1. -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes
AP Physics C
Mrs. Coyle

2. Tangential Velocity of an Orbiting Satellite

3. Satellites At a certain r the speeds of the satellites are the same.
Geosynchronous: satellite that have the same period as earth.

4. Escape Velocity
The minimum speed required to launch an object from the earth’s surface in order for it to escape the earth’s pull.

5. To find the escape velocity of an object use conservation of energy

6. For a Earth-Satellite System
Total energy E = K U
Note: in a bound system, E < 0

7. Escape Velocity

8. Escape Velocity
For any planet:

9. Note:
According to Newton’s Law of Universal Gravitation the gravitational field even at infinity is does not equal to zero but approaches zero.
Some planets have atmospheres and others do not because their escape velocities vary and some gas molecules have high enough speeds to escape.

10. Two Particle Bound System

11. Energy in a Circular Orbit

12. Note: Energy in a Circular Orbit
K>0 and is equal to half the absolute value of the potential energy.
|E| = binding energy of the system.
The total mechanical energy is negative.

13. Energy in an Elliptical Orbit
r= 2a=the semimajor axis
The total mechanical energy,E is negative.
E is constant if the system is isolated.

14. Example #63
a) Determine the amount of work (in Joules) that must be done on a 100kg payload to elevate it to a height of 1,000km above the earth’s surface. b) Determine the additional work required to put the payload into circular orbit at this elevation (The radius of the earth is 6.37x106 m, G=6.67x10-11 Nm2 / kg2) Ans: a)8.50x108 J, b) 2.71x109 J

15. Note: For a Two Particle Bound System
Both the total energy
and
the total angular momentum are constant.

16. Compare the Kinetic Energy and Angular Momentum of a Satellite at orbit 1 and 2
Earth

17. How does the speed of a satellite at position 2 compare to the speed at position 1. The distance r2 =2r1. (Hint: Use conservation of angular momentum)
Earth 2 1

18. Black Holes
A black hole is the remains of a star that has collapsed under its own gravitational force
The escape speed for a black hole is very large due to the concentration of a large mass into a sphere of very small radius
If the escape speed exceeds the speed of light, radiation cannot escape and it appears black

19. Black Holes
The radius at which the escape speed equals the speed of light, c, is called the Schwarzschild radius, RS
An imaginary surface of a sphere with this radius is called the event horizon.
If an object is not closer than the Rs , it can still escape the black hole.

20. Material from a nearby star (in a binary system) can be pulled into the black hole and forms an accretion disk around the black hole.
Accretion Disks

21. Black Hole Video Clip