
180 Classical Mechanics
© 2010 Taylor & Francis Group, LLC
orbit as illustrated in Figure 6.16. The orbit of the spacecraft is an elliptical one about the sun with
perihelion at the Earth’s orbit, and the planet and the spacecraft meet at the aphelion. The equation
of the orbit is given by Equation 6.39:
r =
α
where α and ε are determined from the maximum and minimum values of r. For planet Uranus,
r
min
= 1 AU (at Earth), r
max
= 19.2 AU (at Uranus)
where AU is the astronomical unit that is the mean Earth–sun distance (~93 × 10
7
mi. or 1.5 ×
10
8
km). Thus,
rAUr AU
min max
=
==
=
α
α
1
19 2 .
Solving for α and ε, we nd ε = 0.9 and α = 1