Universal Gravitation Ch 12 Notes Universal Gravitation Newton’s idea was that gravity was a universal force acting between any two objects.

Law of Universal Gravitation Ch 12 Notes Law of Universal Gravitation In symbols, Newton’s Law of Universal Gravitation is: Fgrav = G Where G is a constant of proportionality. G = 6.67 x 10-11 N m2/kg2 Mm r 2

Orbits

The Gravitational Field Ch 12 Notes The Gravitational Field During the 19th century, the notion of the “field” entered physics (via Michael Faraday). Objects with mass create an invisible disturbance in the space around them that is felt by other massive objects - this is a gravitational field.

The Gravitational Field Ch 12 Notes The Gravitational Field All objects with mass create a gravitational field.

Gravitational Field Strength Ch 12 Notes Gravitational Field Strength To measure the strength of the gravitational field at any point, measure the gravitational force, F, exerted on any “test mass”, m. Gravitational Field Strength, g = F/m

Gravitational Field Strength We can calculate the gravitational field produced by any mass by using the equation g = GM/r2 where r is the distance from the source mass, G is the universal gravitational constant, and M is the mass of the source mass.

Problem 1 Use the gravitational force law to find an approximate value for the mass of the Earth.

Ch 12 Notes Problem 2 If an object weighs 270 N at the Earth’s surface, what will it weigh at an altitude equal to twice the radius of the Earth? 30 N

Ch 12 Notes Problem 3 Determine the magnitude of the free fall acceleration at an altitude of 500 km. By what percentage is the weight of the body reduced at this altitude? 8.43 m/s^2

Ch 12 Notes Problem 4 Two ocean liners, each with a mass of 40,000,000 kilograms are moving on parallel courses, 100 m apart. What is the magnitude of the acceleration of one of the liners towards the other due to their mutual gravitational attraction? Model the ships as particles 2.67 x 10^-7

Ch 12 Notes Problem 5 On the way to the Moon the Apollo astronauts reached a point where the moon’s gravitational pull became stronger than the Earth’s. Determine the distance of this point from the center of the Earth. What is the acceleration due to the Earth’s gravity at this point? a)3.46 x 10^8 m b) 3.34 x 10^-3 m/s^2 toward the center

Problem 6 Three uniform spheres of mass 2 kg, 4 kg, and 6 kg are placed at the corners of a right triangle as shown. Calculate the net gravitational force on the 4 kg sphere, assuming the spheres are isolated from the rest of the Universe.

Ch 12 Notes Problem 6 (-100i + 59.3j) pN