Placing a cargo on a parabolic orbit from europa moon of Jupiter

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Discussion Overview

The discussion revolves around determining the minimum velocity required to place a cargo of waste on a parabolic orbit from Europa, one of Jupiter's moons, while considering the implications for pollution of Jupiter's moons. The scope includes theoretical calculations related to escape velocity and orbital mechanics.

Discussion Character

  • Technical explanation, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant introduces the problem of calculating the minimum velocity needed to launch waste from Europa into a parabolic orbit, emphasizing the need to avoid polluting other moons.
  • Another participant suggests using the concept of "escape velocity" and provides the formula for calculating it, referencing the mass of Jupiter and Europa's orbital radius.
  • A third participant notes the importance of considering the initial velocity of the garbage relative to Jupiter, hinting that it may be similar to the escape speed due to Europa's orbital motion.
  • One participant proposes that achieving escape velocity from Europa would suffice to ensure the garbage is not a threat, suggesting a specific speed of 2.02 km/s and mentioning that this speed is lower than that required from the Moon.

Areas of Agreement / Disagreement

Participants express different views on the approach to the problem, with some focusing on escape velocity calculations while others emphasize the initial conditions of the cargo. The discussion remains unresolved regarding the optimal strategy for launching the cargo.

Contextual Notes

There are assumptions regarding the mass of Europa relative to Jupiter and the initial speed of the cargo that are not fully explored. The discussion also does not clarify the implications of the chosen velocity on the trajectory and potential environmental impact.

Cerdocyon
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Hello,
The problem is quite simple.You are an astronautics engineer in an established colony on europa,one of jupiter's moons and your boss asks you what would be the minimum velocity so that a cargo full of wastes or garbage is placed on a parbolic (neglecting the mass of europa versus the mass of Jupiter)in order to not pollute any of Jupiter's moons.
If you could help me that would be great.
Thank you
 
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You're looking for "escape velocity", also known as "second cosmic velocity"
http://en.wikipedia.org/wiki/Escape_velocity

The equation is simple. Just plug in the mass of Jupiter and Europa's orbital radius.
[itex]v_e = \sqrt{\frac{2GM}{r}},[/itex]
 
Remember to take into account that the garbage already is traveling at some speed releative to Jupiter when it sits on the surface of Europa prior to launch (hint: the speed of Europa in its orbit around Jupiter can be assumed (using what assumption?) to be an expression very similar to the escape speed Bandersnatch gave you).
 
If you're just trying to get rid of garbage, why not give it escape velocity from Europa (as previously specified) and drop it into Jupiter's massive gravity well? No matter what else happens, that garbage will never be a threat to space travel in the future, at that point. 2.02 km/s is fairly easy to attain - it's not even as high as the Moon (at 2.4 km/s) and if you aim in the right direction, Jupiter will catch your garbage.
 

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