# Planetary Motion

- Each planet orbits the Sun in an ellipse
- Straight line joining a planet and the Sun sweeps out equal areas in space and equal areas in time
- Eg. in 60 days a planet will move the same amount of area, no matter how close it is to the body it orbits
- The Law of Equal Areas
- Discovered by observing orbits speeding up as a planet gets closer to the Sun
- Consequence of the conservation of angular momentum
*Figure skater law*

- A planet's orbital period ($P$) squared is proportional to the semi-major axis ($a$) of its orbit cubed
- $P^2 \propto a^3$
- When $P$ is measured in years and $a$ is measured in astronomical units, the two sides are equal
- Applies to all objects orbiting the Sun
- Provides means for calculating objects relative distances from the Sun
*Law of harmonies*

### Newton's Addition to the Third Law

- isaac newton realized that the Sun's mass and a planets mass come into play with regards to the third law
- The proper formula is $a^3 = (M_1 + M_2) \times P^2$
- $M_1$ is the mass of the Sun
- $M_2$ is the mass of the planet
- Both $M_1$ and $M_2$ are expressed in units of the Sun's mass

Space Astronomy Physics