Gravity and Motion Keplers Laws of Planetary Motion

Gravity and Motion

Kepler’s Laws of Planetary Motion 1. Paths are ellipses and Sun at the focus 2. Planets move faster when closer to Sun (equal areas in equal time) 3. Relationship between cube of distance and square of period of orbit

Isaac Newton (1642 -1727) • Published Principia in 1687 that introduces mass, his laws of motion, and mathematical description of gravity • Key: Gravity provides a mechanism and explanation for Kepler’s Laws (explains why Kepler’s laws worked)

Newton’s Laws • 1 st Law: Object in motion…stays in motion (straight line, constant speed) if no net force acts on it. • Ex. Voyager satellite is still moving outside the solar system in a straight line

Newton’s Laws 2 nd Law: F=ma A total net force on an object causes an acceleration. Ex. A 40 N force is applied to an 8 kg bowling ball. What is the acceleration? F = ma 40 = (8)(a) a= 5 m/s 2 [divide on each side by 8]

The Balance of Forces

Newton’s 3 rd Law of Action and Reaction--if A pulls on B, then B pulls on A (the gravitational force between both galaxies is the same…but the smaller one will experience a greater acceleration because it has less mass)

Newton’s Law of Universal Gravitation • Plain english: mass attracts mass for no other reason than just that…. but they need to be large masses. • Ex. Cloud of gas particles will collect together • Ex. Planets will pull on each other • Ex. The moon pulls on earth and vice versa • Ex. You are pulled down toward the earth

Collection of Gases--a stellar nursery…gas clouds pull together to form stars

Newton’s Law of Universal Gravitation • The force depends directly on the two masses (. . . more mass more gravit) • The force is inversely proportional to the distance squared (farther away, less gravity) • If the Earth were moved 3 times farther away, the force between the Sun and the Earth would go to 1/32 = 1/9

Newton’s Law of Universal Gravitation Right now, you are 4000 miles from the center of the Earth. If you were moved 2 x farther away, gravity would be a) ½ as strong b) ¼ as strong c) 2 x stronger d) 4 x stronger

Gravity • Depends on the two masses attracting each other…if both double, then the force between them will (2 x 2=4) quadruple. • Depends on the inverse square of the distance between them. If the distance between them doubles, then F 1/d 2 • F 1/22 ¼ of the force • …if the distance triples, then • F 1/32 1/9 of the force

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. Gravity misconceptions • Q: Is there gravity on the moon? • A: Yes, but it’s weaker than on Earth (g≈1. 6 m/s 2)…not weak enough to “fly away”. • Q: Is there less gravity because the moon is far away from Earth? • A: NO! The moon has its own gravity because it has mass…but it has less mass than Earth, so it has less surface gravity. • Q: If the Earth stopped spinning, would gravity disappear? • A: NO! Gravity exists because mass attracts mass. This has nothing to do with spinning. • Q: Can we make an anti-gravity room? • A: Nope. Mass always attracts mass. It can’t be switched off.

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. There is less surface gravity on the Moon because a) b) c) d) The Moon is farther away from the Earth. The Moon does not have an atmosphere. The Moon rotates very slowly. The Moon has less mass than the Earth.

Centripetal Forces and Circular Motion-anything orbiting must have a force acting on it…in astronomy, that’s usually gravity.

Orbital Motion q. The velocity vector of the object is always directed straight and tangent to the circle q. The gravitational force is always directed inwards towards the central object

Newton’s Thought Experiment on Orbital Motion the same gravity that causes things to fall down is what causes the moon to orbit earth Gravity pulls satellites around the earth…

There IS gravity where the astronauts orbit ……gravity is what is pulling everything around in orbit. “Weightlessness” is simply when everything is freefalling together

The Elliptical Orbit of a Planet

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. Quick check #1 In the diagram, each letter is 1 month apart. According to Kepler’s 2 nd law, the velocity of the planet at A is ______ than the velocity of the planet at H. a) Greater than b) Less than c) Equal to

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. Quick check #2 In the diagram, each letter is 1 month apart. According to Kepler’s 2 nd law, the area swept out by the planet from A to B is ______ than the area swept out from G to H. a) Greater than b) Less than c) Equal to

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. Quick check #3 In the diagram, point G is 4 x farther away from the Sun than point A. Compared to the gravitational force at point A, the gravitational force on the planet at point G is a) ½ as strong b) ¼ as strong c) 1/8 as strong d) 1/16 as strong

q Tides are caused by differences in gravitational Force on either side of Earth q The moon pulls more on the near side, and less on the far side, so there is swelling of water on both sides of Earth q People on Earth will rotate through both tides so that there are 2 high tides in ~24 hours (12 hours apart)

The Tidal Distortions of the Earth and Moon

Tidal Acceleration

Spring and Neap Tides

Einstein and General Relativity • Einstein: space and time are linked together • Mass warps and bends spacetime • Curves in spacetime cause light to bend towards massive objects

Einstein and General Relativity • Curves in spacetime should cause light (which has no mass) to bend in space • Experimental evidence supports theory: light deflects near massive objects to cause them to appear in different positions