Propulsion - Orbital Mechanics (page 2 of 6)
The Transfer:
The mission utilizes a Homhann transfer to move the spacecraft between Earth and Venus orbits. Assuming the craft has broken Earth orbit and lies in a heliocentric orbit close to Earth and orbiting the sun with a velocity similar to that of the Earth, the Δv required to initiate the transfer is -2.682 km/s relative to the Earth’s velocity about the Sun. In 138 days this places the spacecraft at a distance of 40,000 km from the center of mass of Venus. This of course neglects the gravitational effect of Venus on the spacecraft up until this time. It requires that the angular distance ((Venus – θEarth) with respect to the Sun) be 5.283 radians. This limits the dates at which the transfer can be initiated. Given that the next conjunction occurs on 11 JAN 14, working backwards we can place the angular distance between Earth and Venus with respect to the sun on 24 JUL 13 at:
This is where the MATLAB simulation of the transfer will begin. Below is a graph of the feasible dates for the initiation of the transfer:
Figure 2:
Potential
Transfer Initiation Dates
Assuming the transfer in initiated on March 31, 2015 the spacecraft will arrive in Venusian orbit on September 10, 2015. As is seen above, this is too late to take advantage of the inferior conjunction that occurs about a month prior. Being that the mission uses a communications relay satellite this is not a major factor. The mission will run from September 10, 2015 to December 8, 2015.