Calculating the launch date

A reference date must be utilized in order to calculate the launch date. Our first reference would be that on 03/27/97, the Earth was advanced with respect to Mars by an angle of 5.586 degrees or 0.0975 radians, like the figure shows.

We must now calculate the number of days needed for Mars and the Earth to arrange themselves in the proper angle of separation, that is, as we have calculated, when Mars is advanced 44 degrees (0.77 radians) with respect to earth.

If we suppose that Mars remains fixed and the Earth moves around it with a speed equal to the difference in their angular speeds, then :

As we have stated,

Ainitial = 0.0975 radians (reference date 03/27/97)
Alaunch= 0.77 radians

Tlaunch is the time in seconds counted from our reference date when the mission will be launched.

tEarth and tMars are the periods of heliocentric revolution of the Earth and Mars respectively.

Finding Tlaunch :

Substituting :

Tlaunch=58,041,899 seconds or 671 days counted from 03/27/97

This gives us a suggested launch date for our mission of January 27, 1999, coinciding with the 98/99 launch opportunity.