1. Gravitation

2. Flat Earth This is true for a flat earth assumption. Is the earth flat? What evidence is there that it is not? Up to now we have parameterized the weight of an object as

3. Gravitational Force Central Force - Directed between the centers of mass for the two objects. Inverse Square Law Force - Strength drops off as 1/r². r m1m1 m2m2

4. Earth & the Moon What is the gravitational force between the earth and the moon? meme m rere rmrm r em

5. Potential Energy Calculate work needed to change height If U i =0 at r i = ,

6. Kepler’s Laws All planets move in elliptical orbits with the sun at one focal point. Planets sweep out equal areas in equal time intervals. –Conservation of angular momentum Square of the orbital period is proportional to the cube of the semi-major axis of the orbit. A1A1 A2A2

7. Orbital Motion Assume only gravitational force and circular motion at constant speed. v r M m Newton’s 2nd LawT = orbital time period

8. Earth Satellites Landsat-7 has an orbit altitude of 705 km. What is its acceleration, speed, and orbital period?

9. Geostationary Satellites One orbit = One Day Types of Satellites –Weather –Communications

10. Digital Globe - Quickbird 2 foot resolution Altitude of 280 mi  = 1.3  rad

11. Moon’s Orbit What is the period of the moon’s orbit? T = 27.5 days 27.3 days 29.5 days 0 days Sidereal (w.r.t. stars) Synodic (w.r.t. sun)

12. Escape Velocity Escape velocity - Velocity a projectile needs to escape the gravitational force. At r max = , v e = 11.2 km/s

13. Tides Tides--rise and fall of ocean levels –12-hour cycle –Interaction between the moon’s gravity and the earth’s centripetal acceleration. a = ga < ga > g Centripetal Acceleration Gravitational Acceleration