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In a typical, modern satellite launch, what triggers the cutoff of the orbital insertion stage's rocket engines?

I can think of three basic possibilities:

  1. Compute how much fuel you need for the trajectory, load exactly that much, and burn all the fuel
  2. Bring a little extra fuel and cut off the engines at a specific time
  3. Bring a little extra fuel and cut off the engines when telemetry indicates you're at the desired altitude and speed

The first two seem like they'd be susceptible to small variations in atmospheric conditions, engine performance, and so on.

A historical example: Apollo 13's second stage. The center engine cut off early due to pogo oscillation, when the fuel pressure dropped below a shutdown threshold which was intended to make sure the engine stopped cleanly when the stage started to run out of fuel (which itself implies that option 1 is a little uncertain; not all the fuel is going to get burned).

To compensate, they simply ran the second stage longer. Was that a natural result of consuming all the remaining fuel through four engines instead of 5 (implying option 1), or did they have to explicitly command a later cutoff time (implying option 2), or was the compensation completely automatic (option 3)?

Note that I'm asking about the initial launch and orbital insertion phase, not about fine-tuning the orbit and/or rendezvousing with a target via multiple incremental burns.

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Option #1 is out. You always bring more fuel than you think you need. Then you bring a little more yet. SpaceX just showed us what happens when you don't do that.

Option #2 is still used to some extent. Rockets initially did use timed burns, but improved sensors and onboard computers lead to a better way. Russia still uses programmed burns early on. It uses other approaches when finer control is needed. The US likes more extravagant approaches throughout. This costs more but is more accurate.

Option #3 is used to some extent, during some phases of flight. There is a problem: It can't be done as stated in the question. If the rocket gets to the desired altitude it won't be at the desired velocity, and if it gets to the desired velocity it won't be at the desired altitude. What happens is instead that along the way, the vehicle adjusts its trajectory so that it will come close to having the right velocity when the vehicle reaches the desired altitude. Then it shuts down when it thinks it has reached the target altitude.

A related option is to calculate the delta v needed to get from the current orbit to the desired orbit and stop thrust when the sensed accumulated delta v reaches the desired value.

There is an additional problem: The vehicle isn't where it thinks it is, nor is it going at the velocity it thinks it is. The sensed accumulated delta v is erroneous as well. This brings up the need for additional options.

Option #4: Make corrections along the way. Burns tend to be short once the vehicle is on orbit. The vehicle is only thrusting all the time during launch. After that, space vehicles use a burn-coast-burn strategy. This gives the vehicle time to figure out that the burn that started the transfer wasn't quite right. Correction burns put the vehicle back on a trajectory that will more or less bring the vehicle to the desired place, at the desired velocity, and at the right time.

Option #5: Don't do it all at once. Nobody goes from launch to the target orbit. Everyone sneaks up on the target. A direct flight from ground to the International Space Station would take about ten minutes. The Automated Transfer Vehicle sometimes takes many days to get from the ground to the the International Space Station. Even the Soyuz rapid launch takes six hours.

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  • $\begingroup$ Re. #3, that seems a little counter-intuitive to me; I feel like you could get any pair of (altitude, velocity, orbital phase) with attitude control during the burn (but my intuition is probably wrong). Re. #4 and #5, I'll edit my question to be clear that I'm asking about the initial launch and orbital insertion phase. I'm specifically not asking about fine-tuning the orbit with separate burns, nor about rendezvous orbits. $\endgroup$
    – Russell Borogove
    Jan 20, 2015 at 3:34
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    $\begingroup$ The vehicle makes closed loop corrections all the way up (or all the way since first stage termination, which oftentimes is still open loop guidance). By the time the trigger is reached that terminates thrust, the vehicle is close to being at the desired point of the desired orbit. The Powered Explicit Guidance used on the Shuttle used VGO (velocity to go) as the trigger. A lot of ascent guidance schemes still use variants of PEG. $\endgroup$
    – David Hammen
    Jan 20, 2015 at 4:13
  • $\begingroup$ Your answer implies that velocity threshold cutoff is done by the vehicle's onboard integrated velocity estimate; is velocity determined from the ground less accurate, or is there another reason? $\endgroup$
    – Russell Borogove
    Jan 20, 2015 at 17:14
  • $\begingroup$ It's not a simple numerical integration of the accelerometer output. (In fact, it can't be because the vehicle is rotating while it climbs.) The navigation system determines the vehicle's state using Kalman filter that receives a number of inputs such as navigation sensors and GPS. Noise and biases in the nav sensors show up as a discrepancy between the integrated position and the GPS position. This computed position error is strongly correlated with state velocity error, which means velocity gets a Kalman update along with position. $\endgroup$
    – David Hammen
    Jan 20, 2015 at 17:47
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    $\begingroup$ With regard to relying on ground telemetry, that adds several points of failure and thus a significant safety risk. Safety dictates that it's best if active regimes of flight are more or less autonomous. The ground does monitor for problems and occasionally sends commands to the spacecraft. But a continuous, real-time data link that is essential to proper operation of the spacecraft, that's a bad idea. $\endgroup$
    – David Hammen
    Jan 20, 2015 at 17:51

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