Universal Gravitation You are attractive to the person next to you!
Falling Bodies Newton knew that bodies continued in a straight line unless another force acted on it (___ Law). What force kept the moon around the earth? Moon must have _________ velocity to keep going, not away and not into, but around the Earth This would have to be tested to be proven true to go from hypothesis to theory (law). 1 st tangential
Falling Bodies (cont.) Decided to use an apple to compare movement of moon Known for Newton: Moon 60 times farther than an apple Apple fell 4.9 m in first second Gravity is “diluted” by distance Moon should “fall” about 1.4 mm (and it did as he proved by Geometry)
Falling Bodies (cont.) Newton put his findings away for 20 years until his “new branch” of mathematics (_______) helped further prove his calculations This also proved the Copernican theory that the _____ revolves around the sun Nothing crashes into the sun unless its tangential velocity is ______ Calculus Earth zero
Newton’s Law of Universal Gravitation Law states: “Every object attracts every other object with a force that for any two objects is directly proportional to the mass of each object and inversely proportional to the square of the distance between them” Or… F ~(m 1 )(m 2 )/d 2
Newton’s Law of Universal Gravitation (cont.) Newton didn’t discover gravity, just that it is universal. To put his law into a useable equation, we have to establish the universal gravitational constant, G. G = _________________ This is very small because the force is very weak 6.67 x 10 -11 Nm 2 /kg 2
Try One! Calculate the force of gravity between a newborn baby (mass = 4.0 kg) and the planet Mars (mass = 6.4 x 10 23 kg) when Mars is at its closest to Earth (distance = 8.0 x 10 10 m). 2.67 x 10 -8 N
May I have another? Calculate the force of gravity between the same newborn and the obstetrician (mass = 75 kg), who is 0.30 m from the baby. Which exerted more force on the baby, Mars or the obstetrician? 2.22 x 10 -7 N, Obstetrician
The Inverse-Square Law (cont.) Similar to Mr. Hewitt’s butter gun, the inverse square law is also applied to _________ and __________ If the distance between two objects doubles, the force between them is cut in ___________ In other words, the greater the distance from the Earth’s center, the less an object will weighweigh gravity light fourth
The Inverse-Square Law (cont.) See How to use the Rule of 1 on the board... Two parts: Replace whatever changed by the change factor Replace everything else with a “1”. What happens to your weight if the distance between the earth and you triples? What happens to the force of gravity if both masses double?
Universal Gravitation Results Natural Proofs: the Earth is round Planets deviate from their orbits when they are near each other (perturbation) Neptune and Pluto were found
Kepler’s Laws of Planetary Motion 1. The paths of the planets are ellipse with the center of the sun as one focus. 2. An imaginary line from the sun to a planet sweeps out equal areas in equal time intervals. Therefore, faster closer to sun, slower away from sun 3. (T a /T b ) 2 =(r a /r b ) 3
Kepler’s Laws of Planetary Motion First two laws deal with a planet or satellite individually. Third law relates multiple planets or satellites to each other. “r” in the third law is the average distance from the sun.