In this lecture we cover Kepler's Laws and Newton's Laws. There are no
slides for these. Please read the relevant chapters in the book.
We observer retrograde motion (the planet appears to move
backwards) in the movement of the
planets.
Hipparcos was the first to consider the motions of the planets and
proposed the geocentric model. Ptolomy came up with the most
famous/detailed version of this model. He said
the planets move on circles around the earth. This is the main
deferent. On top of this motion is a small correction called an
epicycle. This can give rise to retrograde motion.
Moves quickly at the top of the epicycle
and slowly at the bottom
Retrograde motion is easier to explain in a heliocentric (sun
centered) universe. This was first suggested by Aristarchus. Also know
that the sun is larger than the earth so more natural to be at the
center of things. Idea forgotten until...
Copernicus (1473-1543) came along. He named Mercury and Venus as
interior planets and Mars etc as superior planets. However, Copernicus
insisted on circular orbits.
Definition of opposition and conjunction, he saw that venus and
mercury were always found close to the sun, something more natural in
a heliocentric model.
The next figure is Tycho Brahe (1546-1601). Tycho realized that is the
earth was moving we would see a parallax effect (see below). Didn't
see one so he said earth wasn't moving - a blow to Copernicus
model. However, Brahe made very accurate measurements of the motions
of the planets.
Parallax - a nearby object will appear to move against the background
stars as the earth rotates. All the stars in the sky are so far away
that a parallax is hard to observe. Will discuse this more later.
Kepler (1571-1630) used Brahe's data to form equations for the motions
of the planets
K1: The orbit of a planet about the Sun is an ellipse with the sun at
one focus
K2: A line joining a planet and the Sun sweeps out equal areas in
equal intervals of time (conservation of angular momentum)
K3: The square of the sidereal period of a planet is directly
proportional to the cube of the semimajor axis of the orbit P^2
proportional to a^3 (watch the units!)
An example of K2. Definition of perihelion and aphelion.
Kepler's third law in action. P^2 propto a^3. See the HW and class
examples for more of these.
Galileo Galilei (1564-1642) provided evidence for the sun centered
universe. He was the first person to use a telescope. He saw mountains
on the moon, rings of Saturn
He noted that Venus had phases (like the moon) and appeared sometimes
larger and sometimes smaller
This is a natural consequence of a heliocentric orbit
but very hard to explain in a geocentric orbit
Galileo also saw that Jupiter had moons that were orbiting around
it. Another body with things moving round it removed the importance of
earth in the solar system. He was placed under house arrest for his
troubles as it went against the ideas of the Catholic church.
How the moons appear to move
Other pieces of evidence.
The next person to come along was Newton (1642-1727). He was a great
mathematician and the first person to use maths to derive the motions
of the planets and laws of gravity.
The laws we will use here are
F = ma = mg (the acceleration due to gravity on Earth = g = 10 m/s^2)
F = GMm/r^2 - Newton's law of Gravitation
Newton found that elliptical orbits were a very natural consequence of
his laws. If a planet was moving at a special speed it would make
exactly circular orbits but the planet can still rotate round the sun
in elliptical bound stable orbits. The speed determines the shape.
Other orbits would be possible but hyperbolas and parabolas are not
bound orbits. These are all examples of conic sections.
