Kepler's Laws

Keplers First Law

Every orbiting object follows an elliptical path. The object orbited is located not at the center of the ellipse, however, but at a point called the focus.

Ellipse

an oval shape

Ellipse Equation

x²/a² + y²/b² = 1

What is a?

semimajor axis, the longest distance x-axis

What is b?

semiminor axis, the shortest distance y-axis

Perihelion

when the object is near or close to the focus

Aphelion

when the object is distant from the focus

Ellipse Eccentricity Equation

e = square root (1-b²/a²)

Kepler’s Second Law

A planet’s speed in orbit is not constant; the planet moves fastest when it is closest to the sun and slowest when it is the farthest away.

How many days shorter is Earth’s fall equinox to its spring equinox than the time from the spring equinox to the fall equinox?

5 days shorter

eccentricity changes over a cycle spanning between

100,000 and 400,000 years

(AU) astronomical units

one AU is the length of Earth’s semimajor axis

how can i find a, the semimajor axis?

(GMT²/4pi²)^1/3