Download Universal Gravitation

Kepler’s Laws
Newton’s Law of Universal Gravitation was based
on the work of Johannes Kepler.
Kepler’s 3 laws:
1. Planets move in elliptical orbits with the
sun at one focus.
Kepler’s 3 laws:
2. A line joining the sun and a planet sweeps
out equal areas in equal times
Note: this means that planets must travel
faster when it is near the sun, and slower
when it is farthest
Kepler’s 3 laws:
3. The following ratio is the same for all the
planets or satellites which orbit around the same
central body
3
R
2
T
Where R = radius of orbit (metres or
astronomical units)
And T = period of orbit
Note: 1 AU = average radius of Earth
orbit = 1.49 x 10 11 m
Click here for more info on AU
3
*Ksun = R = 3.35 x 1018 m3/s2
T
2
All objects orbiting the sun have this ratio of
radius cubed to period squared.
2
m /s
Sample 1: How fast in
is an
area being swept out by a line
joining the Earth and the sun?
2
area
total
area(

R
)
Area per second =

time
period(T)
A/s =
R 2  (1.49x1011 )2

7
T
3.16x10
6.97x1022
15 m2 / s
A/s =

2.21x10
7
3.16x10
Sample 2: A planet in our solar
system has a period of revolution
of 7.6 x 106 seconds. Find the
radius of the planet’s orbit and
identify the planet from the table
in the booklet.
3
Ksun = R
2
T
3.35x1018 
R3
(7.6 x106 ) 2
R 3 3.35x1018 (7.6 x106 ) 2
R 3 1.93x1032
R  5.79 x1010 m
The planet is Mercury
• Sample 3: Mars has a radius of orbit of 1.52
astronomical units, and revolves around the
sun once every 690 days. If Venus has an
orbit of radius of 0.72 AU, how long does it
take Venus to go around the sun?
3
3
R R

2
2
T T
3
3
1.52  0.72
2
2
690
T
2
T  50601
T  225 days
• Read textbook pages 217 – 220 for more
info on Kepler’s Laws.