Chapter 3: Motion of Astronomical Bodies

Chapter 3: Motion of Astronomical Bodies

A bit more on the Celestial Sphere and motions

This works OK if we only consider the stars. What happens when we add the Sun, Moon and planets?

The Celestial Sphere is an Earth-centered model with lots of

problems

The model developed by Ptolemy (an ancient Greek) used 52 spheres to explain all the observed heavenly

motions

Nicolaus Copernicus1453 – 1543

Proposed that the celestial sphere model was not

reality. Instead, he placed the Sun at the center of the solar system with Earth spinning on

it’s axis and orbiting the Sun in

a circular orbit

The Copernican Solar System

De Revolutionibus Orbium Coelestium was published in 1543, the year of his death.

The orbits were circles so he needed small “adjustments” to make it fit observations. Thus, there were problems, it wasn’t perfect.

Tycho Brahe: The Father of Observational Astronomy

1546 – 1601

The Observatory at Uraniborg

Johannes Kepler 1571 – 1630

Tycho hired Kepler to come work for him as an assistant. When Tycho died Kepler stole his data from Tycho’s heirs and used them to develop his Laws of Planetary Motion.

Kepler’s Laws of Planetary Motion are

empirical lawsThe laws are based on the observational data of Tycho Brahe. They fit the data but do not try to explain why the planets move as they do.

Kepler’s 1st Law

The Law of Ellipses

The planets move in elliptical orbits with the Sun located at one focus

Kepler’s 2nd Law

Law of Areas

A line drawn from a planet to the Sun will sweep out equal areas in equal time periods

Kepler’s 3rd Law

The Law of Harmonies

The ratio of the square of the orbital period to the cube of the semimajor axis (the orbital radius) is the same for all the planets

Why study Kepler’s Laws? Isn’t this Stellar Astronomy?

Look at the Eclipsing Binary Simulator on the ClassAction website Binary and Variable Star module

Isaac Newton1642 – 1727

Kepler didn’t try to explain why the planets moved as they did, just how they moved. It was another 50 years after Kepler before Isaac Newton explained why things moved as they did in the heavens and on Earth. He did it with three laws of motion and a law of universal gravitation

Newton’s 1st Law of Motion The Law of Inertia

An object in straight line uniform motion will continue that motion unchanged unless some external force acts on it

Newton’s Second Law The Force Law: F = maThe acceleration a body experiences is directly proportional to the net force acting on it and inversely proportional to its mass

changetotakesitlongHow

changesvelocitymuchHowonAccelerati

There can be an acceleration even when there isn’t a

change in speed

Mass plays an important part in Newton’s 2nd Law

A large mass requires a large force to produce a reasonable acceleration

F = ma

Newton’s Third LawThe Action-Reaction Law

For every force there is an equal and oppositereaction force

The Action-Reaction forces always apply to different

objects

While the force on each object may be the same, the acceleration (and thus damage) each experiences depends inversely on their mass according to Newton’s 2nd Law