Physics - Kepler's Laws

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 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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