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Kepler, Newton, Gravity, and Orbits
Kepler’s 3 Laws of Planetary Motion.
Planets follow elliptical orbits around the sun. (1610)Planetary orbits sweep out equal areas in equal times. (1610)A planet’s year squared equals the orbit size cubed. (1618)
What is Jupiter’s orbital period? It orbital size is 5.2 A.U. Astronomical Unit = earth to sun distance =
×
6
km
p
2
a
3
p
a
3
3
years.
Describing Motion. Speed: 60 miles/hour means a car travels 60 miles in an hourVelocity tells both speed and direction. 60 mph going north.Acceleration: Measure of change in speed and/or direction.Acceleration due to gravity. 9.8 meters/second per second.
Momentum, Angular Momentum, and Force Momentum = mass
×
velocity
Force changes object’s momentum (speed and/or direction)Angular Momentum = mass
×
velocity
×
lever arm
Thursday, 1 September 2011 Astronomy 104
Kepler, Newton, Gravity, and Orbits
(page 1)
Dr. Don Summers
U. of Mississippi–Oxford
Weight (pounds) and Mass (kilograms) Weight is how hard gravity pulls on your mass, which is fixed.In free fall your weight vanishes, e.g. astronauts in orbit.
Newton’s 3 Laws of Motion (published in 1687) An object has constant velocity unless acted on by a force.Force = mass
×
acceleration. F = ma.
a = F/m.
For any force, there is an equal and opposite reaction force.
Newton’s Universal Law of Gravitation
F
GM m/d
2
F
is force.
M m
are masses.
d
is distance.
G
is constant.
On earth:
F
ma
GM m/d
2
, a
GM/d
2
= 9.8 m/s
2
All objects fall at the same rate regardless of their mass.
Orbits:
F
GM m/d
2
p
2
= [
π
2
G
M
m
))]
a
3
Newton gives both 9.8 m/s
2
on earth and
p
2
a
3
in orbit.
Connects apples falling on earth to Kepler’s 3rd Law of orbits.Adds measurement of mass from orbital period and size.Sirius A/B: M + m
a
3
/p
2
= (20 A
U
3
(50 yr
2
= 3 M
sun
Sirius A/B orbit a common center of mass. M = 2, m = 1Sirius B has the mass of the sun but the size of the earth.Double stars fall around each other. Elliptical orbits.
Thursday, 1 September 2011 Astronomy 104
Kepler, Newton, Gravity, and Orbits
(page 2)
Dr. Don Summers
U. of Mississippi–Oxford
