This is a tricky question to answer because there are a lot of variables. Realistically, most of the propellant expended is going to be earth escape. You need ~11180 m/s delta-v to reach escape velocity from the earth's surface ignoring the effect of atmosphere which is significant. Using SpaceX starship as an example with a 210 day flight to Mars launched from the earth's surface now, for the 120t (dry mass) starship you need 2246.4t of propellant for earth launch and escape and then 64.5t propellant for mars velocity match. However, spacex plans on aerocapture at mars so we can disregard the propellant at the end of the flight but we must limit ourselves to a 7.5 km/sec entry velocity at mars. This all presuming Isp of 600s.

Given that we are fine, velocity difference at mars is 2.5 km/sec (at infinity) which ends up being about 5.56 km/sec at 100 km altitude over Mars, so that would work, and we don't need to carry the propellant for deceleration with us which improves the situation so that we only need 1419t propellant for launch and TMI.

Compare that to the propellant needed if we disregard the problem of earth escape velocity, only 110t. A 130 day flight time would have a mars atmosphere entry of 7.33 km/sec and would need 1596t propellant launched from Earth or 136t propellant disregarding earth escape.

With a 30 day flight time mars atmosphere entry velocity would be 37.4 km/sec, you'd need 122488t propellant launched from Earth or 18214.6t propellant disregarding earth escape. But in short it could easily be 100s of times more propellant for a short flight duration.

On Wed, Jul 29, 2020 at 10:49 AM <xxxxxx@gmail.com> wrote:
If I'm using rockets to get to Mars (or back) and I know that there's a point of closest approach to Earth based on each planet's orbit, what's the difference in fuel used going to be between that close-approach transit and the 'farthest distance' transit? Are we talking about 10%, 30%, 50% of fuel? I know there are other factors that will apply, but assuming one wants to make the transit (it might really, one supposes, be two answers - closest approach vs. furthest approach with each different origin (Earth or Mars)?

I don't need hard numbers, but I'm curious what sort of order of magnitude might be involved? I know it has to use more fuel and/or time to make the longer transit vs. the shorter, but I have literally no concept of even a rough % of difference in this respect.

I imagine it isn't just a ratio of separation distances because of ballistics and how we'd accelerate with a rocket, etc.  And giving a lot of the trip might be coasting, the difference might be almost all time and very little fuel (or a lot more fuel to hit higher speeds so the time is not a lot more).

For simplicity, I'd imagine you'd want to consider an instant impulse vs. the real situation of 'ship gets lighter as fuel burns, thus thrust produces more delta V'.

I guess aligned with this would be a related question:

What are the most likely lengths of time for Earth to Mars / Mars to Earth for a) fuel/mass economy and b) shortest time Earth to Mars given typical engines we might have access to? I ask just to get a ball park idea of how long it will usually take a crew to get to Mars and how fast one could get there if it was urgent given the limits of limited fuel/mass?

TomB




--
“The only stable state is the one in which all men are equal before the law.” ― Aristotle

-----
The Traveller Mailing List
Archives at http://archives.simplelists.com/tml
Report problems to xxxxxx@simplelists.com
To unsubscribe from this list please go to
http://www.simplelists.com/confirm.php?u=wkJZDVdDoS21PvuTrsXSMsmho7pwDsoN