Apollo 8 lunar orbit circularization burn

[Willoughby]

I'm reading a book on Apollo 8 and it mentions a 4+ minute burn for lunar orbit insertion, but that only puts them into a 60.5 X 160.5 nautical mile elliptical orbit.  On a subsequent orbit, the circularized this orbit with a mere ~11 second burn.  The reason given was that the 60.5 X 160.5 was the best they could do in one shot.  I am baffled by this because it seems that a mere extra 11 seconds on what is already a 4+ minute burn doesn't seem significant.  Can anyone explain the physics of this or some other reason?  It seem if they had simply started the burn about 5.5 seconds sooner and engine cutoff was 5.5 seconds later, they would have been in the 60 X 60 orbit in one shot.

[Peter B]

IANAP (I am not a physicist) but my guess is that it's an acceleration thing.

As the engine burns it uses fuel. Therefore mass goes down and acceleration increases during the course of the burn. This means that each extra second of burn changes the velocity of the spacecraft by a steadily greater amount.  This in turn increases the effect of an error if the engine burn is too long or if the engine's thrust differs from expected by a serious amount.

The first burn is as short as is needed to place the spacecraft into a stable orbit, even if it's elliptical. Then, once they know exactly what the shape of the orbit is, they do a second burn to adjust it into what they actually want.

However, happy for the physicists to explain where I'm wrong.

[Allan F]

I'm reading a book on Apollo 8 and it mentions a 4+ minute burn for lunar orbit insertion, but that only puts them into a 60.5 X 160.5 nautical mile elliptical orbit.  On a subsequent orbit, the circularized this orbit with a mere ~11 second burn.  The reason given was that the 60.5 X 160.5 was the best they could do in one shot.  I am baffled by this because it seems that a mere extra 11 seconds on what is already a 4+ minute burn doesn't seem significant.  Can anyone explain the physics of this or some other reason?  It seem if they had simply started the burn about 5.5 seconds sooner and engine cutoff was 5.5 seconds later, they would have been in the 60 X 60 orbit in one shot.

What altitude was the insertion burn performed at?

[Peter B]

I'm reading a book on Apollo 8 and it mentions a 4+ minute burn for lunar orbit insertion, but that only puts them into a 60.5 X 160.5 nautical mile elliptical orbit.  On a subsequent orbit, the circularized this orbit with a mere ~11 second burn.  The reason given was that the 60.5 X 160.5 was the best they could do in one shot.  I am baffled by this because it seems that a mere extra 11 seconds on what is already a 4+ minute burn doesn't seem significant.  Can anyone explain the physics of this or some other reason?  It seem if they had simply started the burn about 5.5 seconds sooner and engine cutoff was 5.5 seconds later, they would have been in the 60 X 60 orbit in one shot.

What altitude was the insertion burn performed at?

60nm.

[smartcooky]

The point where the orbit insertion burn was made was not the right place in the orbit to circularize it with the minimum energy/fuel use. The desired orbit was circular at 60nm, but the 250s lunar insertion burn took place at 75nm altitude, not 60nm. The burn put them into a 60nm x 168nm orbit. IANARS, but if understand orbital mechanics correctly it would have taken a lot more energy to enter the desired "final" circular orbit in a single burn than it would doing it in two steps - adding an extra 10 seconds to that burn would not have worked.

In order to circularize a 60 x 168 orbit to 60 x 60, you need to make the burn at the perigee (or in this case perilune), the 60nm point...

https://history.nasa.gov/SP-4029/Apollo_08a_Summary.htm

See the end of the  "Translunar Phase" section and the beginning of the "Lunar Orbit Phase" about half way down the page.