About a spacecraft trip to the asteroids

[Emspak]

This was something I was kicking around and wanted some advice on.

Let's assume you had a big spaceship -- the kind you'd use t set off on a trip to the Asteroids, and were willing to take some time about it, on the order of a couple of years. Maybe you want to do asteroid mining or mine iceteroids for volatiles.

You're in Earth orbit, where the thing was built. You have a nice, big, NERVA type engine.

Which is the better plan, with the best combination of shorter travel time with energy efficiency:

-- Increase the ship's orbital speed around Earth -- let's say it starts in MEO - and get it to escape velocity in the direction retrograde to Earth's orbit. That will slow it down relative to the Sun, and the ship can fall in and slingshot around to the asteroids. When the ship is deep in the sun's gravity well you could even do a burn and boost its speed further, and get a nice long parabolic / extremely elliptical trajectory to the relevant spot.

-- Same thing, but going prograde, and using the free velocity you get from being around Earth and traveling with it to boost out to Mars and past it, since the delta-V would be (I think) less to get the same nice orbit out to between Mars and Jupiter, which is approximately where you want to be.

-- Some kind of VEGA trajectory.

I was also curious about how to set of a good langrangian for this. Was thinking of using the sun as my origin, but if anyone has a better idea please!

(And I was thinking of modeling this on Mathematica for giggles, but I don't know if it would work at all well as I am a beginner)

 

[mfb]

Getting close to the sun (to use the Oberth effect there) needs such a large delta_v that it is not reasonable for most solar system missions. To reach the asteroid belt (similar to Dawn), and without gravitational slingshots at planets, a Hohmann orbit is the best way.

I was also curious about how to set of a good langrangian for this.

The potential is known, the kinetic energy term is easy... setting up a Lagrangian is not the issue, finding solutions (if you include thrust or planets) is.

 

[Emspak]

thanks -- this helps a lot...

 

[Lsos]

If you first drop down deep in the sun's gravity well and set up an elliptical orbit that gets you to an asteroid, you still have to make a burn when you get to the asteroid to match its orbit (if you want to rendezvous). That means that you have to bring that part of the orbit deep in the sun's gravity well up to the asteroid, and that's going to be extremely costly.

 

[PJC01]

I would suggest considering all factors before deciding on the best plan for a spacecraft trip to the asteroids. Some key considerations would include the specific goals of the mission (i.e. asteroid mining or collecting volatiles), the capabilities and limitations of the spacecraft, and the availability of resources (such as fuel) for the journey.

In terms of the proposed plans, the first option of using a slingshot maneuver around the Sun could potentially offer a shorter travel time, but it would also require a significant amount of energy and precise calculations to execute successfully. Additionally, the spacecraft would need to have enough fuel to perform a burn while deep in the Sun's gravity well, which may not be feasible for a two-year journey.

The second option of using a prograde trajectory and taking advantage of Earth's orbital velocity to boost out to the asteroids may offer a more energy-efficient approach. However, it would also likely result in a longer travel time due to the indirect route and potential gravitational interactions with other planets along the way.

The VEGA trajectory, which involves using multiple gravitational assists from different planets, could potentially offer a combination of shorter travel time and energy efficiency. However, it would require precise calculations and a sophisticated navigation system to execute successfully.

As for setting up a good Langrangian, I would suggest considering the position and velocity of the spacecraft relative to the Sun and the asteroids, as well as any relevant gravitational forces from other celestial bodies. This would also depend on the specific goals and constraints of the mission.

In terms of using Mathematica for modeling, it could be a useful tool for simulating different trajectories and assessing their feasibility. However, as a beginner, it may be best to seek guidance from more experienced colleagues or consult with experts in the field to ensure accurate and reliable results.