What is the fastest way to travel from Earth to Jupiter?

[THC]

I have zero understanding on astrophysics, but hope to have help on determining the plausibility of an element to a story, traveling from Earth to Jupiter in four months, increasing acceleration with an orbit around first the Earth then the Sun,

Orbit Earth to increase acceleration of ship max speed from 20,000 meters per second to 57,716 meters per second

Trip to Sun
Seconds in one 30 days 2,592,000
Earth to Sun 149,600,000,000 meters
the ship must reach 57,716 meters per second to travel this distance

Trip to Jupiter
7,776,000 seconds in 90 days
With an average distance the Sun to Jupiter 778,500,000,000 meters
the ship must reach 100,115 meters per second to travel 778,500,000 kilometers

The Question
For a human body to survive, they would be in a gravity compensation chamber, so my question is how many "G"s would the chamber need to accommodate. or am I completely off the boil. :-)Kind Regards
Steve

 

[Bandersnatch]

Hi Steve, welcome to PF!

The good news is, accelerating from 0 to 100km/s takes little time even at a leisurely acceleration of 1g. Should be about 3h of constant thrust. You don't need super tech to compensate for the inconvenience.

The bad news is, not a whole lot of the maneuvers you described make much sense. If you explain in more detail what you're aiming for conceptually, then we can help you harden the SF.

For example, you can't be in orbit around Earth and moving at 20km/s. Or rather, the "orbit" will be a hyperbolic trajectory. A stable circular orbit near Earth (LEO) is about 7km/s. The escape velocity at that distanceis about 11km/s. Lower for higher orbits. If you get your craft moving faster than that, it'll fly away never to return.
50+km/s is enough to escape the Solar System from Earth's orbit.

Why do you want the craft to "orbit" the sun, and what do you exactly mean by that? A fly-by? As a means of boosting velocity, these work only with planets.

There's more, but it can wait.

 

[THC]

Hi Bandersnatch

Thank you very much for your reply,I have done a bit of reading Hyperbolic/parabolic orbits hence my late reply (thanks for pointing me in the right direction)

The goal is for a ship which is already in Earths orbit to reach a Hyperbolic Orbit to increase speed to get to Jupiter in 3months

(Distance Earth to Jupiter 628,743,036 km to 928,081,020 km)
Trip to Jupiter
7,776,000 seconds in 90 days
Earth to Jupiter 778,500,000,000 meters
100,115 meters per second to travel 778,500,000 kilometers takes 90 days

So my original idea for the ship to first sling shot round the Earth to reach the Sun in a month then sling shot round the sun to pickup speed of 100,115 mps, so if I understand your comment above if you were to ignor my idea about sling shot, a simple ship acceleration of 2g allows us to reach 100mps in 3hours ish, or have I misunderstood.Kind Regards

Steve

 

[Bandersnatch]

1g(10m/s^2) acceleration gets you to 100km/s in 10000s. You don't need 2g(I assume you meant to counter Earth's gravity) if you start already in orbit. It's a simple calculation: $V=at$

Furthermore, you don't need extra 100km/s, but just about 70 due to the fact that you've already got some speed by the virtue of being in orbit around Earth(7km/s), and Earth being in Orbit around Sun(30km/s).

There will be some slowing down due to constant pull from the Sun, but at this kind of speed you can just handwave it.

There's no point in trying any of the standard orbital maneouvres like gravity assist(which you can't do with Sun), powered slingshot, Hohmann transfer orbit etc. if you've got a ship capable of acceleration to 100km/s and then decelerating. With such fantastic capabilities, you can just go pretty much in a straight line to your target.

 

[THC]

Hi Bandersnatch

Thanks for your reply, you make it sound so simple, Let's hope my next question taxes you brain a little more :-)

Take it Easy
Steve

 

[ellipsis]

I'd like to add a bit: I forgot what it's called, but there's a certain orbital trajectory that minimizes the amount of time to reach somewhere, but maximizes delta-v usage (The amount of velocity you're able to accelerate, and decelerate). The maneuver simply consists of full acceleration until the midpoint is reached, then you turn around and full decelerate.

Ah, finally found it: http://en.wikipedia.org/wiki/Brachistochrone_curve.

It's the Brachistochrone trajectory... if you do write this in, please use this! I find the whole idea of wasting all that precious fuel to get there in the least amount of time; just because you technologically /can/, quite cool.

Also, it's been done it seems: https://en.wikipedia.org/wiki/Torchship