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When Apollo astronauts departed the lunar surface in the Lunar Module's Ascent Stage, it appeared to rise vertically ($\beta$ = 0) for ~10 seconds and then begin the "tipover" (videos of Apollo 15, 16 and 17), the program of increasing $\beta$ ( = $\pi/2 - \gamma$) with time, transitioning from vertical flight to orbit, where $\beta$ was just short of $\pi/2$ at ASP shutdown.

In the videos, especially the out-the-window video, it is apparent that the $\beta$ vs. time program is not a smooth pitch-over but instead has discrete (short) intervals of increasing $\beta$ with intervals of nearly-constant $\beta$ between.

QUESTION: Given the physical and performance parameters of a fully loaded Ascent Stage, what would be the optimal time profile of $\beta$ to minimize propellant use attaining the initial (@RussellBorogove's answer to another question specifies 18 x 87 km) lunar orbit?

Assume launching from central Mare Tranquillitatis, so no mountains around, and no margins.

When Apollo astronauts departed the lunar surface in the Lunar Module's Ascent Stage, it appeared to rise vertically ($\beta$ = 0) for ~10 seconds and then begin the "tipover" (videos of Apollo 15, 16 and 17), the program of increasing $\beta$ ( = $\pi/2 - \gamma$) with time, transitioning from vertical flight to orbit, where $\beta$ was just short of $\pi/2$ at ASP shutdown.

In the videos, especially the out-the-window video, it is apparent that the $\beta$ vs. time program is not a smooth pitch-over but instead has discrete (short) intervals of increasing $\beta$ with intervals of nearly-constant $\beta$ between.

QUESTION: Given the physical and performance parameters of a fully loaded Ascent Stage, what would be the optimal time profile of $\beta$ to minimize propellant use attaining the initial (@RussellBorogove's answer to another question specifies 18 x 87 km) lunar orbit?

Assume launching from a spherical moon and from central Mare Tranquillitatis, so no mountains around, and no margins.

When Apollo astronauts departed the lunar surface in the Lunar Module's Ascent Stage, it appeared to rise vertically ($\beta$ = 0) for ~10 seconds and then begin the "tipover" (videos of Apollo 15, 16 and 17), the program of increasing $\beta$ ( = $\pi/2 - \gamma$) with time, transitioning from vertical flight to orbit, where $\beta$ was just short of $\pi/2$ at ASP shutdown.

In the videos, especially the out-the-window video, it is apparent that the $\beta$ vs. time program is not a smooth pitch-over but instead has discrete (short) intervals of incresing $\beta$ with intervals of nearly-constant $\beta$ between.

QUESTION: Given the physical and performance parameters of a fully loaded Ascent Stage, what would be the optimal time profile of $\beta$ to minimize propellant use attaining the initial (@RussellBorogove's answer to another question specifies 18 x 87 km) lunar orbit?

When Apollo astronauts departed the lunar surface in the Lunar Module's Ascent Stage, it appeared to rise vertically ($\beta$ = 0) for ~10 seconds and then begin the "tipover" (videos of Apollo 15, 16 and 17), the program of increasing $\beta$ ( = $\pi/2 - \gamma$) with time, transitioning from vertical flight to orbit, where $\beta$ was just short of $\pi/2$ at ASP shutdown.

In the videos, especially the out-the-window video, it is apparent that the $\beta$ vs. time program is not a smooth pitch-over but instead has discrete (short) intervals of increasing $\beta$ with intervals of nearly-constant $\beta$ between.

QUESTION: Given the physical and performance parameters of a fully loaded Ascent Stage, what would be the optimal time profile of $\beta$ to minimize propellant use attaining the initial (@RussellBorogove's answer to another question specifies 18 x 87 km) lunar orbit?

Assume launching from central Mare Tranquillitatis, so no mountains around, and no margins.

When Apollo astronauts departed the lunar surface in the Lunar Module's Ascent Stage, it appeared to rise vertically ($\beta$ = 0) for ~10 seconds and then begin the "tipover" (videos of Apollo 15, 16 and 17), the program of increasing $\beta$ ( = $\pi/2 - \gamma$) with time, transitioning from vertical flight to orbit, where $\beta$ was just short of $\pi/2$ at ASP shutdown.

In the videos, especially the out-the-window video, it is apparent that the $\beta$ vs. time program is not a smooth pitch-over but instead has discrete (short) intervals of incresing $\beta$ with intervals of nearly-constant $\beta$ between.

QUESTION: Given the physical and performance parameters of a fully loaded Ascent Stage, what would be the optimal time profile of $\beta$ to minimize propellant use attaining the initial (18 x 87 km) lunar orbit?

When Apollo astronauts departed the lunar surface in the Lunar Module's Ascent Stage, it appeared to rise vertically ($\beta$ = 0) for ~10 seconds and then begin the "tipover" (videos of Apollo 15, 16 and 17), the program of increasing $\beta$ ( = $\pi/2 - \gamma$) with time, transitioning from vertical flight to orbit, where $\beta$ was just short of $\pi/2$ at ASP shutdown.

In the videos, especially the out-the-window video, it is apparent that the $\beta$ vs. time program is not a smooth pitch-over but instead has discrete (short) intervals of incresing $\beta$ with intervals of nearly-constant $\beta$ between.

QUESTION: Given the physical and performance parameters of a fully loaded Ascent Stage, what would be the optimal time profile of $\beta$ to minimize propellant use attaining the initial (@RussellBorogove's answer to another question specifies 18 x 87 km) lunar orbit?