Kepler's Laws of Planetary Motion

Tycho Brahe was a Danish nobleman who lived by himself on an island.  He became very interested in the motions of the planets and stars that he saw in the night’s sky.  He became so interested that he made careful observations of what the stars were doing each day for 20 years.

After he died, another astronomer, Johannes Kepler inherited all of Brahe’s lab notebooks.  Using his notebooks Kepler was able to develop three laws that describe the exact motions of the planets as they revolve around the Sun.

Law 1:  All objects travel around the Sun on an elliptical path.

Kepler's first law describes the shape of every objects orbit around the Sun as an ellipse.

An ellipse is a stretched out circle with two centers called foci.

Ellipses come in many shapes and sizes, so describing them can be tricky.  To describe the exact shape of an ellipse we must measure and calculate its eccentricity.

Eccentricity

eccentricity is a measure of how stretched out the ellipse is

To find the eccentricity of an ellipse we have to make two simple measurements.

Focal distance = distance between the foci

Major axis = the width of the ellipse measured by a line passing through both foci

Effects of elliptical orbits

Since planets orbit on an elliptical path with the sun at one focus, several thing change during the planet's orbit:

1. Distance to the Sun
• Perihelion = closest point.
• Aphelion = farthest point

2.  Orbital velocity - speed of the planets orbit

• faster when planet is close to the Sun
• slower when planet is far from the Sun

Law #2:  all planets cover equal areas of their orbit in equal times

Because their orbital speed changes, all planets will cover an equal area of their orbits in equal amounts of time.

law #3:  The farther a planet is from the sun, the longer it's orbital period.

Orbital period is the amount of time required to orbit the Sun once.

Planets that are farther from the Sun have longer orbital periods for 2 reasons:

1. The farther a planet is from the Sun, the slower it's orbital velocity.
2. The farther a planet is from the Sun, the larger the distance it has to travel to complete an orbit.

USING THE ESRT

pg 15 Solar System Data

The Solar System Data Table on page 15 of the ESRT contains all of the relevant details you may need to know for all of the bodies in our solar system including:

• distance from Sun
• period of rotation
• period of revolution
• eccentricity
• equatorial diameter
• mass
• density