[Request] Total delta-V of a Saturn V rocket?
Say I was to take a fully fueled Saturn V (such as the one for Apollo-11, complete with command and service modules and lunar excursion module). Then I was to put it into mission configuration with 3 astronauts and all the normal consumables on the flight and launch it. Let's say that, instead of trying to land on the moon and return, I was just to take each stage and try for the maximum amount of velocity. You fire each stage in turn and discard it. Then when you've exhausted the third stage, you do the transposition and docking maneuver and extract the LEM from the S-IVb booster. Then you turn around and fire the SPS engine on the CSM to depletion. Then you put the astronauts in the LEM and discard the CSM, then fire the descent engine on the LEM to depletion, then eject the descent stage and fire the ascent engine on the LEM to depletion. Obviously this is a one-way mission, because we are traveling far faster than escape velocity. No way to get back home unless you encounter the earth after going all the way around the sun, and by then you are out of consumables and long dead. So get good life insurance policies on the astronauts before they go.
What is the total amount of Delta-v in this scenario? How fast would the LEM ascent module be going in this scenario if it was inserted into an escape trajectory?
Posted Dec 7, 2015, 2:17 PM UTC
Someone on stackexchange already went through the process of looking up the numbers on wikipedia and entering them into a calculator. This might not fit your exact mission profile but the weight of the people is probably pretty insignificant compared to the weight of the craft.
It also does not include the lunar landing modules engines, Ill leave a more detailed analysis as an exercise for someone else.
http://space.stackexchange.com/questions/3972/maximum-speed-reachable-by-saturn-v
If theres 17km/s of delta-v, then to calculate the final speed after flying away from earth, just subtract earths escape velocity.
You end up with about 7km/s of delta-v. It will be in an orbit around the sun starting that initial velocity (relative to the earth) and position (near earth). The shape of the orbit will be determined the heading on which you flew. But all headings result in a sun-centric orbit. The velocity relative to the sun will be higher. You started with about 30km/s on earth and added a bunch. If your orbit is not circular then the highest velocity will occur when the craft is closest to the sun. This might take years depending on how you started your new orbit, but if you pass very close (dangerously close) to the sun on an eccentric orbit, the velocity relative to the sun could easily be a few hundred km/s (see keplers second law).
If you wanted more delta-v though, you could steal it from the moon, as well as the earth itself, and other planets. So the total potential delta-v could be theoretically much higher if the trajectory is chosen very carefully.
Hmmmm, this is a very good answer. I hadn't thought of trying to use the Oberth effect on the Sun! That would be insane.
Thank you sir. I mostly just pieced together what I know from KSP and actually launching several similar missions. You play?
Oooooooh yeah. Jeb4Lyfe.
Also, my understanding of the oberth effect is that it is more related to kinetic energy than to our problem of delta-v. The ship will still have the same amount of delta-v when it is close to a planet, but that delta-v is "worth more" kinetic energy at higher speeds.
So a change of 1km/s at apoapsis will give you less kinetic energy than a change of 1km/s at the periapsis of the same orbit. Speed change is constant, but where the speed change occurs significantly affects the final momentum.
Since your original question is just trying to achieve the highest relative velocity, falling into the sun and converting all of your potential energy to kinetic is the best way to do that. That's not the oberth effect though. Firing your engines near the sun to escape the solar system would be.
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