Gravitation

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

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 m2 m1

Earth & the Moon What is the gravitational force between the earth and the moon? rm mm re rem me

Potential Energy Calculate work needed to change height If Ui=0 at ri=,

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. A1 A2

Orbital Motion Assume only gravitational force and circular motion at constant speed. v r M m Newton’s 2nd Law T = orbital time period

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

Geostationary Satellites One orbit = One Day Types of Satellites Weather Communications

Digital Globe - Quickbird 2 foot resolution Altitude of 280 mi At this resolution you would need to be 15 km away to read a license plate. q = 1.3 mrad

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

Escape Velocity Escape velocity - Velocity a projectile needs to escape the gravitational force. At rmax = , For Jules Verne’s cannon the Columbiad, the length was 274 m long. This would result in an acceleration of 2.3 e 5 m/s^2. If the cannon were ½ mile long (804 m) the acceleration would be reduced to 7.8 e 4 m/s^2 ve = 11.2 km/s

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