# Maximum speed reachable by Saturn V

If we launch a Saturn V rocket from space (far away from Earth so that Earth's gravity has no effect on it) then what would be the maximum velocity achievable? How close could it get us to the speed of light?

• Could be easily calculated from the mass and thrust of each stage which you can easily look up on wikipedia, but I am too lazy to do so right now ;). But I can say with certainty that it wouldn't even bring it close to relativistic speed. Mar 13 '14 at 14:57
• By the way, being close to a gravity-well could actually help to reach higher speeds. Mar 13 '14 at 14:58
• @phillip if you could take the mass of the S-V, and replace the hydrogen/oxygen/RP1 with say Xenon and use a constant thrust Ion style thruster, how fast could you go? That could get much faster than LOX/LH or LOX/RP1. Mar 13 '14 at 14:59
• @geoffc The NSTAR Xenon-ion thruster has an Isp of 3120 seconds, and the NEXT 4190, roughly ten times that of Saturn V's chemical engines, and Δv increases proportionally to Isp, so you'd be in the ballpark of 170km/s or 0.05% c. Remember that you'll have to get your Xenon-Saturn out of atmosphere and into orbit by some other means; you won't have nearly enough thrust to overcome gravity and atmospheric drag. en.wikipedia.org/wiki/NEXT_(ion_thruster) Mar 13 '14 at 20:41
• @MarkAdler - It's too bad you deleted your answer. It was a very good WAG. I'm not using that term demeaningly. The other way around: It's a complement. One problem that keeps this site as a beta site is that too many questions only get one answer. There's nothing wrong with having a selected answer and a non-selected one. Apparently, it's a good thing in the eyes of the stackexchange powers that be that questions have multiple answers. Mar 13 '14 at 21:15

The amount by which a spacecraft is able to change its velocity is called it's Δv (delta-velocity) budget. You can calculate the Δv-budget of each stage of a rocket using the Tsiolkovsky rocket equation which reads: $$\Delta v = I_{sp} * 9.81 * \ln \frac {Mass_{full}} {Mass_{dry}}$$

where Isp is the specific impulse ("fuel-efficiency") of the engine. The factor of 9.81 (the gravity of earth) in this context is the factor used to convert specific impulse to exhaust velocity. You could also express the formula above using exhaust velocity, but I decided to use the specific impulse, because the numbers I found for the efficiency of the Saturn V were in Isp.

The masses and Isp of each stage can be looked up on wikipedia. I made an overview as a table and calculated the delta-v using this handy online calculator:

      | Individual stage    | Total vessel         |
Stage | Full mass | Dry mass| Full mass | Dry mass | Isp   | Δv
------+-----------+---------+-----------+----------+-------+--------------
I     | 2,300,000 | 131,000 | 2,900,000 | 731,000  | 263s  | 3554.2 m/s
II    |   480,000 | 36,000  |   600,000 | 156,000  | 421s  | 5561.5 m/s
III   |   120,800 | 10,000  |   120,800 |  10,000  | 421s  | 8796.2 m/s
===========
17911.9 m/s
* masses are in kg


That means a Saturn V started in space could reach a speed of about 18 km per second or 64,500 km/h relative to its initial frame of reference. The speed of light is about 300,000 km per second, so this is still just about 0.006% of the speed of light.