Phys211C12 p1 Gravitation Newton’s Law of Universal Gravitation: Every particle attracts every other particle Force is proportional to each mass Force is inversely proportional to the square of the separation G determined by Henry Cavendish in 1798 using torsion balance For extended spherically symmetric objects, distances are from center to center m1m1 m2m2 r r ˆ F

Phys211C12 p2 Example: What is the force of attraction between two 1.00 kg objects separated by 1.00 m? Example: What is the gravitational force on a.0100 kg object located at the origin by two kg objects located at (0.200 m, 0 m) and (0.200 m, m).

Phys211C12 p3 Weight: the total gravitational force exerted on a body by all other bodies in the universe. usually dominated by one particular gravitational source for a mass m near the surface of the earth: once G is determined the mass of the Earth is known! g = 9.81 m/s 2 R E = 6.38E6 m  M E = 5.98E24 kg  = 5500 kg/m 3

Phys211C12 p4 Surface gravity of a planet Example: Mars, at surface and at altitude of 6.00 E 6m m = 6.42 E23 kg r = 3.40 E6 m find weight of object which weighs 3.92 E4 N on Earth’s surface

Phys211C12 p5 The work done on a mass m in the presence of another mass M

Phys211C12 p6 More fun with gravitational potential energy

Phys211C12 p7 Orbital Motion: object “falls around” orbited body

Phys211C12 p8 Escape velocity: particle has just enough kinetic energy at surface to escape gravitational attraction (r  )

Phys211C12 p9 Example: Find the orbital distance for a geosynchronous orbit Example: Find the escape velocity from the surface of the earth and from the surface of Mars.