Quick! How far away is that asteroid?

How might an enterprising spacer, mining the rings of Saturn, go about quickly measuring/estimating the velocity of and distance to a nearby moving object (asteroid, habitat, pirate, etc)? Bonus points for measuring acceleration.

The lower tech, the better! The Saturnians would rather a microprocessor not be in the loop at all. They are a tough bunch, and would prefer a more reliable method with less electronics/moving parts, even if it meant lots of training or practice. Human>mechanical>electronic.

Note that this is more for quick maneuvering, rather than plotting trajectories that will be accurate over long distances/times (though if the method works for those, that's great too). Distances are tens of kilometers (maybe 150km at the outside), and the relative velocities are on the order of 100km/hr.

• You have a space-faring civilization that draws the line at using microprocessors? I mean, we did send men to the moon without a computer on board that, but all the calculations were done beforehand on Earth. – Halfthawed Mar 12 at 3:34
• They use microprocessors most of the time, but would like to have a low-tech backup in case windows decides to update or a stray gamma-ray flips an important bit in RAM during a pitched battle with pirates. (world is also fairly rocketpunk, so computers are limited anyway). – user73226 Mar 12 at 3:40
• Humans get tired and bored. That's why automated is more reliable than human based. – L.Dutch - Reinstate Monica Mar 12 at 7:51

Coincidence Range Finder Since we understood optics and trigonometry, we’ve been able to estimate range to far away objects.

This is a schematic of a range finder that mechanically computes the distance when an object is clearly viewed in the objective lens. The operator adjusts the compensating mechanism to overlay the image from the left and right prism.

This diagram gives a clear functional statement about the operation of these kinds of devices.

Once you have an estimate of the range, and you know your velocity, you can use Time Motion Analysis (TMA) to quickly derive the asteroid’s velocity (speed and heading). One method that is performed by hand, as a back up and sanity check, by submarines tracking targets, is Ekelund Ranging. I did this during battle station drills using a sharpie, graph paper, and a ruler, and was expected to nearly as fast as the analog computers we used for fire control.

Ekelund ranging

One of the best known Time Motion Analysis techniques is Ekelund ranging. It is a method that is specifically designed for a 2leg-1zig scenario. This method works by first estimating the bearing rates during the first and second leg ($$BR_1$$ and $$BR_2$$ respectively)

Secondly, one calculates the speed of advance (SOA) along the line of sight with the target on the first and second leg ($$SOA_1$$ and $$SOA_2$$ respectively

The rule then states that the range of the target at the moment of second leg is given by:

$$R_2 = \frac{SOA_2 - SOA_1}{BR_1-BR_2}$$

• Modern times uses lidar, with time-of-flight for ranging and Doppler shift for distances. No moving parts. But, yeah, those Saturnians and their steampunk mining vessels! – Adrian Colomitchi Mar 12 at 4:34
• @AdrianColomitchi, agreed. just trying to answer with the question’s parameters. – EDL Mar 12 at 4:37