Presentation on theme: "Sample Determine the net gravitational force acting on the Earth during a total lunar eclipse. msun = 1.99 x1030 kg mmoon = 7.36 x 1022 kg rsun = 1.5."— Presentation transcript:
8Translation: planets move faster when closer to the Sun. Kepler's Second LawA line connecting the Sun and a planet sweeps out equal areas in equal times.slowerfasterTranslation: planets move faster when closer to the Sun.
9Kepler's Second LawA line connecting the Sun and a planet sweeps out equal areas in equal times.The speed of the planet in orbit is dependent on its distance from the sunvoro = vf rfslowerfaster
10SampleIf the Earth has an orbital speed of 29.5 km/sec at apogee, determine the orbital speed at apogee.ra = 1.52 x 108 kmrp = 1.47 x 108 km
11Kepler’s Second Lawvoro = vf rfNote where the highest speeds of tornados and hurricanes are.
12Kepler’s Third LawThe square of a planet’s orbital period is proportional to the cube of its semi-major axis.Translation: the further the planet is from the sun, the longer it will take to go around
13Why Does it Work?Newton discovers that ellipses are pretty close to circular, just with the sun offsetFc = Fg
14SampleHow fast must a satellite move to maintain an orbit of 500 km over the Earth’s surface?What is the period of rotation?
15Kepler’s Third LawNewton took the idea of centripetal force and applied it to the Kepler problemFc = Fg
16Solution . Where M is the mass being orbited (as opposed to orbiting) T is the period of the orbitr is the radius of the orbit