1/8
2. 1/4
3. 1/2
4. √1⁄2
5. 1
Answer: 2.The centripetal force on each satellite is provided by the gravitational
force between the satellite and Earth.

2. Two satellites A and B of the same mass are going around Earth in concentric orbits. The distance of satellite B from Earth’s center is twice that of satellite A. What is the ratio of the tangential speed of B to that of A?
1. 1⁄2
2. √1⁄2
3. 1
4. √2
5. 2
Answer: 2. For each satellite, the centripetal force is equal to the gravitational
force between the satellite and Earth, and is proportional to the
square of the tangential velocity and the inverse of the distance.

3. 1. be much less than g (because the ball doesn’t fall to the ground).
Suppose Earth had no atmosphere and a ball were fired from the top of Mt. Everest in a direction tangent to the ground. If the initial speed were high enough to cause the ball to travel in a circular trajectory around Earth, the ball’s acceleration would
1. be much less than g (because the ball doesn’t fall to the
ground).
2. be approximately g.
3. depend on the ball’s speed.
Answer: 2.The ball’s acceleration is caused by the only force exerted on
the ball: gravitation. Near the surface of Earth, the value of this acceleration
is g (perhaps a little less because of the altitude of Mt. Everest).

4. The Moon does not fall to Earth because
1. It is in Earth’s gravitational field.
2. The net force on it is zero.
3. It is beyond the main pull of Earth’s gravity.
4. It is being pulled by the Sun and planets as well as by Earth.
5. all of the above
6. none of the above
Answer: 6.The Moon is accelerating toward Earth because of the gravitational
attraction between the two.This attraction supplies the centripetal
force necessary to keep the Moon in orbit.

5. Black Holes
Event Horizon
(Point of no return)
Rs – Schwartzchild radius
What is a black hole?
Gravitational well with extremely high gravitational forces.
Creation of a black hole:
Massive star explodes – Supernova
Mass that does not travel far enough gets pulled back and the mass collapses under gravitational forces to form one of the following:
White Dwarf – M < 1.4 Msun
Neutron Star – M > 1.4 Msun
Black Hole – M > 3 Msun Rs
Singularity
Extremely dense star (R ~ 10 km) 1 teaspoon weighs 5 billion tons!
For a black hole the mass is compacted into a single point called a singularity. Ideally this point would have zero volume and therefore infinite density.
Everything that enters a black hole (passes the event horizon) is pulled into the singularity, including light!

6. A star loses mass to a black hole
A star loses mass to a black hole. This is the result of a single star of a binary pair collapsing into a black hole, or possibly a single star exploding and creating a black hole and another star.
The black hole can emits high energy electromagnetic radiation, as shown in the illustration below. This electromagnetic radiation is not in the visible spectrum.
An astronaut entering a black hole. The gravitational forces are so strong that the gravitational force at the astronauts head is stronger than the gravitational force at his feet. This causes the stretching and eventually the astronaut would be torn apart.