Gravity and Motion

Kepler’s Theory of Planetary Motion 1. Paths are ellipses and sun at the focus 2. Planets move faster when closer 3. Relationship between distance and period of orbit

Isaac Newton ( ) 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 1st 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 2nd 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 3rd 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

Gravity Depends on the two masses attracting each other…if both double, then the force between them will (2x2=4) quadruple. Depends on the inverse square of the distance between them. If the distance between them doubles, then F  1/d 2  F  1/2 2  ¼ of the force …if the distance triples, then F  1/3 2  1/9 of the force

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

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…

The Elliptical Orbit of a Planet

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Kepler’s Third Law Explained by Newton Balancing the force (called “centripetal force”) necessary to keep an object in circular motion with the gravitational force  expression equivalent to Kepler’s third law, P y 2 = a AU 3

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Einstein and Relativity (p.100) Einstein (1879 – 1955) noticed that Newton’s laws of motion are only correct in the limit of low velocities, much less than the speed of light.  Theory of Special Relativity Also, revised understanding of gravity  Theory of General Relativity

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Two Postulates Leading to Special Relativity (1) 1.Observers can never detect their uniform motion, except relative to other objects. This is equivalent to: The laws of physics are the same for all observers, no matter what their motion, as long as they are not accelerated.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Two Postulates Leading to Special Relativity (2) 2.The velocity of light, c, is constant and will be the same for all observers, independent of their motion relative to the light source.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. General Relativity A new description of gravity Postulate: Equivalence Principle: “Observers can not distinguish locally between inertial forces due to acceleration and uniform gravitational forces due to the presence of massive bodies.”

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.  New description of gravity as curvature of space-time! This bending of light by the gravitation of massive bodies has indeed been observed: During total solar eclipses: The positions of stars apparently close to the sun are shifted away from the position of the sun.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Another manifestation of bending of light: Gravitational lenses A massive galaxy cluster is bending and focusing the light from a background object.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Gravity according to general relativity You feel gravity because Earth’s mass causes a curvature of space-time. The mass of your body responds to that curvature by accelerating towards Earth’s center. All masses cause curvature. The larger the mass, the more severe the curvature. That’s gravity.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The Tides (see p. 98 in textbook) Caused by the difference of the Moon’s gravitational attraction on the water on Earth  2 tidal maxima Excess gravity pulls water towards the moon on the near side Forces are balanced at the center of the Earth  12-hour cycle Excess centrifugal force pushes water away from the moon on the far side

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Tides, In Review The side of the earth facing the moon experiences high tide because it is closest. The side of the earth opposite the moon experiences low tide because it is farther away.

Differences in Gravitational Force --why there are tides on earth

The Tidal Distortions of the Earth and Moon

Tidal Acceleration

Spring and Neap Tides