Interplanetary Gate Orbits

[keermalec]

This topic came about while trying to understand gravity losses on the Missions & Launches Forum but to me the subject seemed important enough for it to merit its own thread.<br /><br />I believe this is an important discovery, as it demonstrates the fact that certain specific orbits around a planet offer minimum delta-v gates for interplanetary travel.<br /><br />.............................<br /><br />There is an "optimal altitude" at which the delta-v needed to send a ship to Mars (with 2.94 km/s at SOI) on a Hohmann transfer is minimal. IE: the delta-v is more important at lower or higher orbits than this one. The "optimal altitude" is: <br /><br />85'800 km above the surface of the Earth, or about 92'300 km from its center. <br /><br />At this altitude the necessary delta-v required to get to Mars is 2.08 km/s. Above, or below, this orbit the necessary delta-v's are higher...<br /><br />On Mars the optimal altitude is at 8'900 km above the surface, or 12'300 km from the center. Here the required delta-v to attain 2.64 km/s at MSOI for Hohmann transfer to Earth is only 1.87 km/s. <br /><br />It seems strange but the math checks out right.<br /><br />At the moment it seems the best location to launch a Mars expedition from is at the 92'300 km orbit. Getting there requires 5.63 km/s delta-v for orbital transfer, but getting from there to Mars requires only 3.95 km/s!!! and this does not include any speed saving by aerobreaking or otherwise at Mars.<br /><br />This gives us a 31% payload capacity if using a 372s ISP CH4/O2 drive... (assuming the ship is tugged to the IGO and refuelled there by another ship). This capacity can certainly be augmented if we optimise the arrival burn at Mars by aerobreaking.<br /><br />Just imagine what we could do with the extra delta-v or capacity: <br /><br />1. make the Mars mission cheaper by making the ship smaller <br />2. make the mission safer by launching 2 ships <br />3. get there faster by choosing faster-than-Hohmann transfers, thereby also <div class="Discussion_UserSignature"> <p><em>“An error does not become a mistake until you refuse to correct it.” John F. Kennedy</em></p> </div>

 

[jimfromnsf]

"This gives us a 31% payload capacity if using a 372s ISP CH4/O2 drive... (assuming the ship is tugged to the IGO and refuelled there by another ship)."<br /><br />That is a big assumption. So why is it a better node if the same total energy is required? Actually, why would it be better than L2 or other lunar orbit? So now the launch vehicle has to be larger

 

[gunsandrockets]

Now first off I should say that I am just beginning to learn the ins and outs of orbital mechanics, and my math skills are rudimentary. That said I have a question about the gateway orbit idea...<br /><br />I had the impression that the neccessary delta-V to attain a particular trajectory was minimized by making the engine burn at as low an altitude as possible. That obviously contradicts the gateway notion.<br /><br />It supposedly works this way - orbital velocity is highest at the low point of an orbit, potential energy trading for kinetic energy as the spacecraft falls from apoapsis. Because the kinetic energy of a spacecraft is due to the square of it's velocity, adding delta-V when the spacecraft is speeding along at periapsis increases the kinetic energy of a spacecraft much more than adding the same delta-V when the spacecraft is crawling along at apoapsis.<br /><br />It's counterintuitive since the result appears to look like getting something for nothing. But the spacecraft gains more energy at periapsis than at apoapsis even though the same amount of fuel is burned. <br /><br /><br /><br />

 

[keermalec]

Hi G&R, the IGO is a circular orbit, and therefore has no apoapsis nor periapsis.<br /><br />The low delta-v required to get from there to Mars is not free, because you first have to get up to the IGO, which will cost you about 5.63 km/s from LEO (@150 altitude).<br /><br />From LEO to IGO: 5.63 km/s<br />From IGO to Mars capture: 2.08 km/s<br />Total from LEO to Mars capture: 7.71 km/s<br /><br />If you were to go straight from LEO to Mars capture:<br /><br />From LEO to Mars capture: 3.62 km/s + 0.2 km/s by gravity losses = 3.82 km/s<br /><br />It seems that launching from LEO is a better idea, doesn't it?<br /><br />The fact is, a ship launched from LEO must be ready for the whole trip to Mars, ie 3.82 km/s + 1.87 km/s for Mars capture = 5.69 km/s. using a 372 ISP CH4 drive that would give a payload portion of only 18%.<br /><br />A ship launched from IGO would be fuelled and boarded there by the crew transfered from LEO. It will only have to accelerate for 2.08 km/s (negligeable gravity losses) + 1.87 km/s at Mars capture = 3.94 km/s. This allows a payload portion of 31%.<br /><br />If we assume Mars capture to be only 0.9 km/s as it is in most scenarios, the fuel portion for launch from LEO will be 24%, and that launched from IGO: 41% !! <br /><br />The IGO is not a free ride, it is a convenient refuelling stop. <div class="Discussion_UserSignature"> <p><em>“An error does not become a mistake until you refuse to correct it.” John F. Kennedy</em></p> </div>

