planetary motion it’s what really makes the world go around
TRANSCRIPT
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Planetary Motion
It’s what really makes the world go around.
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What is a year and a day? (write this down!!)
• A year = time it takes for the Earth to travel around the sun once (orbital period)
• A day - how long it takes a planet to spin on its axis
• AU - Astronomical Unit - distance from
Sun to Earth
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Satellites
• Satellites are bodies in orbit around a central point.
• The moon is a satellite of Earth and Earth is a satellite of the Sun.
• Most satellites are the result of passing objects that get caught by the pull of a larger body and are not moving fast enough to get away.
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Speed : life or death
• Too slow, the satellite will get pulled into the planet and crash into it.
• Too fast, it just shoots on by with a change in its path.
• Just right, it enters into an elliptical orbit around the body.
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Drawing an ellipse
• The black line is a piece of string
• The thumb tacks are the “foci” of the ellipse
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Johannes Kepler
• 1571-1630• Made many
observations of the motions of Mars
• Supported Galileo• Kepler didn’t know why
his Laws worked—a law summarizes observations, it doesn’t explain the reason!
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Kepler’s Laws
How can we describe how the planets move?
Decades of observations + (Math afterwards) = SUCCESS
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Kepler’s First Law
• Planets travel in elliptical orbits about the sun
• The sun is at one foci of the ellipse
• Eccentricity (e) is used to describe the shape.
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Orbits in the Solar System
• The planets have nearly circular orbits
• Lower e = closer to a circle
• Icarus, an asteroid, has a very elliptical orbit
• Comets have the most elliptical orbits
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Halley’s cometDirect Motion: Planet will generally move from East to West across the sky
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• Retrograde motion: planet will move from East to West across the sky but occasionally move West to East- caused by differences in speed of orbit
• As we see from the animation, Mars isn’t really moving backwards, but it appears to when viewed from Earth!
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An edge on view of the solar system
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First Law
• Kepler’s First Law was developed from the data he collected.
• It explained the Retrograde motion observed for planets in the sky.
• It was the first relationship that did not have special conditions for various times of the year.
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Kepler’s Second Law• The planets sweep out equal areas in equal times
• T1=T2, A1=A2• The planets move faster on the side of the orbit closer to
the sun• The planets slow as they get further from the sun
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2nd Law In Motion• On the right is a
circular orbit• On the left is an
elliptical orbit.• What can you tell
about the speed of the satellite? What about the blue areas?
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Kepler’s Third Law
13
2
R
T
• The square of the period of the rotation is proportional to the cube of the semi-major axis of the ellipse.
• For every body orbiting the same foci, the ratios of T2/R3 are equal to each other.
• For all bodies in orbit around the sun,
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Semi-major axis
• The arrow represents the semi-major axis.
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Kepler’s Third Law
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Does Kepler’s 3rd Law Work?
• Astronomical unit = A.U.= average distance between the earth and the sun
– A.U. = 150 million km or 93 million miles
• 1 year = period of Earth’s orbit• T2 = R3 if T is in years and R is in A.U.
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Does Kepler’s 3rd Law Work? Prove that T²/R³=1 for each planet below and turn
in for credit. Show at least one set of calculations!
Planet Period T (yr)
Semi-Major Axis R (AU)
T2 R3
Mercury 0.24 0.39 0.06 0.06
Venus 0.62 0.72 0.39 0.37
Earth 1.00 1.00 1.00 1.00
Mars 1.88 1.52 3.53 3.51
Jupiter 11.9 5.20 142 141
Saturn 29.5 9.54 870 868
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So What?
• Kepler didn’t know why his laws worked! Remember a law just describes a relationship, it does not tell you why.
• Newton was able to show that he could derive Kepler’s Laws from Newton’s three laws and the theory of universal gravitation.
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Newton’s Law of Universal Gravitation
• If one of the masses doubles the force doubles• If the radius doubles the force decreases to 1/4
221
r
mmGF
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What does the gravitational force look like as a function of distance?
Universal Gravitation
0
20
40
60
80
100
120
140
160
180
200
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Distance between objects
Fo
rce
m1,m2=1
m1=1, m2=2
m1=1,m2=10