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

Question

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.

Answer 1

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)

Answer 2

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.

Answer 3

The transition from orbital mechanics to intuitive “driving a car” maneuvering is not determined by distance or time, but by orbital phase angle change during the maneuver.

If the planned maneuver is completed in a small orbital phase angle (say, 5* or 2 minutes in LEO), orbital mechanics will play a small part in the relative trajectory between target and interceptor. If the planned maneuver takes 180* (an hour in LEO), orbital mechanics will have its maximal effect. The orbital mechanics effect never disappears for brief maneuvers… it just shrinks in magnitude until it becomes lost in “station keeping”.

A useful analogy is Coriolis force on a Merry-go-Round. You can’t play snooker on a Merry-go-round because the ride rotates a significant amount during the trajectory of the ball. However, a handgun will still ‘shoot straight’ on a Merry-go-Round since the duration of the bullet’s flight is only a tiny fraction of the ride’s rotation.