Determination of return date
Knowing the angle of separation needed for the return trip, the actual day when the spacecraft will be launched can be determined with respect to our reference date of 03/27/97.
If we imagine that Mars is fixed in space and that the faster Earth moves around it with a speed equal to the relative angular speed between the two planets, then
1.3rad+Ainitial(03/27/97)+TLaunchRet*2*pi*(1/tEarth-1/tMars) = 2*pi
TLaunchRet = 2*pi-1.3rad-Ainitial/[2*pi*(1/tEarth-1/tMars)]
This would give us the first alignment of the planets in that position after our reference date of 03/27/97. Substituting :
But of course we haven't even launched our spacecraft then. All angular positions between the planets will repeat themselves periodically, with a period that can easily be calculated :
where TMars and TEarth are the periods of revolution of Mars and the Earth. This results in
The following favorable alignment would then be on 9/10/99, one month before our arrival. So we must wait for the next return opportunity, which will take place on 8/26/2000. This would give us a stay on the Martian surface of more than ten months, good enough for an initial expedition.