Lecture 4: Gravity and the planets motion

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Lecture 4 Gravity and the planets motion
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Planet wanderer (in Greek)
The motion of Mars
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Copernicus SUN IS IN THE CENTER
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Cassiopeia
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Johannes Kepler
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Used the data accumulated by Tycho Brahe
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Ellipses!
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Keplers first law
The orbit of a planet is an ellipse with the Sun
at one focus
Least elongated Venus e0.007
Most elongated Pluto e0.248
The speed of the planet varies along its orbit.
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Keplers second law
A line joining a planet and the sun sweeps out
equal areas in equal intervals of time
Law of Equal areas
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Keplers third law
The square of the sidereal period of a planet is
directly proportional to the cube of the
semi-major axis of the orbit
Period in YEARS
Semimajor axis in AU
This formula is valid only for a planet around
the Sun
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Isaac Newton (1642-1727)
Introduced the basic laws of motion
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Newtons third Law
Whenever a body exerts a force on a second
body, the second body exerts an equal an opposite
force on the first
To any action there is a reaction equal and
opposite
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Gravity centrifugal force
Question of the day Why do astronauts feel
weightless?
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Newton law of universal gravitation
Two bodies attract each other with a force that
is directly proportional to the mass of each
body and inversely proportional To the square of
the distance
Units!!!!
Universal constant of gravitation
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Gravity, planets, satellites and tides
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Newton law of universal gravitation
Two bodies attract each other with a force that
is directly proportional to the mass of each
body and inversely proportional to the square of
the distance
Units!!!!
Universal constant of gravitation
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Newtons laws include Keplers laws (and much
more)
Nature of gravity? elliptical orbits actually
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Newtons form of Keplers third law
Sidereal period
This IS Universal
Thats how one infers masses of planets
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Phase of the moon?
Other cases?
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Finding planets around other stars
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How to see them if they are there?
Planets should make star wobble
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Reading assignment pp 61-85 in The Universe