Chapter 7

Orbital Velocity The maximum and minimum velocities in kilometers per second of a celestial body moving in an elliptical orbit can be calculated by \(v_{\max }=\frac{2 \pi a}{P} \sqrt{\frac{1+e}{1-e}}\) and \(v_{\min }=\frac{2 \pi a}{P} \sqrt{\frac{1-e}{1+e}}\) In these equations, \(a\) is half the length of the major axis of the orbit in kilometers, \(P\) is the orbital period in seconds, and \(e\) is the eccentricity of the orbit. (a) Calculate \(v_{\max }\) and \(v_{\min }\) for Pluto if \(a=5.913 \times 10^{9}\) kilometers, the period is \(P=2.86 \times 10^{12} \mathrm{sec}\) onds, and the eccentricity is \(e=0.249\) (b) If a planet has a circular orbit, what can be said about its orbital velocity?

Explain how the distance between the foci of an ellipse affects the shape of the ellipse.

Given the standard equation of an ellipse, explain how to determine the length of the major axis. How can you determine whether the major axis is vertical or horizontal?