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My first question so show mercy! Earth to Mars 150,000,000 miles. Earth escape velocity ~20,000 MPH (at maximum fuel consumption). The journey takes 8 Months at that speed.

The Question: If launching from Moon or LEO using same amount of fuel, Would it reach a speed of ~100,000 MPH due to lower Gravity enter image description here

Ruskes
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    I suggest to edit the title. Btw, launching things from the Moon is not easy (last time it happened in 1971). – peterh Mar 13 '21 at 09:52
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    Your question is somewhat unclear. I am having trouble making sense of the photo. How does this apply to launching from the Moon? Also, what does this have to do with [tag:spacex-starship]? – Jörg W Mittag Mar 13 '21 at 10:01
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    This question might be relevant: Why don't we launch spacecraft from the Moon. – Fred Mar 13 '21 at 15:40
  • @peterh-ReinstateMonica: Apart from the Apollo lunar landers returning to their command modules (Apollo 17 being the last in December 1972), what was launched from the Moon in 1971? Soviet Luna 24, in 1976, was the last lunar sample mission conducted by the Soviets. – Fred Mar 13 '21 at 16:36
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    @peterh-ReinstateMonica There was Chang'e 5 in December 2020. – notovny Mar 14 '21 at 00:08
  • @peterh-ReinstateMonica, I think the challenge in 1971 was landing on the moon, not launch from there ;-) –  Mar 14 '21 at 23:12
  • @JörgWMittag ignore the photo, it is symbolic, I do not have a photo from Starship taking of from Moon. – Ruskes Mar 14 '21 at 23:51
  • @peterh-ReinstateMonica no one said it is easy, but SpaceX is building a ship that can land and take off. The question is simple: if using the same amount of fuel as on Earth will it go faster since it does not has to fight the GRAVITY AND AIR. – Ruskes Mar 14 '21 at 23:55
  • @Ruskes Ok, but then 1) you need to create the fuel on the Moon (requires factory on the Moon) 2) or you need to transport that fuel to the Moon (makes the thing much harder than using LEO). – peterh Mar 15 '21 at 08:02
  • @peterh-ReinstateMonica I know all that, My question is very specific to the speed. Does a rocket goes faster using same amount of fuel, launched from no or low gravity and no air. – Ruskes Mar 16 '21 at 02:35
  • @Ruskes Yes, of course. Delta V needed from Earth surface to the Earth escape trajectory is about 13km/s. From the Moon it is about 3km/s. – peterh Mar 16 '21 at 04:01

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Most of a rocket’s energy goes to increasing its orbital speed and only a relatively small proportion of that energy is lost to gravity, so lower gravity will not have that much effect. Also the force of gravity in LEO is not that much lower than on Earth’s surface anyway.

The most important things to consider when calculating how fast a rocket can go are the starting mass (mass of the rocket + propellant), the final mass (just the mass of the rocket) and the exhaust velocity (how fast the burning gaseous are rushing out of the back of the rocket).

Earth orbits the Sun at an average speed of around 67,000mph. Mars orbits the Sun further out at 54,000mph on average. Neither orbit is circular and Mars orbit is inclined at an angle from the plane of the ecliptic. So the whole Earth to Mars transfer is a complex continuously whirling high speed dance and is not a point A to point B transfer.

Slarty
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    Thank you for your answer. However I disagree with some of your statements. Most energy is spend on fighting the gravity during the take off. The force of gravity decreases with distance to Earth. On Moon the Gravity is 1/5 of Earth (the Moons Gravity). A rocket departing Moons orbit will have to fight 1/5 of Earths Gravity, thus use less fuel and go faster. If you trow a rock on the Moon it will fly 5 times further. – Ruskes Mar 17 '21 at 07:21
  • This sort of discussion can easily get stuck as there are a lot of different connected issues. But the heart of the problem is the rocket equation and understanding what it means. In layman’s terms what it means is that the faster you go the harder it gets to go faster still. If you burn 90% of the rocket as propellant to go at one speed, in order to go twice as fast you must burn 99% of the rocket as propellant. Try this link https://www.youtube.com/watch?v=uWjdnvYok4I and see how you get on. I suspect what you think should happen would only happen if extra propellant could be found in orbit. – Slarty Mar 17 '21 at 14:35
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    @Ruskes, during a launch from Earth's surface to low orbit, about 15% of a typical rocket's delta-V is lost fighting gravity, and 85% goes into getting up to orbital speed -- and when going off to Mars from low Earth orbit, you get to keep all that orbital speed. Launching from the Moon might save you most of that 15%, but you still need to build up that 85% when heading off to Mars. (Mostly. Orbital mechanics is tricky.) – Mark Mar 18 '21 at 02:43
  • @Mark are you saying it is beneficial for the fuel and acceleration when launching from LEO or even Moon ? – Ruskes Mar 19 '21 at 03:15
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A useful concept here is delta V rather than speed. To achieve a stable orbit from Earths surface requires going ~9kms faster than you started, to boost that orbit to escape to a roughly circular orbit in vicinity Earth requires a further 3kms and boosting that out to intercept mars another 1kms (on an orbit that would fall back an intercept Earths orbit again if unchanged). Matching up with mars needs another ~1.4kms.

So it is possible to draw maps like this that while useless for navigation allow you to get a feel for how much rocket is needed to get somewhere. in particular note that the difference between a moon intercept and escaping earth is on 90ms so almost identical in space travel terms.

All of these numbers assume optimal trajectory choice (half orbit travel time) of a classical transfer orbit. If you burn more fuel you can take several short cuts by leaving Earth later and arriving 'sooner' at mars, the resulting charts are called pork chop plots. Looking at the one on the wikipedia page. the red angled lines are transit times in days. so optimal trajectory was 400 days and 15.5kms from Earth, there was a 200 day option lower down for 16kms and if you went to 30kms you could get under 125 days.

Looking at the solar system DV map, the difference between a moon launch and a Earth launch is around 10kms (running to earth escape), so a rocket capable of getting a given payload from Earth to Mars optimally (16kms and 200 days) would have another 10kms to burn allowing us to look on the pork chop plot around the 26kms line and get ~125 days. Other option of course rather than shaving 75 days is to instead just take more stuff with you.

To get 30 day travel times you need something like a torch ship doing a continuous 0.25G burn that is well beyond plausibility on current tech.

GremlinWranger
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