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During the intercept (terminal) phase of orbital rendezvous, the intercepting spacecraft must use Proportional Navigation or Orbital Mechanics to develop an intercept course: all that counterintuative “back up to catch up” stuff. However, during braking and docking phase, the interceptor uses intuitive “boating around” maneuvering.

Question: During orbital rendezvous, at what distance and approach velocity does the transition from orbital mechanics to “boating around” occur?

Buzz Aldrin’s doctoral thesis on orbital rendezvous is available at https://dspace.mit.edu/handle/1721.1/12652 It has a general overview which is surprisingly readable.

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    $\begingroup$ I don't know how it's done in practice, but my guess is that the general rule of thumb would be that you can more or less ignore orbital mechanics when the time to docking is much smaller than the orbital period. $\endgroup$
    – Litho
    Nov 15 at 10:54
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    $\begingroup$ @Litho I second that, but I would replace "time to docking" with "duration of the maneuver" $\endgroup$
    – asdfex
    Nov 15 at 11:17
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    $\begingroup$ @Ludo I'm not quite sure what the OP means by "boating around", but there is a transition, possibly multiple transitions, that vary from chaser to chaser and from target to target. The key transition occurs when the chaser vehicle's relative navigation sensors become active. $\endgroup$ Nov 15 at 14:24
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    $\begingroup$ Based on my experience in KSP, the answer is "never". But if you can complete your maneuver in under 1/4 of an orbit, the effect is minor. If you can complete the maneuver in under 1/10th of an orbit, you do not even notice the "orbital dynamics" part of it. OTOH, if your maneuver takes exactly half an orbit, then... you are <<censored expletive>> everything works exactly and equally opposite of what you expect, unless you plan for the opposite, then it happens 90 degrees from where you though it would be. $\endgroup$ Nov 15 at 14:32
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    $\begingroup$ Re: "Boating around", I meant it in the same sense as Wally Schirra's description of his Gemini rendezvous, "play the game of driving a car or driving an airplane or pushing a skateboard ." Basically, it means ignoring orbital mechanics. $\endgroup$
    – Woody
    Nov 15 at 17:22
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Orbital mechanics always apply.

For shuttle the two different operational phases were referred to as Rendezvous Ops and Prox Ops

The breakpoint between the two was defined in the Space Shuttle Flight Rules, Rule A2-116 (emphasis mine)

A. RNDZ OPS ARE DEFINED TO INCLUDE ALL ORBITER RNDZ MANEUVERS AND ASSOCIATED RNDZ ACTIVITIES TERMINATING WITH THE INITIATION OF PROX OPS.

B. PROX OPS BEGIN AT THE COMPLETION OF RNDZ OPS WHEN THE ORBITER RANGE TO THE TARGET IS <1000 FEET AND THE LVLH RELATIVE VELOCITY IS <1 FPS IN EACH AXIS.

RNDZ OPS utilize closed loop guidance, navigation, and control to achieve a desired relative state. PROX OPS is a post-RNDZ activity where different techniques used to “control” the orbiter trajectory than those used during RNDZ OPS. These techniques rely on crew visual observations and piloting techniques to achieve a desired relative state. These definitions are provided for reference.

Orbital mechanics effects during prox ops are covered in this excerpt from the JSC Rendezvous Crew Training Handbook (not currently online)

scan of a textbook page showing graphs of different relative motions. excerpts: Posigrade velocity results in radial-up acceleration; retrograde velocity results in radial-
down acceleration / Radial-up velocity results in retrograde acceleration; radial-down velocity results in
posigrade acceleration / Radial position results in acceleration away from target / Out-of-plane position results in acceleration toward plane

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  • $\begingroup$ Where can we get this manual?? $\endgroup$
    – Innovine
    Nov 17 at 11:09
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Captain Wally Schirra was the first person to ever successfully pull off a space rendezvous. Here is, more or less, how he would have answered the question (this is a quote from Capt. Schirra after Gemini 6A):

"Somebody said ... when you come to within three miles (5 km), you've rendezvoused. If anybody thinks they've pulled a rendezvous off at three miles (5 km), have fun! This is when we started doing our work. I don't think rendezvous is over until you are stopped – completely stopped – with no relative motion between the two vehicles, at a range of approximately 120 feet (37 m). That's rendezvous! From there on, it's stationkeeping. That's when you can go back and play the game of driving a car or driving an airplane or pushing a skateboard – it's about that simple."

Once the rendezvous has proceeded to the point where the range between the "chaser" and "target" vehicles is down to ~1000 ft or less, the chaser vehicle's pilot will find that, if all relative motion with respect the target vehicle is reduced to zero (or, almost zero), the task of maintaining a steady position (again with respect to the target vehicle), or stationkeeping, becomes quite simple - as Captain Schirra put it, "That's when you can go back and play the game of driving a car or driving an airplane or pushing a skateboard – it's about that simple."

In other words, once the chaser vehicle has attained the conditions necessary to set up stationkeeping, the effects of orbital mechanics become almost imperceptible - and get less noticeable the closer the two vehicles are to each other (relative motion being kept low)...

To put things into perspective, NASA's Rendezvous Crew Training Handbook (dated November 1998) states that, for the Space Shuttle Orbiter, stationkeeping, when on the Vbar at a range of 1000 feet and in a circular orbit of 160 nautical miles, should require no more than ~70 lbs. of propellant per orbit. That's pretty low. Alternatively, said reference also states that, if said stationkeeping is instead set up at 40 feet on the Rbar (with the same target vehicle orbital parameters), said prop consumption should be on the order of 100 lb/rev.

FYI, one can generally infer that, the simpler the piloting task, the lower the rate of prop consumption.

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