Orbiter-Forum Delta-V for "direct descent" to the lunar surface?
 Register Blogs Orbinauts List Social Groups FAQ Projects Mark Forums Read

 Math & Physics Mathematical and physical problems of space flight and astronomy.

 09-02-2012, 06:42 AM #1 RGClark Mathematician Delta-V for "direct descent" to the lunar surface? I was trying to get a lower roundtrip delta-V for lunar missions by flying directly to the lunar surface rather than going first into lunar orbit then descending, the "direct descent" mode. Here's a list of delta-V's of the Earth/Moon system: Delta-V budget. Earth–Moon space. http://en.wikipedia.org/wiki/Delta-v...0.93Moon_space If you add up the delta-V's from LEO to LLO, 4,040 m/s, then to the lunar surface, 1,870 m/s, then back to LEO, 2,740 m/s, you get 8,650 m/s, with aerobraking on the return. I wanted to reduce the 4,040 m/s + 1,870 m/s = 5,910 m/s for the trip to the Moon. The idea was to do a trans lunar injection at 3,150 m/s towards the Moon then cancel out the speed the vehicle picks up by the Moons gravity. This would be the escape velocity for the Moon at 2,400 m/s. Then the total would be 5,550 m/s. This is a saving of 360 m/s. This brings the roundtrip delta-V down to 8,290 m/s. I had a question though if the relative velocity of the Moon around the Earth might add to this amount. But the book The Rocket Company, a fictional account of the private development of a reusable launch vehicle written by actual rocket engineers, gives the same amount for the "direct descent" delta-V to the Moon 18,200 feet/sec, 5,550 m/s: The Rocket Company. http://books.google.com/books?id=ku3...elta-V&f=false Another approach would be to find the Hohmann transfer burn to take it from LEO to the distance of the Moon's orbit but don't add on the burn to circularize the orbit. Then add on the value of the Moon's escape velocity. I'm looking at that now. Here's another clue. This NASA report from 1970 gives the delta-V for direct descent but it gives it dependent on the specific orbital energy, called the vis viva energy, of the craft when it begins the descent burn: SITE ACCESSIBILITY AND CHARACTERISTIC VELOCITY REQUIREMENTS FOR DIRECT-DESCENT LUNAR LANDINGS. http://ntrs.nasa.gov/archive/nasa/ca...1970023906.pdf The problem is I couldn't connect the specific orbital energy it was citing to a delta-V you would apply at LEO to get to that point. How do you get that? Bob Clark
 09-02-2012, 07:59 AM #2 Urwumpe Donator C3? It is a standard measure of transfer orbits. It is in all launch vehicle user manuals. Do you know the vis-viva integral? (typing a latex formula on Android screen keyboard is a challenge) PS:Remember that the eccentricity and inclination of the moons orbit means changing DV requirements Last edited by Urwumpe; 09-02-2012 at 08:08 AM.
 09-02-2012, 10:14 AM #3 dgatsoulis Orbinaut Quote: Originally Posted by RGClark   I wanted to reduce the 4,040 m/s + 1,870 m/s = 5,910 m/s for the trip to the Moon. The idea was to do a trans lunar injection at 3,150 m/s towards the Moon then cancel out the speed the vehicle picks up by the Moons gravity. This would be the escape velocity for the Moon at 2,400 m/s. Then the total would be 5,550 m/s. This is a saving of 360 m/s. This brings the roundtrip delta-V down to 8,290 m/s. I think that you are not taking into account the encounter velocity in that calculation. Having done quite a few Earth-Moon trips in Orbiter, I know from experience that a direct descent (without orbital insertion) wouldn't save Δv. When you begin the descent burn you are lowering your eccentricity from a hyperbolic trajectory >1 to an elliptical one <1. The most efficient place/time to do that would be the periapsis of the initial orbit. But since that's going to be under the lunar surface, you'll have to begin the burn before reaching periapsis, making the burn inefficient and end up using more Δv. Interestingly -if you take into account the Δv for reaching Earth orbit- what could save Δv is a direct ascent from Earth, instead of going to LEO first. In any case I think an Earth-Moon round trip would make a great challenge. I'll try to set up a scenario with a lua script and post it in the tutorials and challenges thread. Last edited by dgatsoulis; 09-02-2012 at 10:28 PM.
 Thanked by:
 09-02-2012, 10:01 PM #4 Hlynkacg Aspiring rocket scientist Quote: Originally Posted by dgatsoulis  I think that you are not taking into account the encounter velocity in that calculation. Having done quite a few Earth-Moon trips in Orbiter, I know from experience that a direct descent (without orbital insertion) wouldn't save Δv. When you begin the descent burn you are lowering your eccentricity from a hyperbolic trajectory >1 to an elliptical one <1. The most efficient place/time to do that would be the periapsis of the initial orbit. But since that's going to be under the lunar surface, you'll have to begin the burn before reaching periapsis... this is exactly what I was about to point out. Specific orbital energy in this case is actually your rVel to surface of the body in question. In essance it defines an absolute minimum of dv needed to make a soft landing as no matter what you do you'll have to finish with a rVel of 0 (or close enough that your landing system can absorb the shock) otherwise you're crashing not landing.
