Kepler’s Laws & Orbits
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Class Business
HW4 online, due Monday 4 October
Quiz 2 on Wednesday 6 October
In-class questions
From Last Lecture...
Retrograde motion is the apparent “backwards motion” of the
planets in the sky over the course of weeks and months.
Though geocentric models attempted to explain this, the heliocentric
model explained retrograde motion simply and accurately.
Copernicus, Tycho, Kepler, and Galileo all made extensive contributions
to astronomy that led to the acceptance of the heliocentric model.
What is an ellipse?
semi-major axis = average distance of planet from Sun
a reminder... 1 astronomical unit (AU) = average distance
of Earth to the Sun = length of Earth’s semi-major axis
Eccentricity = how much the
ellipse is “squashed”
Perfect circle’s eccentricity = 0
Earth’s eccentricity = 0.0167
Table of Eccentricities
Mercury
Venus
Earth
Moon
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
0.206
0.007
0.0167
0.05
0.09
0.05
0.05
0.05
0.009
0.249
Kepler’s First Law of Planetary Motion
The orbit of each planet around the Sun is an ellipse with the Sun at one focus.
Kepler’s First Law of Planetary Motion
What does it mean??
A planet’s distance from the Sun varies during its orbit.
Kepler’s Second Law of Planetary Motion
As a planet moves around its orbit, it sweeps out equal areas in equal times.
Kepler’s Second Law of Planetary Motion
What does it mean??
A planet travels faster when it is nearer to the Sun, and
slower when it is further from the Sun.
Sound familiar?? It should! -- conservation of angular momentum
Kepler’s Third Law of Planetary Motion
A planet’s average distance from the Sun, and the amount of time it takes to
complete one orbit around the Sun, obey a precise mathematical relationship.
Kepler’s Third Law of Planetary Motion
2
p
=
length of year (in years)
3
a
semi-major axis (in AU)
2
p
=
3
a
Earth: 1 * 1 = 1 * 1 * 1
Jupiter: 11.862 * 11.862 = 5.2 * 5.2 * 5.2
Kepler’s Third Law of Planetary Motion
What does it mean??
More distant planets orbit the Sun at slower average speeds.
Isaac Newton demonstrated that Kepler’s Laws were a
consequence of his laws of motion and law of universal gravitation.
Newton also went on to extend and generalize Kepler’s Laws
into his theory of gravity.
Satellites around the Earth
Moons around other planets
1. Kepler’s Laws apply to all orbiting objects, not just
planets around the Sun!
Planets around other stars
Asteroids and Comets
2. An ellipse is not the only possible orbit shape.
3. Objects actually orbit around
their common center of mass.
How can we measure the mass of objects in space?
4. We can use Newton’s version of Kepler’s Third
Law to measure the mass of objects in space.
2
p
= (constant) x
3
a
The constant above depends on the masses of the two
objects.
4. We can use Newton’s version of Kepler’s Third
Law to measure the mass of objects in space.
Note: The constant in Newton’s version of Kepler’s Third Law is not
universal. It depends on the combined mass of the two objects.
(The simple version of the law shown earlier only works for objects orbiting the Sun, and in the
given units.)