Hyperbolic interplanetary transfer

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SUMMARY

The discussion centers on calculating hyperbolic excess speed for a spacecraft departing from Earth's parking orbit towards Jupiter. The initial formula proposed, v_{\infty} = v_{park} - v_{earth/jupiter}, was identified as incorrect. The correct approach is to use v_{\infty} = Δv, where Δv represents the initial impulse required for a Hohmann heliocentric transfer. Additionally, the conversation touches on the complexities of transitioning from a hyperbolic orbit relative to Earth to an elliptical or hyperbolic orbit relative to the Sun.

PREREQUISITES
  • Understanding of hyperbolic and elliptical orbits
  • Familiarity with Hohmann transfer orbits
  • Knowledge of orbital mechanics and velocity calculations
  • Basic principles of patched conic approximation
NEXT STEPS
  • Research the calculations involved in Hohmann transfer orbits
  • Explore the concept of patched conic transfer orbits
  • Study the effects of gravitational influences from multiple celestial bodies
  • Learn about hyperbolic excess velocity and its applications in interplanetary travel
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Aerospace engineers, astrophysicists, and students of orbital mechanics who are interested in spacecraft trajectory planning and interplanetary mission design.

dilasluis
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Could someone tell me if I'm right or wong...

I want to calculate de hyperbolic excess speed for a spacecraft that leaves Earth parking orbit on a hyperbolic orbit in direction to Jupiter to arrive there in optimum conditions.

It's not an Hohmann heliocentric transfer!

so, i though that:

[tex]v_{\infty} = v_{park} - v_{earth/jupiter}[/tex]

Is it right, or is it worng?
 
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I'm totally dumb!

Sorry, this tread can now be safely closed (and it only passed less than 10 min)...

The hyperbolic velocity that I previosly wrote is totally wrong!

In fact, [tex]v_{\infty} = \Delta v[/tex] where [tex]\Delta v[/tex] is the first impulse from the hohmann heliocentric transfer...
 
dilasluis said:
Sorry, this tread can now be safely closed (and it only passed less than 10 min)...

The hyperbolic velocity that I previosly wrote is totally wrong!

In fact, [tex]v_{\infty} = \Delta v[/tex] where [tex]\Delta v[/tex] is the first impulse from the hohmann heliocentric transfer...
You could work up a dissertation on the patched conic transfer orbit, starting with a hyperbola relative to Earth and changing over--abruptly or interpolatively?...how does one treat the region where the sun's influence and Earth's are commensurate? -- to an ellipse or hyperbola relative to the sun.

Jerry Abbott
 

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