Fg W mg g ag Do you know the difference??

Newton’s Law of Universal Gravitation Every body in the universe attracts every other body with a force that is directly proportional to the product of the masses of the bodies and inversely proportional to the square of the distance between the bodies.

Newton’s Law of Universal Gravitation When 2 masses are separated by a distance (r) r Fg -Fg m1 m2 The proportionality constant, G is called the universal gravitational constant. Its value in the SI system of units is, G = 6.67  10-11Nm2/kg2. Cavendish link

The Law of Universal gravitation states that every object in the universe is attracted to every other object in the Universe! Greater the masses = greater the force of attraction Greater the distance = smaller the force of attraction

Effects on Mass

The more mass an object has, the greater its force of attraction. You are extremely attractive.

Effects of Distance

Sample Problems Find the gravitational attractive force between two identical 50 g spheres with centers .8 meters apart? G = 6.67x10-11 N m2/kg2 So you use the equation Fg = GMm/r2 Fg = 6.67E-11*.05*.05/.82 Fg = 2.61E-13 N

Weight and Gravitational Attraction. Find the weight of a 75 kg person on the planet earth. 2. Find the gravitational force of attraction between a 75 kg person and the Earth? mearth = 5.98 x 1024 kg rearth = 6.37 x 106 m W= 75 X 9.8=735 N Fg = GMm/r2= 6.67E-11(5.98E24 )(75) / (6.37E6)2 Fg = 737.46 N

Acceleration Due to Gravity Calculate g for planet Earth at sea level.

Example 6 The mass of the Hubble Space Telescope is 11,600 kg. Determine the weight of the telescope (a) when it was resting on the earth and (b) as it is in its orbit 598 km above the earth's surface. Mearth = 5.98 x 1024 kg Rearth = 6.37 x 106 m G = 6.67 x 10-11 N m2/kg2 Answer: 114, 027 N =25,623 lbs 95,295 N = 21,414 lbs

INNER SPACE Down in a cave below the surface of the earth there is: More gravity than at the earth’s surface Less gravity than at the earth’s surface The same gravity as at the surface

Newton’s Law of Universal Gravitation: Conceptual Questions 1. The moon and the Earth are attracted to each other by gravitational force. Does the more massive earth attract the moon with a greater force than the moon attracts Earth? Explain. 2. What happens to the gravitational force between two masses when the distance between the masses is doubled? 3. If the Earth were twice as massive but remained the same size, what would happen to the value of G? g? 4. Jupiter has about 300 times the mass of Earth and about 10 times earth’s radius. Estimate the size of g on the surface of Jupiter.

Newton's Thought Experiment on Orbital Motion

Cannonball A cannonball is fired horizontally from a tall mountain to the ground below. Because of gravity, it strikes the ground with increased speed. A second cannonball is fired fast enough to go into circular orbit but gravity does not increase its speed. Why Refer to #19 & #23 in conceptual physics

MOON MOTION Draw a FBD and sum the forces acting on the moon as it orbits the earth. If the moon orbits the earth every 27.3 days at a radius of 3.8 x 108 meters. Determine the velocity and the acceleration due to gravity that the moon experiences.

Speed of a Satellite: Mem mv2 Fg = G = _________ ____ r² r

Speed of a Satellite: √ GMe v = r

v = velocity (m/s) G = gravitational constant Me = mass of Earth (kg) r = distance to center of the Earth (m)

Satellites What is the minimum velocity needed for a satellite to stay in orbit at 1500 km above the earth’s surface. Given Mearth = 5.98 x 1024 kg Rearth = 6.37 x 106 m And the answer is…. 7913.047866 m/s

TREETOP ORBIT If the earth had no air (atmosphere) or mountains to interfere, could a satellite given adequate initial velocity orbit arbitrarily close to the earth’s surface – provided it did not touch? Yes, it could. No, orbits are only possible at a sufficient distance above the earth’s surface where gravitation is reduced. Explain.