Lecture 10 2/6/2013 12:23:00 PM
Does the Universe Revolve around you? Part II
Review: Ptolemaic Model:
Geocentric (centered on Earth)
Based on uniform circular motion (objects move in circles at
Explain retrograde motion of planets using epicycles (circles on
Review: Copernican Model:
Heliocentric (centered on the sun)
Kept the idea of uniform circular motion.
Explains retrograde motion as the result of inner planets moving
faster and overtaking the outer ones.
Mercury and Venus are inside the earth’s orbit, so they always
appear close to the sun.
o The planets that orbit farther away from the sun.
o (from earth, the superior planets are Mars, Jupiter, Saturn
and Uranus and Neptune.)
o The planets that are closer to the sun
o (from earth, these are Mercury and Venus.)
superior planets can appear in the opposite direction from the sun,
but inferior planets are always on the same side of the sky as the
Retrograde motion occurs when Earth and a superior planet are on
the same side of the sun
Tycho Brahe and Johannes Kepler:
Using Brahe’s observations, Kepler developed a new, more accurate
Abandoned uniform circular motion Keplers second law: a line from a planet to the sun sweeps over equal areas
in equal times:
This means that a planet moves fastest at is perihelion (closest to
the sun) and slowest at its aphelion (farthest away)
Keplers third law: a planets orbital period squares is proportional to its
average distance from the Sun cubed:
Note: the first and second laws describe each planet’s orbit, but the
third law describes a comparison between orbits of different
If we use the earth to compare all the other planets to, then we can
say P^2 = a^3
Where P is the orbital period in earth-years and a in the planets
average distance from the sun in a.u.
o An asteroid orbits at a distance of 4 au from the Sun. How
long does it take to make an orbit?
o A = 4
o P^2 = a^3 = 4^3 = 64
o P = the square root of 64 = 8
o ANSWER: 8 years
o Another object orbits the sun once every 27 year. What is its
average distance from the sun?
o A^3 = P^2 = 729
o A- 9, because 9^3 = 9x9x9=729
o ANSWER: 9 au
Helped solidify the Copernican revolution by overcoming some
objections to the heliocentric view.
Made telescope observations that helped confirm the heliocentric
picture and weaken the justification for the geocentric model.
Though experiments, began to understand motion better, a process
continued later by Newton. He did not invent the telescope, but he was the first person known
to have used telescopes to look at astronomical objects.
Galileo’s Telescope Discoveries:
Observed spots (imperfections) on the sun, and mountains and
valleys on the moon,
These observations challenged the idea of perfect, unchanging
heavens, and suggested other worlds like Earth.
Saw four moons orbiting Jupiter
This showed that orbits could happen around other objects besides
Observations of the phases of Venus confirmed that Venus orbits
(in Ptolemaic model, Venus would only appear as a crescent—
Galileo saw a whole cycle of phases.
can you ever see Jupiter in a crescent phase?
Sir Isaac Newton:
Understood planetary motion as governed by universal laws that
also apply on earth.
Completing the work Galileo had begun, completely revised our
understanding of motion, weeping away more of the objections to
the heliocentric model.
Invented a new type of math.
o (Calculus) to use in studying motion.
Newton’s First Law:
An object at rest remains at rest unless a force acts on it; an object
in motion continues in a straight line at constant velocity unless a
force acts on it.
That means there’s nothing “perfect” or natural” about circular
Any change in either speed or direction is called acceleration and
requires force. Acceleration:
Which of the following are accelerating (as scientists use the
o A stopped train that starts moving again
o A ball speeding up as it falls
o A car slowing down by breaking
o A car going around a curve at a constant speed
o A figure skater making a figure eight.
All of the above. According to Newton’s first law,
none of those can happen without a force.
The moon and planets undergo accelerated motion, so there must
be a force acting on them (otherwise, the