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Kepler’s Laws of Planetary Motion
A bit of History
• Tycho Brahe – Danish Astronomer 1547• He was given an island in the North Sea to set up an observatory. Tycho observed the stars for 20 years and collected data.
• The man with the gold replacement nose!
Johannes Kepler
Polish Astronomer born 1571
Interpreted Brahe’s data.
Kepler’s Laws
• 1st Law - All objects in the solar system travel in elliptical paths.
• An ellipse has two focal points.
• The sun is at one focal point.• The eccentricity of an ellipse is a ratio
of the two major axes.
Kepler’s Laws
• 2nd Law – All objects sweep out equal areas in equal times.
• S = Sun is at one of the focal points.
Kepler’s Laws
• 2nd Law – • Area of triangle
ASB(green) equals
area of triangle CSD(blue)
This is true because of the conservation of angular momentum.
Kepler’s Laws
• Point B is summer for New York
• Point D is winter for New York
• Is the speed of the Earth constant?
• When is the Earth moving fastest in its orbit around the sun?
Kepler’s Laws
• 3rd Law - R2/T3 is a constant for every object in the solar system moving around the sun.
• This is true because of Newton’s 2nd Law of motion
• F = G M1M2/r2 = M2v2
Sir Isaac Newton
• Describes why the planets behave the way they do – Gravity – It’s everywhere! Not just on the Earth!
Gravitation
• What variables affect the gravitational attraction between two objects.
1) Mass of object #1
Earth
This is a direct and linear relationship.
F
M earth
Gravitation
2) Mass of object #2
You
This is a direct and linear relationship.
F
M you
Gravitation
• 3) Distance between the centers of the two
objects - r.
This is an inverse square relationship.
F
r
Newton’s Law of Gravitational Attraction
• F = G M1M2/r2
• G = Universal Gravitational Constant =
6.7 x 10-11 N-m2/kg2
Newton’s Law of Universal Gravitation
• It is only an attractive force. • It acts at a distance.• It is an inverse square law.• It describes the gravitational
force that exists between all bodies.
Force of Attraction
• What is the force of attraction between a 50 Kg girl and a 70 Kg boy standing 1 meter apart?
Force of Attraction
• F = G M1M2/r2
• M = 50 Kg
• M = 70 Kg
• r = 1 m
• G = 6.7 x 10-11
• F = ?
The Cavendish Experiment -1798
• Proves that even small objects have gravitational attraction for each other.
Newton’s 2nd Law
• F = m2a = G MeM2/r2
So a = G Me/r2
This is the acceleration due to gravity on a planet with mass - Me and a radius of r.
Distance from the Earth’s Center
Local g
m/s/s
Local Weight w = mg
½ Re 39.2 2800 N
1 Re 9.8 700 N
2 Re 9.8/4 = 2.45 172 N
3 Re 9.8/9 = 1.1 77 N
4 Re 9.8/16 = 0.61 43 N
Suddenly, through forces not yet fully understood, Darren Belsky’s apartment became the center of a
new black hole.
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