Physics Laws & Theorems
Advanced

Kepler's First Law

Planets orbit the Sun in ellipses with the Sun at one focus.

Formula

r=a(1−e2)1+ecos⁡θr = \frac{a(1-e^2)}{1 + e\cos\theta}

Variables

aSemi-major axis
eEccentricity
\thetaTrue anomaly

Example

Earth’s orbit is a slight ellipse, so we are a little closer to the Sun in January.

Did You Know?

Kepler shattered 2,000 years of dogma by showing planets orbit in ellipses, not perfect circles.

keplerorbitellipselaw