Introduction
Transfer
Calculations
Launch
Windows

Trajectory
Calculations Let
= period of free return orbit
= = 730 days (twice
365) because when the spacecraft returns to its starting point, Earth
has orbited the sun twice and is in the same spot.
Launch Windows, Durations of Flights, and Stay on Mars The following are calculations detailing the times of transfer for both the Hohmann and Free Return Trajectories. Additional Definitions of Variables Let = period of Earth's orbit = 365.25 days = period of Mars' orbit = m = Earth's semimajor axis = m = Mars' semimajor axis Q = =
Earth's lead on 3/27/1997
Hohmann Transfer Launch Windows, Duration of Flight, and Stay on Mars Calculations days= 258.6 days = =timeof Hohmann transfer = At beginning of transfer, Mars must lead Earth by = = 258.6 days = = At the end of the transfer, Mars leads Earth by = Mars to Earth: days = 258.6 days = = At the beginning of the transfer, Mars must lead by = = degrees Earth moves relative to Mars during the stay = = =period of Earth relative to Mars f = frequency = = = = = 780.1 days = =455 days Free Return Trajectory Launch Windows, Duration of Flight and Stay on Mars days =215 days = = At the beginning of the transfer, Mars must lead Earth by = days = 215 days = At the end of the transfer, Mars leads Earth by =
Earth to Mars (Hohmann transfer) At the beginning of the transfer, Mars leads Earth by = = = =388.1 days Launch opportunities occur every for both transfers, and they can be determined by similar methods to those shown above if is known for some . The following chart shows the results of these calculations for Mars = ahead of earth on 3.27.1997. The comments are based on the solar flare and dust storm chart that follows. Launch opportunities for free return occur 455+258388215 = 110 days later than those for the Hohmann transfers, and landings occur 455388 =67 days later than those of the Hohmann transfer. Summary of Above Calculations Hohmann Transfer (both directions) Earth to Mars: D=6.6 km/s D=7.2 km/s Mars to Earth: D=6.6 km/s D=7.2km/s D= 27.6 km/s = 258 days =455 days = 258 days
Free Return (to Mars, Hohmann return) Earth to Mars: D=11.6 km/s D=27.6 km/s Mars to Earth: D=7.2 km/s D=6.6 km/s =53 km/s = 215 days =386 days =258
days
References:

Copyright
© 2000 Massachusetts Institute of Technology
Comments and questions to mission2004students@mit.edu Last updated: 10 December, 2000 