4.2 Trajectory

The software package used to design the trajectory is the Trajectory Optimizer marketed by Scientific Applications International Corporation, which uses a multiple impulse code (MULIMP). The trajectory is designed to impart the lowest total $\Delta V$ possible.

The proposed trajectory for Asterius begins from an Earth parking orbit with a perigee of 200 km altitude and an eccentricity of 0.73. This parking orbit is the same as a geosynchronous transfer orbit (GTO). The planned date of launch is March 23, 2004. The trajectory has only one major event prior to Jovian capture: An unpowered gravity assist swingby of Mars, with a periapsis constraint of 1.05 body radii, will provide the velocity boost to propel Asterius out of the inner solar system and on to Jupiter. After a total trip time of about five years, Asterius will arrive at Jupiter on February 23, 2009. Table 2 lists a summary of the flight profile.

  

Table 2: Summary of Asterius' Flight Profile

Launch Energy: 29.376 km

/s

 

Event	Date	Elapsed Time		$\Delta V$
		Days	Years	(km/sec)
Earth Departure (from GTO)	23-Mar-04	0.00	0.00	2.032
GA Swingby @ Mars	5-Jan-06	652.46	1.79	3.642
Jovian Capture	23-Feb-09	1797.44	4.92	0.906

To reduce the braking $\Delta V$ on arrival at Jupiter, Asterius will insert itself into a highly elliptical Jovian orbit. This orbit has a perijove of 9.397 Jovian radii, which is the same as Europa's semi-major axis, and an apojove of approximately 280 Jovian radii. This capture orbit is designed after Galileo's capture orbit. However, unlike Galileo, Asterius must insert itself into orbit around a Jovian moon, Europa. The $\Delta V$ needed to do this is quite substantial. The $\Delta V$ required to circularize a highly elliptical orbit, such as the proposed insertion orbit, via a Hohmann Transfer as a function of apojove is shown in Figure 3.

  

Figure 3: $\Delta V$ Required to Circularize Asterius' Orbit at Europa vs. Apojove

The solution proposed by Project Asterius is to utilize the Jovian moons in a series of gravity assist swingbys to reduce the energy, thus providing the necessary $\Delta V$ with minimal use of the on-board propulsion system. However, the complexity of such a maneuver is beyond the scope of this proposal. Therefore only an estimation of the planned flybys is provided.

The maximum $\Delta V$ attainable from each of the Jovian moons is calculated with the a minimum miss ratio (M=1.1), and the circular velocity (v_c) of the moon at the corresponding miss ratio. Knowing these two, the equation for $\Delta V$ is

$$\Delta V = \frac{v_c}{\sqrt{M}}$$ (1)

The values for the Galilean moons are given in Table 3.

  

Table 3: Maximum $\Delta V$ for GA Swingbys of Jupiter's Moons

Jovian Moon	Maximum $\Delta V$ (km/s)
Io	1.645
Europa	1.324
Ganymede	1.761
Callisto	1.571

For the sake of simplifying the solution, only the four major moons of Jupiter are considered. From Figure 3, 5.32 km/s is needed to circularize the insertion orbit. With the maximum $\Delta V$ values from the table above, Asterius has to execute a minimum of four flybys to circularize its orbit to the semi-major axis of Europa. The simplified estimation of the Jovian moon gravity assist slowdown does not consider the targeting, positioning, and timing intricacies of such a complex tour. The design of this proposed trajectory derives its confidence from the success of the Galileo mission performing a fairly similar cruise.

Because the best place to change apojove is at perijove, which in this case is at the same altitude as Europa, Asterius will use four Europa gravity assists. On each flyby, Asterius will be carefully targeted so that it returns to Europa. At the fifth Europa encounter, Asterius will fire its rockets to insert itself into Europa orbit.