Transcript Slide 1
Planets move through the sky with More complicated paths than Stars do. We begin with Kepler’s Laws in Order to find out how. Kepler’s Laws of planetary motion Are stated as… 1)The paths of planets are ellipses, With the sun at one focus. 2) An imaginary line from the sun To a planet sweeps out equal Areas in equal time intervals. Thus planets move faster when They are closer to the sun, and Vise-versa. 3) The square of the ratio of the Periods of any two planets Revolving about the sun is Equal to the cube of the ratio Of their average distances From the sun. TA 2 = TB rA 3 rB TA 2 = TB rA 3 rB T = the planets’ periods Of revolution r = the average distance From the sun (or another focus) The first 2 laws apply to each Individual planet, moon, or Satellite. The 3rd law relates to the motion Of several satellites about a Single body. Io has a period of 1.8 days and is 4.2 units away from Jupiter. Callisto has a period of 16.7 days. What is the distance away From Jupiter? rc = 19 units The moon has a period of 27.3 Days and a mean distance from Earth of 3.9 X 105 km. Find the Period of a satellite that is in Orbit 6.7 X 103 km. 88.6 mins Newton also played around With a few formulas for gravitation. Newton said that there was an Attractive force between All objects, this is called the Gravitational force. Newton was so confidant that He came up with a law to find The quantity of gravity. The Law of Universal Gravitation mAmB F=G d2 mAmB F=G d2 m = mass d = distance between The center of the objects G = 6.67 X 10-11 Nm2 / kg2 Without showing all the math, The force equals something else. mp4π2r msmp F= =G 2 T d2 And rearranged again… T2 = 4π2 Gms r3 Jeff (75 kg) and Racheal (60 kg) sit about 4 Meters away from each other. Racheal looks up and feels an Attraction. Find the gravitational Force between them. F = 1.87 X 10-8 N An object that is falling at the Same rate at which the earth is Curved is said to be in orbit. Use Newton’s thought experiment On page 179 to see how. For an object to be in orbit, air resistance Must be taken away, which Means that it must be at least 150 km above the earth. We can continuously derive New formulas to find out things. v= T = 2π GmE r r3 GmE These formulas only Work for the earth. A satellite orbits Earth 225 km Above its surface. What is its Speed in orbit and its period? v = 7760 m/s T = 1.5 hr As you move farther from Earth’s Center, the acceleration due To gravity changes. rE 2 a=g d There are 2 kinds of mass… Inertial mass And Gravitational mass Inertial mass is a measure of an Object’s resistance to an type Of force. minertial = Fnet a The gravitational mass is the size Of the gravitational force Between the objects. mgrav r2Fgrav = Gm Einstein proposed that gravity Is not a force, but an effect Of space itself. According to Einstein, mass Changes space itself, Making it curved. Bodies are thus accelerated Because they follow this Curved space toward the center. This is Einstein’s Special Theory of Relativity.