 

[keermalec]

Jimfrom, L2 is also an interesting point for launch to Mars because it has the moon's velocity but a larger orbital radius from Earth. Due to these particular circumstances a ship launched from there will have an extra 0.07 km/s.<br /><br />However, this is still less interesting than the IGO:<br /><br />Delta-v for launch from L2 = 2.28 - 0.07 = 2.21 km/s<br /><br />Delta-v for launch from IGO = 2.08 km/s<br /><br />Supplying L2 from LEO requires only 5.24 km/s while supplying the IGO from LEO requires 5.63 km/s. So L2 is a bit cheaper to supply than the IGO, but what counts is the payload capacity to mars I believe.<br /><br />From L2 the capacity would be 39%. From IGO 41%.<br /><br />Plus, getting to L2 is an expedition in itself, requiring 5.8 days of transfer. <br /><br />Getting to the IGO requires 0.6 days only.<br /><br />I believe going from a 0.6 day trip to a 6 day trip has important life-support and security implications, which will drive up mass and cost for the Mars Mission preparation phase. <div class="Discussion_UserSignature"> <p><em>“An error does not become a mistake until you refuse to correct it.” John F. Kennedy</em></p> </div>

 

[gunsandrockets]

<br /><Hi G&R, the IGO is a circular orbit, and therefore has no apoapsis nor periapsis. /><br /><br />Well one way you could consider an IGO circular orbit vs a LEO circular orbits is that LEO is all periapsis all the time vs IGO is all apoapsis all the time!

 

[keermalec]

My understanding is that periapsis is the low point of en elliptical orbit and apoapsis is the high point. A circular orbit can therefore be considered all apoapsis or all periapsis. The IGO is a circular orbit which is higher than LEO for a Mars transfer. <br /><br />Just to demonstrate how delta-v required for Hohmann to Mars changes with altitude, here is the data for some circular orbits around Earth (note how the delta-vs are high for orbits above and below the IGO):<br /><br />Orbit alt (km), Delta-v for Hohmann to Mars (km/s) <br /> 200.00, 3.61171614 <br /> 400.00, 3.56933647 <br /> 1'000.00, 3.45358207 <br /> 2'000.00, 3.29152303 <br /> 10'000.00, 2.63792025 <br /> 20'000.00, 2.34707106 <br /> 40'000.00, 2.15097673 <br /> 85'800.00, 2.07889399 <-- IGO<br /> 150'000.00, 2.11040475 <br /> 300'000.00, 2.21282694 <br /> 500'000.00, 2.30932528 <br /><br /><br />And here are the IGOs for Hohmann transfers to the other planets:<br /><br />Planet, Required dv (km/s), IGO (km from surf.), IGO (km from center)<br /><br />Mercury, 9.83, 1'900, 8'300<br />Venus, 2.74, 99'800, 106'200<br />Mars, 2.94, 85'800, 92'200<br />Ceres, 4.24, 37'900, 44'300<br />Jupiter, 8.77, 4'000, 10'400<br />Saturn, 10.28, 1'200, 7'600<br />Uranus, 11.25, -, -<br />Neptune, 11.63, -, -<br />Pluto, 11.78, -, - <br /><br />Coming back to your post, G&R, you can now see that the IGO for Mercury or Saturn, at 1'900 km and 1'200 km, may be considered Low Earth Orbits as well.<br /><br />Subject continued here.<br /> <div class="Discussion_UserSignature"> <p><em>“An error does not become a mistake until you refuse to correct it.” John F. Kennedy</em></p> </div>