9th Edition:
51) Mars Orbit. Find the perihelion and aphelion distances of Mars.
Perihelion distance: a(1-e)
→ 227.9 (1-0.093) =206.705AU
Aphelion distance: a(1+e)
→ 227.9 (1+0.093) =249.095AU
52) Eris Orbit. The dwarf planet Eris orbits the Sun every 557 years. What is its
average distance (semimajor axis) from the Sun? How does its average distance
compare to that of Pluto?
p^2=a^3
a^3= (557)^2
a= 67.69AU
aEarth/aPluto
67.69/39.48 = 1.715
53) New Planet Orbit. A newly discovered planet orbits a distant star with the same
mass as the Sun at an average distance of 112 million kilometers. Its orbital eccentricity
is 0.3. Find the planet’s orbital period and its nearest and farthest orbital distances from
its star.
112 million km= 0.749 AU
p^2=a^3
p^2= (0.749)^3
p=0.648 —> orbital period
a(1-e)
0.749(0.5) = 0.375AU= 56,099,202km
a(1+e)
0.749(1.5) = 1.124 AU = 1.68148 *10^8km
54) Halley Orbit. Halley’s Comet orbits the Sun every 76.0 years and has an orbital
eccentricity of 0.97.
a. Find its average distance from the Sun (semimajor axis)
p^2=a^3
76^2=a^3
a=17.9AU
b. Find its perihelion and aphelion distances
Perihelion: a(1-e)
17.9(1-0.97)= 0.537AU
Aphelion: a(1+e)
17.9(1+0.97) = 35.263AU
