Launch and Orbital Systems

Launch Vehicles

For the mission to Venus, an exact total spacecraft mass has yet to be determined. However, based off of past missions and their mass requirements, the team can provide estimates for what the mass of our spacecraft should be. Since Venus is the target, the team examined the past missions to Venus and gaged what their mass requirements were and what launch vehicles were used to place them in the right orbital trajectory in order to get to the planet. Particularly, it was noticed that the Soviet Venera missions [8] that involved physically landing on the surface. Other systems were also considered that had similar mission objectives, particularly the Cassini-Huygens mission to Saturn [7]. Even though this mission did not land on Venus, the mission still required the Huygens probe to be launched from the main Cassini orbiter, to enter the atmosphere of Saturn’s moon Titan, and soft land on the surface of Titan in order to conduct scientific experiments. Looking at these types of missions as a reference, the team estimated which launch vehicles currently available can deliver the spacecraft to Venus with the lowest cost possible. 

Currently, the Delta II rocket, initially thought to be ideal for the mission, is going to be phased out by NASA. Current figures for the launch of this rocket put it over $65 million. Instead, the Falcon 9 rocket operated by SpaceX can send the spacecraft into Low Earth Orbit for about $54 million, which is considerably less than the current Delta II price. Other rockets such as the Ariane (~$120 million) and others are proving to cost too much for the current mission. Once in orbit, the plan calls for an Apogee Kick Motor located on the Venus orbiter to impart a change in velocity that will place the orbiter in a transfer orbit to go from Earth to Venus.

In-Space Propulsion

For the mission, once the vehicle has attained Low Earth Orbit (LEO), a Hohmann Transfer orbital maneuver [9] will take place in order to position the Venus spacecraft into orbit around Venus. Basically, this type of procedure involves imparting a change in velocity on the spacecraft so that it enters an elliptical orbit around the sun rather than a nearly circular orbit around the Earth (from LEO). This new elliptical orbit will have an aphelion equal to the distance between the Earth and the Sun, and the orbit’s perihelion will be equal to the distance between Venus and the Sun. This will enable the spacecraft to go from one planetary orbit to the next.

An Apogee Kick Motor [10]is used to add a change in velocity, Δv [11], to the initial velocity of the spacecraft that will 1) send it away from Earth’s gravity, and 2) enter it into the orbital path of Venus. For these estimates, it was assumed that the Earth’s and Venus’s orbits are nearly circular, which is a fair approximation given the radius of their orbits do not exceed more than 1.35% for Venus and 3.34% for Earth. This delta v will be applied in the tangential direction (relative to the sun) so as to minimize the amount of energy required for the transfer. The following equations will be used to generate the orbits.

Figure 1: Hohmann Transfer Orbit [9]

These equations describe the necessary velocities required to make this transfer happen, where G is the gravitational constant, M is the mass of the primary body (the sun), r_A is the distance from the sun to the transfer orbits perihelion, r_B is the distance from the sun to the transfer orbits aphelion, and a_transfer is the transfer orbit’s semi-major axis. For this transfer, basically the spacecraft needs to decelerate so that it will enter the elliptical transfer by going at a slightly slower velocity relative to the sun than the Earth goes around the sun. This is basically lowering the energy of the spacecraft’s total orbit so that it will start to move toward the sun.

After the spacecraft leaves Earth’s orbit, it will move towards Venus’s orbit. Since the team can calculate the semi-major axis of the Hohmann transfer orbit using the Earth-sun distance and the Venus-sun distance, Kepler’s Third Law of Planetary Motion was used to calculate the period of the transfer orbit:

Then the half period of the spacecraft’s orbit can be determined. The half period of the transfer orbit is especially important because it represents the amount of time that our spacecraft will take to get from Earth to Venus. The spacecraft with then arrive at Venus after the half period time of 146 days (about 5 months).  The Apogee Kick Motor (AKM) will then impart another delta v on the craft so that it decelerates again and begins to orbit Venus. Below are Matlab estimates of the delta v’s and the Forces required by the AKM at the aphelion and perihelion or the Hohmann Transfer orbit (assumed m = 1300 kg). The negative sign corresponds to a deceleration of the satellite with respect to the Earth’s velocity around the sun to achieve the lower energy state for the orbital transfer (calculations are located in the attached Matlab Code).

The resulting orbit around Venus is seen in the figures below.

Figure 2: Orbit Polar Plot