Table of Contents

Orbital Mechanics

Student Activity

Rendezvous With the Planets: Answer Key

Assignment

1. Using Kepler's 3rd Law, calculate the time required to reach Mars using a Hohmann Transfer Ellipse. Mean orbital radius of Mars is 1.52AU.

   Mars
   2a = 1 + 1.52
   a= 1.26
   a³ = 2.00
   a³ = p²
   p = 1.4
   t (one way) =
   0.7 years
   
   
   

2. Using Kepler's 3rd Law, calculate the time required to reach Jupiter using a Hohmann Transfer Ellipse. Mean orbital radius of Jupiter is 5.50AU.

   Jupiter
   2a = 1 + 5.50
   a= 3.25
   a³ = 34.3
   a³ = p²
   p = 5.86
   t (one way) =
   2.9 years
   
   
   

3. Using Kepler's 3rd Law, calculate the time required to reach Saturn using a Hohmann Transfer Ellipse. Mean orbital radius of Saturn is 9.58AU.

   Saturn
   2a = 1 + 9.58
   a= 5.29
   a³ = 148
   a³ = p²
   p = 12.16
   t (one way) =
   6.08 years
   
   
   

4. Using Kepler's 3rd Law, calculate the time required to reach Pluto using a Hohmann Transfer Ellipse. Mean orbital radius of Pluto is 39.4AU.

   Pluto
   2a = 1 + 39.4
   a= 20.2
   a³ = 8242
   a³ = p²
   p = 90.8
   t (one way) =
   45.4 years
   
   
   

Major axis of the Hohmann Transfer Ellipse