PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 15 1 How much less do you weigh at the earth's equator than if you were standing at the north or south pole? Assume a spherical earth with radius R = 6400 km, and one rotation per day. Enter your answer as a decimal, a fraction of your weight at the north pole, to 3 places after the decimal. For example, if your weight would be 150 lbs at the pole but 135 lbs at the equator, your answer would be 135/150 = 0.900

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 15 2 ANNOUNCEMENTS

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of of 3 Satellite A moves in a circular orbit of radius R. Satellite B moves in a circular orbit of radius 2R. The magnitude of the gravity force acting upon B is 1.Four times that acting upon A. 2.Twice that acting upon A. 3.Equal to that acting upon A. 4.Half that acting upon A. 5.One-quarter that acting upon A. Earth A B

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of of 3 Satellite A moves in a circular orbit of radius R. Satellite B moves in a circular orbit of radius 2R. The speed of B is 1.Twice that of A. 2.Less than twice that of A, but greater than that of A. 3.Equal to that of A. 4.Less than that of A, but more than half that of A. 5.Half that of A. Earth A B

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of of 3 Consider an astronaut aboard the International Space Station. The astronaut weighs: 1.The same as on Earth. 2.Somewhat greater than on Earth. 3.Somewhat less than on Earth (but greater than zero Newtons). 4.Zero Newtons. Name:Anousheh Ansari Nationality:Iranian Born:1966 Mission:Soyuz TMA-9/ISS, 20 Sep 2006 Notes:1 st Iranian in space 4 th self-funded space participant B.S. Engineering, George Mason U. M.S. Engineering, George Wash. U. Created, sold telecom company for $550 million US.

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 15 6 ANNOUNCEMENTS Track ISS at Track satellites at

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 15 M m R R is the distance between centers of gravity 7

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 15 FgFg Newton’s Universal Law of Gravity obeys Newton’s Third Law of Motion 8

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 15 FgFg Newton’s Universal Law of Gravity obeys Newton’s Third Law of Motion 9

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 15 FgFg path of motion Circular Orbit Equation v 10

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of II7 Exit Homework Problem #1

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of II7 Exit Homework Problem #2

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of of 3 Satellite A moves in a circular orbit of radius R. Satellite B moves in a circular orbit of radius 2R. The magnitude of the gravity force acting upon B is 1.Four times that acting upon A. 2.Twice that acting upon A. 3.Equal to that acting upon A. 4.Half that acting upon A. 5.One-quarter that acting upon A. Earth A B

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of of 3 Satellite A moves in a circular orbit of radius R. Satellite B moves in a circular orbit of radius 2R. The speed of B is 1.Twice that of A. 2.Less than twice that of A, but greater than that of A. 3.Equal to that of A. 4.Less than that of A, but more than half that of A. 5.Half that of A. Earth A B

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of of 3 Consider an astronaut aboard the International Space Station. The astronaut weighs: 1.The same as on Earth. 2.Somewhat greater than on Earth. 3.Somewhat less than on Earth (but greater than zero Newtons). 4.Zero Newtons. Name:Anousheh Ansari Nationality:Iranian Born:1966 Mission:Soyuz TMA-9/ISS, 20 Sep 2006 Notes:1 st Iranian in space 4 th self-funded space participant B.S. Engineering, George Mason U. M.S. Engineering, George Wash. U. Created, sold telecom company for $550 million US.

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of PROJECTION SCREEN II7: HAND IN TODAY’S ACTIVITIES SHEETS 6666

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of rotating space station FNFN t y 0 FNFN Path through space-time Albert Einstein taught us that this… …is equivalent to (physically indistinguishable from) this Einstein’s Principle of Equivalence Adapted from Lewis Carroll Epstein’s Relativity Visualized, Insight Press

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of Two Ideas About Gravitation Isaac NewtonAlbert Einstein I am stationary in three dimensions of space and I am not accelerating. mg FNFN t y 0 FNFN I am stationary in three dimensions of space but moving through time (the fourth dimension). Gravitation is a curvature of space-time. Therefore I am following a curved path in four dimensional space, and I am accelerating. Path through space-time Adapted from Lewis Carroll Epstein’s Relativity Visualized, Insight Press

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of Freefall Isaac NewtonAlbert Einstein My position coordinate is changing non-uniformly. I am not obeying my First Law of Motion. I am accelerating. mg t y 0 I am moving uniformly in a straight line through space-time. I am obeying Newton’s First Law of Motion. No force is acting upon me. I am not accelerating. Path through space-time a = g Adapted from Lewis Carroll Epstein’s Relativity Visualized, Insight Press

PHYS-1600/2000PHYS-1600/2000 II7 Gravity and Orbital MotionNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of Tossing a Clock Up in the Air and the Speeding Up of Time t y 0 Clock A’s path Clock B’s path Clock B ends up advanced in time! Adapted from Lewis Carroll Epstein’s Relativity Visualized, Insight Press