1. Universal Gravitation

2. Newton’s Law of Universal Gravitation
The gravitational force between any 2 bodies varies directly as the product of their masses and inversely as the square of the distance between them. Also called the inverse square law. Equation: F= G m1m2/d2 Force equals Universal constant x mass of body 1 x mass of body 2 / distance squared
Newton’s Law of Universal Gravitation

3. A 2 kg mass is at rest on the surface of the Earth
A 2 kg mass is at rest on the surface of the Earth. Find the force of attraction that exists between the mass and Earth. The radius of Earth is 6.4 x 10^6 m. The mass of earth is 6 x 10^24 kg.
Example Problem UG

4. Motion of Planets and Satellites
To solve for the velocity of a satellite the equation is : v = (square root of) Gme/r The time for the satellite to orbit the earth is the period or T. Equation: T = 2 (square root of ) r3/Gme Acceleration of gravity Calculated: a= g(Re/d)2
Motion of Planets and Satellites

5. Universal Gravitation Example Problems
1. What happens to the force of attraction if one mass is doubled?
2. What happens to the force of attraction if the distance between the two objects is doubled?
3. What happens to the force of attraction if both masses are doubled and the distance is tripled?
Universal Gravitation Example Problems

6. 1. What force holds the planets in orbit around the sun?
2. What would happen to the planets if this force was insufficient, or the velocities of planets increased greatly?
Questions