Paul Peter Urone; Roger Hinrichs

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Key Equations

PhysicsKey Equations

7.1 Kepler's Laws of Planetary Motion

Kepler’s third law	$\frac{T_{1}^{2}}{T_{2}^{2}} = \frac{r_{1}^{3}}{r_{2}^{3}}$
eccentricity	$e = \frac{f}{a}$
area of an ellipse	$A = π a b$
semi-major axis of an ellipse	$a = (r_{a} + r_{p}) / 2$
semi-minor axis of an ellipse	$b = \sqrt{r_{a} r_{p}}$

7.2 Newton's Law of Universal Gravitation and Einstein's Theory of General Relativity

Newton’s second law of motion	$F = m a = m g$
Newton’s universal law of gravitation	$F = G \frac{m M}{r^{2}}$
acceleration due to gravity	$g = G \frac{M}{r^{2}}$
constant for satellites orbiting the same massive object	$\frac{r^{3}}{T^{2}} = \frac{G M}{4 π^{2}}$

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- Authors: Paul Peter Urone, Roger Hinrichs
- Publisher/website: OpenStax
- Book title: Physics
- Publication date: Mar 26, 2020
- Location: Houston, Texas
- Book URL: https://openstax.org/books/physics/pages/1-introduction
- Section URL: https://openstax.org/books/physics/pages/7-key-equations

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