Hi, RGClark
Earlier you asked:
I've calculated the total delta-V requirement for doing a capture (Oberth) burn around Jupiter at a radius [MATH]r_0[/MATH], followed by a circular orbit insertion burn around Europa with [MATH]71000\,km \leq r_0 \leq 700000 \,km[/MATH]. This calculation covers the range from the surface of Jupiter out to Europa's orbital radius. I've assumed a hyperbolic excess velocity of around 6.5 km/s and no gravity assists. The resulting delta-V requirement is plotted as the following graph.
The graph shows that the total delta-V requirement to achieve a circular orbit around Europa without gravity assists is between 5.1 km/s and 5.6 km/s - depending on the orbital radius at which the capture burn is executed. It is also easy to see that the best place to do the capture burn is as close to the Jovian surface as possible. With a grazing encounter of the Jovian surface, and without gravity assists, the minimum delta-V requirement is 5.1 km/s.
This minimum of 5.1 km/s is, of course, much higher than the approximately 2.0 km/s that your Europa mission planners budgeted for in their calculations using gravity assists. Roughly speaking, then, one is 3.1 km/s better off with gravity assists than without.
Clearly, this is why the mission planners relied so heavily on gravity assists: without gravity assists, the delta-V requirements of the mission would have been completely impracticable given current budget and technology constraints.
As dgatsoulis has just demonstrated here, http://www.orbiter-forum.com/showthread.php?t=35916, gravity assists are an effective and practicable method for reducing total mission delta-V requirements.
Earlier you asked:
Could we dispense with the Ganymede gravity assist by going deeper into Jupiter's gravity well? Our objective is to wind up at Europa. Perhaps doing capture burn at Europa's distance then performing circularization burn could give lower total delta-v. I doubt it though. Otherwise they would have done it this way in the first place.
But perhaps we could go a deeper distance in to do the capture burn and then circularize at Europa's orbital distance. Would this result in a lower total delta-v?
I've calculated the total delta-V requirement for doing a capture (Oberth) burn around Jupiter at a radius [MATH]r_0[/MATH], followed by a circular orbit insertion burn around Europa with [MATH]71000\,km \leq r_0 \leq 700000 \,km[/MATH]. This calculation covers the range from the surface of Jupiter out to Europa's orbital radius. I've assumed a hyperbolic excess velocity of around 6.5 km/s and no gravity assists. The resulting delta-V requirement is plotted as the following graph.
The graph shows that the total delta-V requirement to achieve a circular orbit around Europa without gravity assists is between 5.1 km/s and 5.6 km/s - depending on the orbital radius at which the capture burn is executed. It is also easy to see that the best place to do the capture burn is as close to the Jovian surface as possible. With a grazing encounter of the Jovian surface, and without gravity assists, the minimum delta-V requirement is 5.1 km/s.
This minimum of 5.1 km/s is, of course, much higher than the approximately 2.0 km/s that your Europa mission planners budgeted for in their calculations using gravity assists. Roughly speaking, then, one is 3.1 km/s better off with gravity assists than without.
Clearly, this is why the mission planners relied so heavily on gravity assists: without gravity assists, the delta-V requirements of the mission would have been completely impracticable given current budget and technology constraints.
As dgatsoulis has just demonstrated here, http://www.orbiter-forum.com/showthread.php?t=35916, gravity assists are an effective and practicable method for reducing total mission delta-V requirements.
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