Isaac and the Apple Tree
Approximate Force of Gravity
𝑚1 ∗ 𝑚2
𝐹~
𝑑2
(~ means approximately)
𝑚1 = Mass of object 1
𝑚2 = Mass of object 2
𝑑 = distance between objects
𝐹 = force of gravity
Exact Force of Gravity
𝑚1 ∗ 𝑚2
𝐹=𝐺
𝑑2
G = Gravitational Constant
G = 6.67 x 10-11 N
𝑚2
𝑘𝑔2
Inverse Square Law
𝑚1 ∗ 𝑚2
𝐹=𝐺
𝑑2
Intensity =
1
𝑑2
d = Distance between objects
Einstein’s Theory of Relativity
 Explains how gravity works
 Spacetime
Warping of Spacetime
Orbits in Spacetime
Demonstration Video
 Gravity in terms of Spacetime.
https://www.youtube.com/watch?v=0w7zc6kvf1o
 What is gravitational lensing?
https://www.youtube.com/watch?v=4qoDHdIsIg4
Gravitational Lensing
 Experiment gave evidence of Einstein’s Theory of
Relativity
Discussion Questions
Somewhere between the Earth and the Moon, gravity
from these two bodies on an object would be equal.
Is this location closer to the Earth or the Moon?
Why?
2. The value of “g” at Earth’s surface is about 9.8m/s2.
What is the value of “g” at twice the Earth’s radius?
How do you know?
3. You weigh a tiny bit less when you are in the lobby of
a massive skyscraper than you do here in school.
Why is that?
1.
Discussion Questions (cont.)
4. What is Spacetime?
5. Why does the Moon orbit the Earth according to
Einstein?
6. If the Sun were to shrink in diameter to the size of a
black hole, but maintain its mass, would the orbit of
Earth change? Why or Why not?
Practice
𝑚1 ∗ 𝑚2
𝐹=𝐺
𝑑2
 Calculate the force between two objects that have masses of 70 kilograms
and 2000 kilograms separated by a distance of 1 meter.
70𝑘𝑔 ∗ 2000𝑘𝑔
𝐹=𝐺
(1𝑚)2
𝐹 = (6.67 ∗
𝑚2
𝑘𝑔2
−11
10 𝑁 )(140,000 )
𝑘𝑔2
𝑚2
=
9.34 ∗ 10-6N
About the amount of gravity between you and a car.
Practice with Scientific Notation
𝐹=𝐺
𝑚1 ∗ 𝑚 2
𝑑2
 Calculate the force between the Earth and a 1 kg object on the Earth’s surface.
 Mass of Earth = 5.9736 x 1024 kg
 Radius of Earth = 6.38 x 106 m
𝐹 = (6.67 ∗
10−11𝑁
𝑚2 5.9736 x 1024 kg ∗ 1 kg
)
𝑘𝑔2
(6.38 x 106 𝑚)2
𝐹 = (6.67 ∗ 10−11𝑁
𝑚2
)(1.4675 x
𝑘𝑔2
1011
𝑘𝑔2
)
𝑚2
= 9.8 N
𝐹
𝑚
=𝑎=
9.8 𝑁
1 𝑘𝑔
=
𝒎
𝟗. 𝟖 𝟐
𝒔
=g
Work Cited
 http://idology.files.wordpress.com/2008/12/isaac_newton_hd.jpg
 http://www.sciencemuseum.org.uk/onlinestuff/snot/~/media/818B16FC66D44386927D7
89A9280BA5D.ashx?db=master
 http://llamabutchers.mu.nu/Earth%20from%20Moon.gif
 http://www.freedigitalphotos.net/images/photos/man-binoculars.jpg
 http://rosettasister.files.wordpress.com/2009/02/alberteinstein.jpg
 http://bierbower.net/images/Gravity%20Its%20the%20Law.jpg
 http://www.math.sunysb.edu/~tony/whatsnew/column/grav-lens0299/images/HSTgravlens.jpg
 http://kwisp.files.wordpress.com/2010/01/e9889d89b84b4324b0d3c35d9d8f6332.jpg