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Newton’s Law of Gravity
Starter

Newton’s Law of Gravity
Starter If the mass of the Earth stayed the same but the radius of the Earth doubles, what happens to your weight? a. it doubles also. b. it stays the same. c. it drops to 1/2 of the original. d. it drops to ¼ of the original. g = MG/R2

Newton’s Law of Gravity
Starter To increase the speed of an Earth satellite, should it be placed in an orbit closer to the Earth or further away from the Earth?

Practice Newton’s Law of Gravity : Every two objects attract each
other with a gravitational force given by: F = m1m2G/r2 m1 = mass of the first object in kg m2 = mass of the second object in kg r = distance between the two masses in meters G = 6.67 x 10-11

Practice / Example Find the gravitational force between the Earth and a 50,000kg asteroid that is 12 x 106 m away. masteroid = x104 kg mEarth = x 1024 kg G = x r = 12 x 106 m F = m1m2G/r2 = (5.00 x104 )( 6.00 x 1024 )(6.67 x ) / (12 x 106 )2 = x 105 Newtons = 139,000 Newtons

Practice / Example Find the gravitational force between Saturn and the sun. msun = x msaturn = x 1026 G = x r = x 109 F = m1m2G/r2 = (1.99 x1030 )(5.71 x 1026 )(6.67 x ) / (1430 x 109)2 = x 1022 Newtons

Where does g come from? Consider a person, mass m, standing on the Earth. His weight is: F = mMG/R2 = mg Cancel the person’s mass m: g = MG/R2 =(6x1024)(6.67x10-11)/(6.4x106)2 = 9.8 m/s2

Circular Orbits Orbit Velocity Period
F = mv2/R = mMG/R2 and v = 2pR / T Orbit Velocity Period R = Orbit Radius M = mass of planet or sun being orbited (The mass of the satellite is not in these 2 equations.)

Example The moon is 385 x 106 m from the Earth’s center.
R = 385 x MEarth = 6 x 1024 What is its orbit velocity? v = (MG/R)1/2 = ( ( 6 x 1024)(6.67 x 10-11)/(385 x106))1/2 = 1019 m/s What is the period? T = 2pR/v = (2p ) (385 x 106)/ = 2.37 x 106 seconds 2.37 x 106 seconds ( 1hr/3600s)(1 day/24 hr) = 27.5 days

Period of revolution, years
Useful Data Quantity Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto Mean distance from sun 57.9 108 150 228 778 1,430 2,870 4,500 5,900 (109 m) Mass (kg) 3.331E+23 4.866E+24 5.97E+24 6.388E+23 1.898E+27 5.677E+26 8.657E+25 1.027E+26 5.97E+22 Period of revolution, years 0.241 0.615 1 1.88 11.9 29.5 84 165 248 Orbital speed, 47.9 35 29.8 24.1 13.1 9.64 6.81 5.43 4.74 (103 m/s) Mass (Earth=1) 0.0558 0.815 0.107 318 95.1 14.5 17.2 0.01 Moon mass Distance to Earth Mass of Sun Mass of Earth Radius of Earth 7.36E22 kg 3.84E8 m 1.99E30 kg 5.97 E24 kg 6.4E6m

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