Universal Law of Gravitation

“If gravity attracts an apple toward the Earth, perhaps it also attracts the Moon, and the moon is falling , or accelerating toward the Earth, under the influence of gravity”

Newton Quantizes Gravity Derived a relationship between mass and distance m2 F12 F21 m1 r Universal Gravitational Constant

Acceleration Due to Gravity g = 9.8 m/s2

ma= 8 kg mc= 6 kg mb= 4 kg F1= ? F2= ? r1= 5 m r2= 3 m

How fast is the Earth traveling right now? Fg r Ms=1.99 x 1030 kg r = 1.5 x 1011 m

What is the total gravitational force on the moon by the sun and Earth during a lunar eclipse? ms= 1.99 x 1030 kg mE= 5.98 x 1024 kg mm = 7.36 x 1022 kg rsE= 1.5 x 1011 m rEm= 3.84 x 108 m Toward the sun

What is the total gravitational force felt by the moon by the sun and Earth during a solar eclipse? ms= 1.99 x 1030 kg mm = 7.36 x 1022 kg mE= 5.98 x 1024 kg rEm= 3.84 x 108 m rsm= 1.496 x 1011 m rsE= 1.5 x 1011 m Toward the sun

At what altitude are geosynchronous satellites? Known: Need to find r

Nick timed himself and found out that if he wore a bright white outfit he ran 20 miles in 80 minutes, but when he wore a dark outfit, he ran 20 miles in one hour and twenty minutes. What does this mean for his next race?

Kepler’s Laws 1st Law 2nd Law The orbit of each planet is an ellipse with the sun at one focus. 2nd Law The line joining the planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse Planets speed up as they get closer to the sun, slow down as they get further from sun

Kepler’s Laws 3rd Law Kepler’s Constant The square of the orbital period of a planet is directly proportional to the cube of the average distance from the sun Kepler’s Constant

Kepler’s Constant Unique to the body being orbited Exp: K for the solar orbits (case of Earth orbiting the sun): Same for any body orbiting the sun

Kepler’s Constant Estimate the mass of the sun: Determine K for objects orbiting Earth Estimate the mass of the Earth: Mass of the sun T = 27.3 days r = 3.87 x 108 m