# Kepler's Laws: Discussion

1. A new planet is discovered in an orbit around the Sun! Briefly state the law which predicts its orbital period, and describe the information you'd need to use this law.

 Kepler's Third Law: P 2/a3 = 1 yr2/AU3 , where P is the period and a is the semi-major axis. To calculate P you need the value of a, measured in AU.

## Question 3D.1

Suppose the new planet has a semi-major axis of a = 4 AU. Using the relationship

P 2 = (1 yr2/AU3) × a3

calculate the period:

1. 2 yr
2. 4 yr
3. 6 yr
4. 8 yr
5. 10 yr

2. The planet's distance to the Sun varies between Rp and Ra. State the law which predicts the shape of the planet's orbit, and explain how to plot this orbit.

 Kepler's First Law: The orbit of a planet is an ellipse with the Sun at one focus. Place one focus (push-pin) at the Sun's position, and the other focus a distance Ra - Rp from the Sun. Use a loop of string long enough to reach from the Sun to Ra, and trace out the ellipse.

## Question 3D.2

Comets orbit along very `skinny' ellipses. To plot such an ellipse, would you place the second focus

1. very close to the Sun?
2. moderately far from the Sun?
3. almost at the other end of the orbit?

3.The planet moves faster in one part of its orbit, and slower in another part. State the law which predicts how its speed varies, and explain how you could use it to find the range of speeds.

 Kepler's Second Law: A line drawn from the Sun to a planet sweeps out equal areas in equal times. The ratio Ra/Rp is also the ratio of maximum to minium speed.

## Question 3D.3

An asteroid travels on an elliptical orbit. Its distance from the Sun varies from Rp = 2 AU at perihelion (P) to Ra = 5 AU at aphelion (A). How much faster is it traveling at P than at A?

1. 1.5 times
2. 2 times
3. 2.5 times
4. 3 times
5. 3.5 times

 Joshua E. Barnes (barnes@ifa.hawaii.edu) Last modified: September 12, 2006 http://www.ifa.hawaii.edu/~barnes/ast110_06/quizzes/disc03.html