1. Gravity is conservative
Gravitational Energy
Gravity is conservative
§ 12.4–12.6

2. Gravitational Potential Energy
Work to bring two objects from separation  to separation r:
PE = –G
m1m2 r
Negative because you must push against gravity to hold them
The farther the d, the less negative the PE

3. Escape Speed
if an object’s E = Ug + Ktr ≥ 0, it can “escape” from a gravitational field.
The force never disappears, but the object does not return. E Ug E r

4. Example Problem
Calculate the escape speed of Earth, that is, the speed with which a rocket must be launched if it is to completely escape the gravitational pull of Earth. (This means that the kinetic energy is zero when it reaches a distance of infinity.)
Mearth = 5.976  1024 kg
Rearth = 6378 km
G = 6.67  10–11 Nm2/kg2

5. Group Question
Would it be possible for a planet to have the same surface gravitational field as earth, but a different escape speed from the surface?

6. Poll Question At which position is the satellite speeding up?
Position A.
Position B.
Position C.
Position D.
None of these.

7. Quick Question At which position is the satellite slowing down?
Position A.
Position B.
Position C.
Position D.
None of these.

8. Poll Question
At which position is the satellite changing its direction but not its speed?
Position A.
Position B.
Position C.
Position D.
None of these.

9. Board Work Rank the positions in descending order of:
Gravitational force.
Acceleration.
Speed.
Kinetic energy.
Gravitational potential energy.
Total energy.
Angular momentum.

10. Tidal Forces
Strongest here
Weaker here
Weakest here
Force of gravity

11. Tidal Forces Tidal bulge Strongest here Weaker here Weakest here
Force of gravity