Goals

• Explain how accurate observations led to Heliocentric model

• Explain retrograde motion

• Describe contributions of Copernicus, Tycho, Galileo, and Kepler

• Explain how we know the size of our Solar system

• Explain Newton’s laws of motion and gravity

Ancient astronomers noticed some of the stars would “wander” against the background of fixed stars. These “planets” were given extreme significance as people tried to find meanings from the heavens.

The planets as well as the Sun and Moon were each given a day of the week in their honor. Saturn-Saturday, Sun-Sunday, Moon-Monday, etc.

Planetary Motion

Early astronomers were obsessed with perfection and thought the motions of the heavenly bodies should be circles.

They also thought the Earth was stationary because they could not fell the Earth move beneath them.

This led to the Earth centered or Geocentric model of which Ptolemy was the main supporter.

While observations were crude the model seemed to work, but as observations improved it became clear that something was wrong.

One main concern was how to account for retrograde motion where the normal eastward motion of the planets is briefly interrupted with the looping motion. In order to modify his theory, Ptolemy had to add circles to circles (deferent and Epicycle) to explain retrograde motion.

Retrograde motion is defined as the brief westward motion that a planet appears to take when a slower outer planet is passed by a faster inner planet.

While the geocentric model required a complicated set of circles on circles to explain retrograde motion, the Sun centered (Heliocentric) model easily explained the observations. Copernicus became the main supporter for the Heliocentric model.

While the Copernican theory did explain the observations better with a simpler model, civilization at the time resisted the model partly because the church of the time had declared the geocentric model was described in the Bible as correct with out regard for scientific observations.

What finally convinced everyone was the observations of Galileo Galilei.

Using his telescope, Galileo discovered:

• the Moon had craters and mountains like the Earth and was not perfect.

• the Sun was imperfect (sunspots) and rotated on its own axis.

• Jupiter had four moons in orbit around it which showed things could orbit other things besides the Earth.

• Venus showed complete set of phases only explainable if it was in orbit around the Sun not the Earth.

Because of his insistence of the Heliocentric model based on his observations, Galileo was arrested by the church and was not forgiven of his “crimes” until 1992.

The only way to explain the phases of Venus was if it orbited the Sun and not the Earth.

Kepler

Now that we have the correct heliocentric model we need to explain why it is the way it is.

• What causes the planets to orbit the Sun ?

• Why do the different planets have different speeds?

• How can we predict their positions in the future?

With new higher accuracy observations of Tycho Brahe, Kepler was able to form three laws of planetary motion.

Kepler’s Laws of Motion

First Law: The orbits of the planets are in the shape of anellipse with the sun at one focus.

Second Law: a vector from the sun to the planet sweeps out equal areas in equal times (conservation of angular momentum).

Third Law: the period of a planet and its semimajor axis are related by.

P2 (in Earth years) = a3 (in astronomical units) Mtotal (in solar units)

While Kepler discovered certain relationships and facts concerning how the planets moved about the Sun he could not explain why. Newton invented calculus to derive Kepler’s Laws and made three of his own.

First Law: objects remain in motion or at rest unless acted upon by a force.

Newton’s Laws

Second Law: F = Ma: where F = force, M= mass, a = acceleration

Third Law: F12 = - F21

Gravity: Fg = GMm/d2 Where Fg is the force due to gravity, G is a constant, and M and m are the mass of the two objects, and d is the distance of their separation.

Thus gravity provides the force which causes objects to orbit other objects. Newton invented calculus to help him solve his problems and also laid the groundwork for the theory of earth orbiting satellites.

Kepler’s third law allows us to detect planets around other stars and determine their mass.

With Kepler’s laws we can now relate the relative sizes of the orbits of the planets. This allows modern astronomers to measure the distance between planets and thus determine the size of the solar system.