Because these probes have to be relatively cheap and small, they don't have much in the way of thrusting capability, but they are built to last. Their aim is to "hop" from asteroid to asteroid, mapping each one for water/mineral resources as they go. Perhaps there is a significant degree of onboard processing which generates a model of each object, so that the data transfer back to Earth is minimised as much as possible. On those (presumably rare) occasions when two asteroids have a close approach, and the distance and velocity is within the capability of the probe to make the jump, it moves onto the next one. And the next one, and so on.

Quote from: mikelepage on 02/18/2018 03:43 amBecause these probes have to be relatively cheap and small, they don't have much in the way of thrusting capability, but they are built to last. Their aim is to "hop" from asteroid to asteroid, mapping each one for water/mineral resources as they go. Perhaps there is a significant degree of onboard processing which generates a model of each object, so that the data transfer back to Earth is minimised as much as possible. On those (presumably rare) occasions when two asteroids have a close approach, and the distance and velocity is within the capability of the probe to make the jump, it moves onto the next one. And the next one, and so on.If the probe is limited in "thrusting capability", shouldn't you look at difference in velocity rather than distance in space? (you're not wanting to "lithobrake", are you?) With a limited delta-V budget I'd think you should be looking for slow rendezvous trajectories that only require little nudges to set up; the closest approach of the asteroids to each other would be less important than the orbits being similar enough that a few nudges could set up a rendezvous over the course of some number of years of phasing.

You still want to know about all close approaches - even if the delta-V to transit is too high - because you would still get some data from a flyby.

I developed software 12 years ago that ran on AutoLISP for AutoCAD and calculated solar system trajectories then plotted the orbits and the transfer path on the screen for any two bodies in solar orbit.The math is not simple, but it is totally doable, I did it partly just to show that it is nothing more than algebra. What it amounts to is a trial and error solution where you specify the time of flight and eventually get the timing and delta v needed. Other inputs are the orbital parameters and position which you get from JPL's system, called Horizon back then.What the software is largely about is doing the arithmetic of keeping track of the true anomaly of the destination, the spacecraft and the origin on their respective orbits.The basic calculation is to find an elliptical path from the specified time of flight, then you check how much you missed the planet in space and time. Adjust and iterate the timing until you miss by less than the sphere of influence, or other specified accuracy.I would love to send what I've got to someone to run with. It is not hard, you just need to get to know the math of elliptical paths.Getting around between minor planets is all about time vs. delta v.

Quote from: spacester on 10/08/2018 04:07 amI developed software 12 years ago that ran on AutoLISP for AutoCAD and calculated solar system trajectories then plotted the orbits and the transfer path on the screen for any two bodies in solar orbit.The math is not simple, but it is totally doable, I did it partly just to show that it is nothing more than algebra. What it amounts to is a trial and error solution where you specify the time of flight and eventually get the timing and delta v needed. Other inputs are the orbital parameters and position which you get from JPL's system, called Horizon back then.What the software is largely about is doing the arithmetic of keeping track of the true anomaly of the destination, the spacecraft and the origin on their respective orbits.The basic calculation is to find an elliptical path from the specified time of flight, then you check how much you missed the planet in space and time. Adjust and iterate the timing until you miss by less than the sphere of influence, or other specified accuracy.I would love to send what I've got to someone to run with. It is not hard, you just need to get to know the math of elliptical paths.Getting around between minor planets is all about time vs. delta v.Not sure I'm too happy with autolisp, but I'd like to see the code for the geometry stuff.