1. Rewind
An astronaut on the moon throws a wrench straight up at 4.0 m/s. Three seconds later it falls downwards at a velocity of 0.8 m/s.
a. What was the acceleration of the wrench after it left the astronauts hand?
b. How high above the point from which it was released
was the wrench at 3.0 s?
c. How long would it take the wrench to return to the
position from which it was thrown?

2. Universal Gravitation
The Big Idea: Everything pulls on everything else.

3. Discussion
Here are some questions and answers which lead towards Newton’s Law of Universal Gravitation:
1. What causes the weight that each student feels?
2. What affects the size of the Earth’s pull on you? Why would you weigh a different amount on the Moon?
3. If the Earth is pulling down on you, then what else must be occurring, by Newton’s 3rd Law?
4. What happens to the strength of the pull of the Earth as you go further away from it?

4. Newton’s Law of Universal Gravitation
Newton discovered that gravity is universal. Everything pulls on everything else in a way that involves only mass and distance.

5. Universal Gravitation
Newton’s law of universal gravitation states that every object attracts every other object with a force that for any two objects is directly proportional to the mass of each object.
Newton deduced that the force decreases as the square of the distance between the centers of mass of the objects increases.

6. Universal Gravitation
The force of gravity between objects depends on the distance between their centers of mass.

7. Universal Gravitation
Your weight is less at the top of a mountain because you are farther from the center of Earth.

8. Universal Gravitation
The Universal Gravitational Constant, G
The law of universal gravitation can be expressed as an exact equation when a proportionality constant is introduced.
The universal gravitational constant, G, in the equation for universal gravitation describes the strength of gravity.

10. Universal Gravitation
The Universal Gravitational Constant, G
The force of gravity between two objects is found by multiplying their masses, dividing by the square of the distance between their centers, and then multiplying this result by G.
>The magnitude of G is given by the magnitude of the force between two masses of 1 kilogram each, 1 meter apart: newton. In scientific notation: G = 6.67 × 10−11 N·m2/kg2
>The units of G are such as to make the force of gravity come out in newtons.
Contributor: J. Flores
Source: Prentice Hall; Conceptual Physics

11. Universal Gravitation
The Mass of the Earth
>Once the value of G was known, the mass of Earth was easily calculated.
>The force that Earth exerts on a mass of 1 kilogram at its surface is 10 newtons.
>The distance between the 1-kilogram mass and the center of mass of Earth is Earth’s radius, 6.4 × 106 meters.
Contributor: J. Flores
Source: Prentice Hall; Conceptual Physics
So the mass of Earth m1 = 6 × 1024 kilograms.

12. Problem
Find the gravitational attraction, which exists between a 60 kg boy and a 50 kg girl at a distance of 3 m.
Now find the gravitational attraction between the 60 kg boy and the Earth using the Law of Universal Gravitation.
Is the result surprising?

13. Field lines represent the gravitational field about Earth.
Universal Gravitation
Gravitational Fields
Field lines represent the gravitational field about Earth.
Contributor: J. Flores
Source: Prentice Hall; Conceptual Physics

14. Gravitational Fields Inside a Planet
Universal Gravitation
Gravitational Fields Inside a Planet
As you fall into a hole bored through Earth, your acceleration diminishes. The pull of the mass above you partly cancels the pull below.
Contributor: J. Flores
Source: Prentice Hall; Conceptual Physics

15. Gravitational Fields Inside a Planet
Universal Gravitation
Gravitational Fields Inside a Planet
Starting at the North Pole end, you’d fall and gain speed all the way down to the center, and then overshoot and lose speed all the way to the South Pole.
You’d gain speed moving toward the center, and lose speed moving away from the center.
Without air drag, the trip would take nearly 45 minutes.
Contributor: J. Flores
Source: Prentice Hall; Conceptual Physics

16. Gravitational Fields Inside a Planet
Universal Gravitation
Gravitational Fields Inside a Planet
At the beginning of the fall, your acceleration would be g, but it would decrease as you continue toward the center of Earth.
As you are pulled “downward” toward Earth’s center, you are also being pulled “upward” by the part of Earth that is “above” you.
When you get to the center of Earth, the net force on you is zero.
There is no acceleration as you whiz with maximum speed past the center of Earth.
Contributor: J. Flores
Source: Prentice Hall; Conceptual Physics

17. Gravitational Fields Inside a Planet
Universal Gravitation
Gravitational Fields Inside a Planet
In a cavity at the center of Earth, your weight would be zero, because you would be pulled equally by gravity in all directions.
Contributor: J. Flores
Source: Prentice Hall; Conceptual Physics

18. Pg 182 # 28 For this problem, use ratios only to obtain the weight of a person at the following distances. Assume the person weighs 980 N on the surface of Earth. Earth’s radius is 6.38 x 106 m.
a) Three times the distance from the centre of Earth
b) km above the surface of Earth

19. Near Earth Approximation
Close to the Earth the field strength, g, is almost constant
Pg #24, 26, 27

20. Pg 182 # 26. On or near the surface of Earth, g is 9. 80 m/s2
Pg 182 # 26. On or near the surface of Earth, g is 9.80 m/s2. At what distance from Earth’s centre is the value of g m/s2 ? At what height above the surface of Earth does this occur?

21. Universal Gravitation and Orbits