After seeing in the digital application of the budget-Dv, the energy “cost” of a trip to Venus, it is necessary to know when it is possible to make this trip.
Data
The Sun’s standard gravitational parameter: mu=132 712 440 018 km3 s-2
Semi-major axis of Venus: av=108 208 930 km
Semi-major axis of the Earth: at =149 597 887.5 km
Calculations
We begin by calculating the angular velocities of the two planets as well as the period of conjunction between these two planets.
Venus passes between the Earth and the Sun every 584 days (1 year and 7 months). We know that the shooting window will open a little before so we can launch towards Venus only every 1.6 years. We must also calculate the angular and relative date to the conjunction where one can make a journey with the least energy-efficient transfer.
The mission must therefore be launched 87 days and 15 hours before the conjunction and an arrival 58 days and 11 hours after. Since the Earth-Venus shooting windows and the same as Venus-Earth, if you want to do a round-trip mission with economic journeys, you have to wait for the next conjunction to be able to return. A round-trip mission to Hohmann’s orbit would take 730 days, or almost two years.