# Physics - Kepler's Laws

> Source: https://ollybritton.com/notes/a-level/physics/topics/keplers-laws/ · Updated: 2021-12-01 · Tags: school, physics, year-2

## Flashcards
### 2021-12-01
##### What do Kepler's laws describe??
The motion of orbits.

##### What is Kepler's First Law??
All of the planets move in elliptical orbits with the sun at one focus.

##### What is Kepler's Second Law??
The radius vector sweeps out equal areas in equal times.

##### What is the "radius vector" for Kepler's Second Law??
The imaginary line between the sun and the planet.

##### ![PHOTO KEPLERS SECOND LAW](keplers-second-law.jpg) Which of Kepler's laws does this show??
Kepler's second law.

##### What is Kepler's Third Law??
The square of the period of a planets orbit is directly proportional to the cube of its mean distance from the sun.

##### How can you derive Kepler's Third Law??
Equate

$$
F = \frac{mv^2}{r}
$$

and

$$
F = \frac{GMm}{r^2}
$$

where $v = \omega r$

##### How would you write Kepler's Third Law in terms of direct proportionality??
$$
T^2 \propto r^3
$$

##### What is the constant of proportionality for Kepler's Third Law??
$$
\frac{4\pi^2}{GM}
$$

##### What is the equation form of Kepler's Third Law??
$$
T^2 = \left( \frac{4\pi^2}{GM} \right) r^3
$$

##### How many seconds are there in a year??
$$
31,536,000
$$

##### Where will a planet's orbit be the fastest, close to the sun or far away from the sun??
Close to the sun due to Kepler's Second Law.

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