1. Newton’s Law of Gravity
Starter

2. Newton’s Law of Gravity
Starter
If the mass of the Earth stayed the same but the radius
of the Earth doubles, what happens to your weight?
a. it doubles also.
b. it stays the same.
c. it drops to 1/2 of the original.
d. it drops to ¼ of the original.
g = MG/R2

3. Newton’s Law of Gravity
Starter
To increase the speed of an Earth satellite, should it
be placed in an orbit closer to the Earth or further away
from the Earth?

4. Practice Newton’s Law of Gravity : Every two objects attract each
other with a gravitational force given by:
F = m1m2G/r2
m1 = mass of the first object in kg
m2 = mass of the second object in kg
r = distance between the two masses in meters
G = 6.67 x 10-11

5. Practice / Example
Find the gravitational force between the Earth and a 50,000kg asteroid that is 12 x 106 m away.
masteroid = x104 kg mEarth = x 1024 kg
G = x r = 12 x 106 m
F = m1m2G/r2
= (5.00 x104 )( 6.00 x 1024 )(6.67 x ) / (12 x 106 )2
= x 105 Newtons = 139,000 Newtons

6. Practice / Example
Find the gravitational force between Saturn and the sun.
msun = x msaturn = x 1026
G = x r = x 109
F = m1m2G/r2 =
(1.99 x1030 )(5.71 x 1026 )(6.67 x ) / (1430 x 109)2
= x 1022 Newtons

7. Where does g come from?
Consider a person, mass m, standing on the Earth.
His weight is: F = mMG/R2 = mg
Cancel the person’s mass m:
g = MG/R2
=(6x1024)(6.67x10-11)/(6.4x106)2
= 9.8 m/s2

8. Circular Orbits Orbit Velocity Period
F = mv2/R = mMG/R2 and v = 2pR / T
Orbit Velocity
Period
R = Orbit Radius M = mass of planet or sun being orbited
(The mass of the satellite is not in these 2 equations.)

9. Example The moon is 385 x 106 m from the Earth’s center.
R = 385 x MEarth = 6 x 1024
What is its orbit velocity?
v = (MG/R)1/2 = ( ( 6 x 1024)(6.67 x 10-11)/(385 x106))1/2
= 1019 m/s
What is the period?
T = 2pR/v = (2p ) (385 x 106)/ = 2.37 x 106 seconds
2.37 x 106 seconds ( 1hr/3600s)(1 day/24 hr) = 27.5 days

10. Period of revolution, years
Useful Data
Quantity
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
Mean distance from sun
57.9
108
150
228
778
1,430
2,870
4,500
5,900
(109 m)
Mass (kg)
3.331E+23
4.866E+24
5.97E+24
6.388E+23
1.898E+27
5.677E+26
8.657E+25
1.027E+26
5.97E+22
Period of revolution, years
0.241
0.615 1
1.88
11.9
29.5 84
165
248
Orbital speed,
47.9 35
29.8
24.1
13.1
9.64
6.81
5.43
4.74
(103 m/s)
Mass (Earth=1)
0.0558
0.815
0.107
318
95.1
14.5
17.2
0.01
Moon mass
Distance to Earth
Mass of Sun
Mass of Earth
Radius of Earth
7.36E22 kg
3.84E8 m
1.99E30 kg
5.97 E24 kg
6.4E6m