Unformatted text preview: 2/11/11 Key concepts Circular mo9on Astro 109 Lecture 8: Newton's Laws of Mo9on and Gravity Feb. 11 Newton's law of gravity <--> orbits Tides Feb. 11 Discussion Ques9on When I swing the ball in a circle at a constant rate, A. B. C. D. E. the ball is not accelera9ng. the ball is accelera9ng toward me. the ball is accelera9ng away from me. the ball is accelera9ng in the "forward" direc9on. the ball is accelera9ng in the "backward" direc9on. Discussion Ques9on So what can we say about the force on the ball? A. B. C. D. E. There is no net force on it. There is a net force toward me. There is a net force away from me. There is a net force in the "forward" direc9on. There is a net force in the "backward" direc9on. Feb. 11 Feb. 11 Mo9on in a circle Requires con9nual applica9on of a force Force is toward the center Discussion Ques9on An astronaut on the Interna9onal Space Sta9on releases a pencil and sees it float in the air. The pencil is A. B. C. D. E. acted on by no forces. accelera9ng toward the Earth. accelera9ng away from the Earth. moving in a straight line at constant velocity. too light to be affected by gravity. Feb. 11 Feb. 11 1 2/11/11 What is the required force? (What puts the "fall" in "free fall"?) Feb. 11 Feb. 11 Newton's Law of Universal Gravita9on "Two objects aaract each other with a force that is directly propor9onal to the mass of each object and inversely propor9onal to the square of the distance between them." Feb. 11 Feb. 11 Each mass feels the same force (Newton's 3rd law). Complicated statement Take two objects, move them farther apart --> force gets weaker. Double the distance --> force goes down 4-fold. Complicated statement Now fix the distance. Increase the masses --> force gets stronger. Double one mass --> force doubles. Double both masses --> force quadruples (22=4). 1 r2
Feb. 11 1 1 = 22 4 Feb. 11 2 2/11/11 Discussion Ques9on Suppose you traveled to a planet with 3 9mes the mass and 3 9mes the diameter of Earth. Compared to your weight on Earth, your weight on the other planet would be A. B. C. D. E. 9 9mes larger. 3 9mes larger. the same. 3 9mes smaller. 9 9mes smaller. Discussion Ques9on During the Apollo 15 mission to the Moon, astronaut David Scoa dropped a hammer and a feather together. What happened? A. B. C. D. The hammer landed first. The feather landed first. The hammer and feather landed at the same 9me. The feather blew away. hammer feather Feb. 11 Feb. 11 Accelera9on by gravity ma = F GM m ma = r2 GM a= 2 r
All objects fall at the same rate! At surface of Earth, a = 9.8 m/s2. Feb. 11 Feb. 11 Discussion Ques9on As you sit in your chair, Earth's gravita9onal aarac9on on your body A. B. C. D. E. does not apply when you are sijng down. is not balanced by any other force. is balanced by the force of the chair on your body. is causing you to accelerate. is weighing on your mind. Mass vs. Weight You feel your weight because: gravity pulls down but the chair pushes up "weight" is a force In free-fall, the chair falls with you. no push --> "weightless" You s9ll have mass. Feb. 11 Feb. 11 3 2/11/11 Discussion Ques9on According to Newton's laws, the Earth and Sun pull on each other with the same strength of force. What can we say about their accelera9ons? A. B. C. D. E.
Feb. 11 Modify Kepler's 1st law Newton's 3rd law: if Sun pulls on Earth, then Earth also pulls on Sun. F = ma The Earth accelerates but the Sun does not. The Earth and Sun have the same accelera9on. The Sun has a higher accelera9on because it is more massive. The Sun has a lower accelera9on because it is more massive. The Sun and Earth accelerate in the same direc9on. Both move! Effect is small in Solar System. a= F m One of the ways we detect extrasolar planets. Feb. 11 Modify Kepler's 3rd law Old: [P (yr)]2 = New: [a (AU)]3 M (M ) [a (AU)]3 m1 + m2 (M ) [P (yr)]2 = With Sun+planet, m2 is small enough that we can neglect it. Feb. 11 4 ...
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