# Chapter 8 Universal Gravitation

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Chapter 8 Universal Gravitation
Quiz 8

Chapter 8 Objectives Relate Kepler's laws of planetary motion to Newton's law of universal gravitation. Calculate the periods and speeds of orbiting objects Describe the method Cavendish used to measure G and the results of knowing G

Chapter 8 Objectives Solve problems involving orbital speed and period
Relate weightlessness to objects in free fall Describe gravitational fields

Chapter 8 Objectives Distinguish between inertial mass and gravitational mass Contrast Newton's and Einstein's views about gravitation

Warm Up How do trains steer?

Kepler’s Laws of Planetary Motion
1. The paths of the planets are ellipses 2. Imaginary line from sun to planet sweeps out equal areas in equal times. 3. Square of the ratio of the periods is equal to the cube of the ratio of average distances

Ellipses: Two Center of Focus (One Empty)

Kepler’s 3rd Law An asteroid revolves around the sun with a mean (average) orbital radius twice that of Earth’s. Predict the period of the asteroid in earth years. Take note that mass doesn’t matter for orbital period Period = 1 complete revolution

Kepler’s 3rd Law The moon has a period of 27.3 days and has a mean distance of 3.90x105 km from the center of the earth. Predict the mean distance from Earth’s center that an artificial satellite that has a period of 1.00 day would have. Satellites that are in geostationary orbit have this period (TV, Weather) Military uses satellites not in geostationary orbits

Newton’s Law of Universal Gravitation
All objects which have mass exert a gravitational pull and are pulled in turn by others of mass. The force is equal to Where m is mass (kg) and d is distance (m) and where G = 6.67 E-11 N*m2/kg2

Newton’s Law of Universal Gravitation
Force is then proportional to the inverse square of distance Distance Force 1m 1 N 2m ¼ N 0.5 m 4 N Also note: Distance is between Center of Masses

Newton’s Law of Gravitation
If dealing with gravitational field strength (acceleration of object) is Large Mass = Large g Small Radius = Large g Because g is gravitational field (N/kg) All objects accelerate at same rate Bigger mass, more force

Newton’s Law of Universal Gravitation
If earth began to shrink, buts its mass remained the same, what would happen to the value of g on Earth’s surface? If earth began to lose mass, but radius stayed the same, what would happen to the value of g on Earth’s surface?

Newton’s Law of Universal Gravitation
Funny Shirt

Newton’s Law of Universal Gravitation
An astronaut is on the moon. a) Can the astronaut pick up a rock with less effort on the moon? b) How will the weaker gravitational force on the moon’s surface affect the path of the rock if the astronaut throws the rock? C) If the astronaut drops the rock, and it lands on their toe, will it hurt more or less than on earth? Explain

Satellites and their Speed
Satellites are constantly falling towards the planet they orbit (just as Earth is constantly falling towards the Sun) Inertia (horizontal velocity) + Falling (centripetal acceleration) leads to orbit

Satellites and their Speed
To slow, Ac to large = fall to Earth To fast, Inertia to large = Leaves orbit

Satellites and their Speed
Where v is speed in orbit, r is radius away from center, G is constant and m is mass of said planet. How does the mass of the planet and your radius influence the speed of V necessary to orbit?

Satellites and their Speed
Calculate the speed that a satellite shot from a cannon must have in order to orbit Earth 150 km above the Earth’s surface. Radius of Earth = 6.38 x106 meters

Satellites and their Speed
Find the speed of Mercury and Saturn around the sun. Does it make sense that Mercury is named after a speedy messenger of the gods and Saturn is named after the father of Jupiter? Mercury is 5.79 E10 meters from the sun, Saturn 1.43 E12 meters, the mass of the sun is 1.99 E30 kg.

Satellites and their Speed
The sun is considered to be a satellite of our galaxy, the Milky Way. The sun revolves around the center of the galaxy with a radius of 2.2 E20 meters. The period of one revolution is 2.5 E8 years. a) Find the mass of the galaxy b) Assuming that the average star has the same mass as the sun, find the number of stars. c) Find the speed with which the sun moves around the center of the galaxy.

Gravity in the Planets Explain the trend in of gravity field strength seen in the interior of planets

Mass revisited again Two types of mass
Inertial Mass : The inertial mass of an object is measured by applying a force to the object and measuring its acceleration Example: Put a block of ice in the back of a truck. When you accelerate forward, the ice will slide to the back of the truck as a result of its inertial mass (resistance to acceleration)

Mass revisited again Gravitational Mass: A measurement of the attractive force between objects of mass (a scale can measure this) Example: Drive up a hill with that ice at a constant rate (no acceleration), yet the block slides, due to gravitational mass. Both masses are always in agreement and are a central point in Einstein’s general theory of relativity

Mass revisited again List three examples of examples of the effects of gravitational mass and inertial mass.

Mass revisited again Einstein said that gravity is not a force, but an effect on space itself. A mass changes the space around it. It causes space to be curved, and other bodies are accelerated by following the curve of space.

Mass revisited again Black holes: So massive, that even light can’t escape the curve

Question The Earth has a radius of million km on average from the sun. Find the following a) Period of the revolution of the earth around the sun b) Tangential speed of the earth around the sun c) Period of the rotation of the earth d) Tangential speed of the rotation of the earth (at the equator). The radius of the earth is 6.38 E6 m.