Philae Lander Found Credit ESA Rosetta MPS Image taken by the Rosetta spacecraft from a distance of 2 7 km The image scale is about 5cm pixel Course Announcements OSIRIS REx successfully launched Please get 3 x 5 Notecards for upcoming Notecard Q s Assignments Reading Assignments Chapter 3 Sections 3 1 3 3 Read for Monday 12 Sept Parallel Lectures CC Astronomy Episode 24 Light Watch for Monday 12 Sept Mastering Astronomy Chapter 2 Homework Due Tuesday 13 Sept at 11 59 PM EDT Newtonian Gravity An inexorable attraction How strong the gravitational force is depends only on TWO components The masses involved and the distance between them The force of gravity is proportional to the product of the masses m1 and m2 divided by inversely proportional the square of the distance between them usually labeled as r or R The Inverse Square Law Know what an inverse square law is Double the distance Reduce gravity by a factor of 22 4 Five times the distance Reduce gravitational force by a factor of 52 25 Newtonian Gravity An inexorable attraction Gravity only operates in ONE direction IT IS ALWAYS ATTRACTIVE AND NEVER REPULSIVE G sometimes called Big G is the Gravitational Constant measured experimentally to be G 6 67 x 10 11 N m2 kg2 You don t have to know this number Double the distance Reduce gravity by a factor of 22 4 Five times the distance Reduce gravitational force by a factor of 52 25 Example Gravity Question M M Distance 1x m Distance 3x M m Triple the Distance m Exact Form You don t need to know the exact form You do need to know the proportionalities i e dependency on masses and distances involved How much stronger or weaker does the force of gravity become when we triple the distance between two masses M and m Example Gravity Question M M Distance 1x m Distance 3x M m Triple the Distance m Exact Form You don t need to know the exact form You do need to know the proportionalities i e dependency on masses and distances involved Answer The force of gravity is inversely proportional to the square of the distance So if I double the distance farther away the inverse proportionality tells me that gravity will be weaker with the larger distance and it will be so by a factor that means number of the distance squared 3x more distance 32 9 x weaker or 1 9th as strong Example Gravity Question M 2M Distance 1x Distance 1x m 4m Same Distance Double One of the masses 4x the other M 2M M 4m Exact Form You don t need to know the exact form You do need to know the proportionalities i e dependency on masses and distances involved How much stronger or weaker does the force of gravity become when we double 2x one of the mass M and quadruple 4x the other mass m Example Gravity Question M 2M Distance 1x Distance 1x m 4m Same Distance Double One of the masses 4x the other M 2M M 4m Exact Form You don t need to know the exact form You do need to know the proportionalities i e dependency on masses and distances involved Answer The force of gravity is directly proportional to the product of the masses With one of the masses doubled M 2M and the other quadrupled m 4m we have 4m x 2M 8mM and therefore the force of gravity is 8 times stronger So the force of gravity is stronger by a factor of 8 Hard Gravity Question m1 3m1 Distance 1x m2 Change masses 2x and 3x Triple Distance Distance 3x 2m2 How much stronger or weaker does the force of gravity become in when we change the masses to be 2x and 3x more massive respectively AND triple the distance between them Hard Gravity Question m1 3m1 Distance 1x m2 Change masses 2x and 3x Triple Distance Distance 3x 2m2 Solution Method Take it one step at a time Step 1 The Mass Dependence Change in the product of the masses m 1 x m2 3m1 x 2m2 3x2 m1 x m2 6m1m2 So due to the masses gravity has increased by a factor of 6 Step 2 The Distance squared Dependence Change in distance is 3 times farther away 32 9 so due to the distance change gravity has decreased by a factor of 9 Step 3 Compare Increase by factor of 6 decrease by factor of 9 Looking at the gravity equation we see the change in gravity is by a factor of 6 9 2 3 So overall the force of gravity has decreased weaker by a factor of two thirds Newtonian Gravity Gravity on Earth Under gravity objects fall back to Earth with an every increasing velocity they are accelerating which makes them move in parabolic paths The Earth has mass a lot of it at 5 87 x 1024 kg A trillion trillion kilograms 1 kg 2 2 pounds on Earth We live in the gravitational field the causes It is always acting on us On Earth the acceleration due to Earth s gravity often written as g is approximately constant and directed toward the center of Earth Earth gravitational acceleration g 9 8 m s2 So called 1 g gee It never stops and is always applying a force to everything In the Universe Always pulling at a constant force of F mg mass x 9 8 m s2 Putting something in orbit The speed at which the Force of Gravity balances out Centripetal Force Circular Motion force is orbital speed Set both forces equal to each other in balance Force of Gravity GmM mv2 Fc Fg R2 R Imagine firing a cannon with progressively more and more force I m falling but constantly missing Centripetal Force Vorb gives you the velocity an object will orbit a object with mass M at a distance R away from it Rocket Science Leaving the Earth If we fire the cannon ball with even more force then we can break orbit and go out into interplanetary space The speed to escape entirely escape speed is the square root of 2 1 414 times greater than orbital speed Need calculus thanks Newton to derive this one Eventually you can apply so much force to something to launch it into outer space i e make it leave Earth and never come back See ya Earth Using Newtonian Gravity to Weigh Things If we can measure the distance and period and thus get velocity we can use Newtonian gravity to solve for mass Can also use these equations to determine mass of the Sun me is Mass of Earth MS is Mass of Sun r is 1 AU Vorb is Earth s orbital speed at 30 km s is the math symbol for Implies Force of Gravity Centripetal Force M rv2 G We know the radius orbital speed and big G The result is M 2 0 x 1030 kg You are not responsible for knowing this It is for instructive purposes only What makes planets orbit Re asking the question …
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