Gravitation Created by Craig Smiley (Harrison HS, West Lafayette, IN) Supported by grant PHY-0851826 from the National Science Foundation and by Purdue University

Gravitation If you used a rocket pack to fly to a height equal to Mars’ radius above the surface of Mars, what would happen to your weight? (ignore the weight of the rocket pack) Decrease to a 1/4 of your weight Decrease to a 1/2 of your weight Stay the same Increase by 2x your weight Increase by 4x your weight You would be weightless

Orbits What would need to happen to maintain Earth’s circular orbit around the Sun if the Earth’s mass suddenly increased? Increase Earth’s radius Increase Earth’s orbiting speed Increase Sun’s mass Decrease the distance between Earth and Sun Nothing would have to change

Orbits What would need to happen to the Earth to maintain a circular orbit if Sun’s mass decreased? Distance from Sun ↑ or Earth’s speed ↑ Distance from Sun ↑ or Earth’s speed ↓ Distance from Sun ↓ or Earth’s speed ↑ Distance from Sun ↓ or Earth’s speed ↓ None of these

Orbits Assuming all the planets have circular orbits around the Sun, what happens to the planets’ period of revolution (time around the Sun) as you get farther away from the sun Get shorter Get longer Stay the same Can’t be determined without the mass of the planet

Orbits Assuming all the planets have circular orbits around the Sun, what happens to the planets’ period of revolution (time around the Sun) as you get farther away from the sun Get shorter Get longer Stay the same Can’t be determined without the mass of the planet

Circular Orbits What would need to happen to maintain Earth’s circular orbit around the Sun if the Earth’s mass suddenly increased? Increase Earth’s radius Increase Earth’s orbiting speed Increase Sun’s mass Decrease the distance between Earth and Sun Nothing would have to change

Circular Orbits The Sun’s mass doubled. What would need to happen to the Earth’s distance from the center of the Sun to maintain a circular orbit moving at its original speed? 4r D. r 2 2r E. r 2 2r F. r 4

Circular Orbits The Sun’s mass is halved. What would need to happen to the Earth’s speed to maintain a circular orbit moving at its original distance from the center of the Sun ? 4v D. v 2 2v E. v 2 2v F. v 4

Suppose the Sun were to collapse into a black hole (shrinks radius, but maintains the same mass). What effect would this have on the Earth’s orbit? A. The size of the orbit would decrease and the orbital period would decrease. B. The size of the orbit would increase and the orbital period would increase. C. The size of the orbit and the orbital period would remain unchanged. D. none of these Answer: C

Circular Orbits Assuming all the planets have circular orbits around the Sun, what happens to the planets’ period of revolution (time around the Sun) as you get farther away from the sun Get shorter Get longer Stay the same Can’t be determined without the mass of the planet

The planet Saturn has 100 times the mass of the Earth and is 10 times more distant from the Sun than the Earth is (assume it also has a circular orbit). Compared to the Earth’s acceleration as it orbits the Sun, the acceleration of Saturn as it orbits the Sun is A. 100 times greater. B. 10 times greater. C. the same. D. 1/10 as great. E. 1/100 as great. Answer: E

Apparent Weight While the space-shuttle orbits the Earth the astronauts appear to be weightless: There is no gravity above the atmosphere The force of gravity is much weaker when they are that far away from the Earth They are constantly “falling” around the Earth None of these

Apparent Weight Show Vomit Comet Video http://www.youtube.com/watch?v=BTkFIE_-kL8 Why were they floating inside the plane? They went high enough so there was very little gravity acting on them. The plane was accelerating downward at 9.8m/s2 so they were “falling” while inside the plane. They had powerful magnets in the plane, but in order for them to work they needed to be off the ground. None of these.

An astronaut is floating around in the space shuttle's cabin. What is her acceleration, as measured from the earth's surface? zero - she's floating very small, directed towards the center of the earth very small, directed along the line of travel of the shuttle quite large, nearly g, directed towards the center of the earth quite large, nearly g, directed along the line of travel of the shuttle

Gravitational Potential Energy

A. does positive work on the satellite. A satellite is moving around the Earth in a circular orbit. Over the course of an orbit, the Earth’s gravitational force A. does positive work on the satellite. B. does negative work on the satellite. C. does positive work on the satellite during part of the orbit and negative work on the satellite during the other part. D. does zero work on the satellite at all points in the orbit. Answer: D

Dropping a rock from r = ∞ If there was nothing else in the universe except the Earth and a rock, and the rock was taken to r = ∞ away and released from rest, how fast would it be going by the time it fell that far before hitting the Earth? Infinitely fast Speed of light, b/c nothing that go faster than the speed of light A little slower than the speed of light because it has mass Significantly slower than the speed of light

Gravitational Equipotential Lines What happens to gravitational potential energy if you move an object with mass from a lower value equipotential line to a higher value equipotential line? increases decreases stays the same 60m 50m 40m 30m 20m 10m 0m 600 J/kg 500 J/kg 400 J/kg 300 J/kg 200 J/kg 100 J/kg 0 J/kg height (m) above ground zero gravitational potential (g = 10m/s2)

Gravitational Equipotential Lines What is the sign for Work done by gravity if you move an object with mass from a lower value equipotential line to a higher value equipotential line? + – 60m 50m 40m 30m 20m 10m 0m 600 J/kg 500 J/kg 400 J/kg 300 J/kg 200 J/kg 100 J/kg 0 J/kg height (m) above ground zero gravitational potential (g = 10m/s2)

Gravitational Equipotential Lines What is the sign for Work done by gravity if you move an object with mass from a lower value equipotential line to a higher value equipotential line and then back to the initial lower value equipotential line? + – 60m 50m 40m 30m 20m 10m 0m 600 J/kg 500 J/kg 400 J/kg 300 J/kg 200 J/kg 100 J/kg 0 J/kg height (m) above ground zero gravitational potential (g = 10m/s2)

Gravitational Equipotential Lines What is the sign for Work done by gravity if you move an object with mass around an equipotential line? + –

Gravitational Equipotential Lines What happens to gravitational potential energy if you move an object with mass from a lower value equipotential line to a higher value equipotential line? increases decreases stays the same

Gravitational Equipotential Lines What is the sign for Work done by gravity if you move an object with mass from a lower value equipotential line to a higher value equipotential line? + –

Gravitational Equipotential Lines What is the sign for Work done by gravity if you move an object with mass from a lower value equipotential line to a higher value equipotential line and then back to the initial lower value equipotential line? + –