Universal Gravitation 3.1-3.2

The Gravitational Field Strength The gravitational field strength is the amount of force acting on each kilogram of mass. It is measured in N/Kg. It is not the same everywhere.

Size of the Gravitational Field Strength The gravitational field strength is a vector quantity whose direction is always toward the center of the earth. As the gravitational field strength and the acceleration due to gravity are numerically equal, the same symbol, g, is used for both. g = 9.8 N/kg, or g = 9.8 m/s2 9.8 N/kg is an average for the earth’s surface

Variation in Earth’s Gravitational Field Strength Latitude (⁰) g (N/kg) Distance to centre (km) 0 (equator) 9.7805 6378 15 9.7839 6377 30 9.7934 6373 45 9.8063 6367 60 9.8192 6362 75 9.8287 6358 90 (north pole) 9.8322 6357

Free Fall, Weightlessness, and Microgravity

Newton’s Law of Universal Gravitation The force of gravitational attraction between any two objects is directly proportional to the product of the masses of the objects, and inversely proportional to the square of the distance between their centres.

The equation for this force is... Units: F (N) m (kg) r (m) G (N.m2/kg2 ) where G is a constant G = 6.67 x 10-11 N.m2/kg2

Cavendish Experiment Used to determine the Universal Gravitational Constant, G

Gravitational Attraction in the Solar system and Beyond What causes the Ocean tides? How do scientists decide where satellites should orbit Earth?

Mass on Planet’s surface (kg) Force of Gravity on this mass (N) Practice Problems Copy and complete the following chart. Assume that the same object is used on each of the three planets. Planet Mass on Planet’s surface (kg) Force of Gravity on this mass (N) g (N/kg) Mercury 57 188 --- b) Venus 462 c) Jupiter 26

2 ) The force of gravity on an astronaut us 600 N at the Earth’s surface. What is the force of gravity on him at each of the following distances from the centre of the Earth, measured in multiples of the Earth’s radius? (a) 2 (b) 5 (c) 10 (d) 20

3 ) Two of the largest oil tankers in the world, the Batilus and the Bellaya, have masses of 492 000 t, fully loaded. If they were moored side by side, 1.0 m apart, their centres would be 64m apart. Calculate the force of gravity between them.

4 ) Sirius B is a white dwarf star, in orbit around Sirius, with a mass of 2.0x 1030 kg, and a radius of 2.4x107 m. What is the force on a 1.0 kg mass on the surface of Sirius B? What is the acceleration due to gravity on the surface of Sirius B?

Coming up.... Static and Kinetic Friction force on Wednesday Quiz on Friday....