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}/a^{3} = 1 yr^{2}/AU^{3} , where P is the period and a is the semi-major axis. To calculate P you need the value of a, measured in AU. |
Suppose the new planet has a semi-major axis of a = 4 AU. Using the relationship
P^{ 2} = (1 yr^{2}/AU^{3}) × a^{3}
calculate the period:
2. The planet's distance to the Sun varies between R_{p} and R_{a}. 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 R_{a} - R_{p} from the Sun. Use a loop of string long enough to reach from the Sun to R_{a}, and trace out the ellipse. |
Comets orbit along very `skinny' ellipses. To plot such an ellipse, would you place the second focus
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 R_{a}/R_{p} is also the ratio of maximum to minium speed. |
An asteroid travels on an elliptical orbit. Its distance from the Sun varies from R_{p} = 2 AU at perihelion (P) to R_{a} = 5 AU at aphelion (A). How much faster is it traveling at P than at A?
Joshua E. Barnes
(barnes@ifa.hawaii.edu)
Last modified: September 12, 2006 http://www.ifa.hawaii.edu/~barnes/ast110_06/quizzes/disc03.html |