 Thanked by:
 09-13-2012, 12:38 PM #5 RGClark Mathematician Quote: Originally Posted by dgatsoulis  I think that you are not taking into account the encounter velocity in that calculation. Having done quite a few Earth-Moon trips in Orbiter, I know from experience that a direct descent (without orbital insertion) wouldn't save Δv. When you begin the descent burn you are lowering your eccentricity from a hyperbolic trajectory >1 to an elliptical one <1. The most efficient place/time to do that would be the periapsis of the initial orbit. But since that's going to be under the lunar surface, you'll have to begin the burn before reaching periapsis, making the burn inefficient and end up using more Δv. Does the Orbiter simulation allow you to set up the encounter velocity? I'm assuming the simulation is using a patched conic approximation. In this approximation once you get sufficiently close to the Moon, at a distance of some 10's of thousands of km, you assume the Moon's gravity is operating only, called the Moon's radius of the sphere of influence, RSOI. Then could you arrange the flight trajectory from the Earth so that the tangential velocity component, relative to the Earth, matches the Moon's by the time the spacecraft reaches RSOI? Bob Clark
 09-13-2012, 03:32 PM #6 dgatsoulis Orbinaut Quote: Then could you arrange the flight trajectory from the Earth so that the tangential velocity component, relative to the Earth, matches the Moon's by the time the spacecraft reaches RSOI? I don't see how that can be done. The moon has an orbital speed of about 1km/s (relative to Earth). Assuming a transfer orbit of 200km x 320000km (Moon's semi major axis minus the Rsoi), the vessel would have a speed of ~ 200 m/s at apoapsis, giving a difference of 800 m/s (roughly). That would be the encounter velocity (for a coplanar transfer). Last edited by dgatsoulis; 09-13-2012 at 03:34 PM.
 09-13-2012, 03:44 PM #7 Urwumpe Donator Quote: Originally Posted by RGClark  Does the Orbiter simulation allow you to set up the encounter velocity? I'm assuming the simulation is using a patched conic approximation. Wrong. Orbiter uses a multi-body solution including solar radiation pressure, non-spherical gravity and exosphere drag. You should really start to use it, not that it is mandatory for posting in Orbiter-Forum, but especially at this point helpful. And yes, you can have encounter velocity set... simply be on the right Earth-relative trajectory before lunar encounter. All a matter of trajectory design.
 09-13-2012, 05:16 PM #8 RGClark Mathematician Quote: Originally Posted by dgatsoulis  I don't see how that can be done. The moon has an orbital speed of about 1km/s (relative to Earth). Assuming a transfer orbit of 200km x 320000km (Moon's semi major axis minus the Rsoi), the vessel would have a speed of ~ 200 m/s at apoapsis, giving a difference of 800 m/s (roughly). That would be the encounter velocity (for a coplanar transfer). The transfer trajectory does not necessarily have to be an ellipse that ends at the Rsoi. It could even be hyperbolic or parabolic as long as aimed to impact the Moon. The spacecraft would have both radial and tangential component to the velocity in that case though. Bob Clark
 09-17-2012, 04:57 PM #9 RGClark Mathematician Quote: Originally Posted by dgatsoulis  ... Interestingly -if you take into account the Δv for reaching Earth orbit- what could save Δv is a direct ascent from Earth, instead of going to LEO first... Do you have an estimate of the delta V you could save by taking the direct ascent approach? Bob Clark
 09-17-2012, 06:06 PM #10 dgatsoulis Orbinaut Quote: Originally Posted by RGClark  Do you have an estimate of the delta V you could save by taking the direct ascent approach? Bob Clark I only have empirical data from Orbiter. I am not on an Orbiter computer right now but IIRC there was a small save ~20 m/s. The things that save the most fuel -in my experience- are these: 1. The transfer orbit has to be exactly coplanar to the Moon. 2. Reach the Moon at the Apoapsis of its orbit. Eventhough this requires ~30 m/s more Δv -for the transfer- than reaching the moon at its periapsis, it allows a less expensive (~80 m/s) orbital insertion. These are numbers out of memory, I'll check them when I get home.
 Thanked by:
 09-17-2012, 06:14 PM #11 Urwumpe Donator 20 m/s is on the magnitude of guidance errors, you should do some more simulations to get better results.
 Thanked by:
 09-20-2012, 07:20 PM #12 RGClark Mathematician Quote: Originally Posted by dgatsoulis  I don't see how that can be done. The moon has an orbital speed of about 1km/s (relative to Earth). Assuming a transfer orbit of 200km x 320000km (Moon's semi major axis minus the Rsoi), the vessel would have a speed of ~ 200 m/s at apoapsis, giving a difference of 800 m/s (roughly). That would be the encounter velocity (for a coplanar transfer). Here's a try at it using an elliptical orbit which extends beyond the Moon, but for which the spacecraft will enter the Moon's Rsoi to be captured by the Moon's gravity, instead of passing beyond the Moon's orbit. First use this formula to calculate how large the semi-major axis has to be, the vis viva equation: The small m is the mass of the spacecraft, and capitol M is the mass of the Earth; so M + m is essentially just M. But what's needed here is the standard gravitational parameter G*M. For the Earth, it's 398,600.4418 km3s−2, with the distance measured in units of kilometers. The spacecraft speed is given as v, the radial distance of the spacecraft from the Earth is given as r, and the semi-major axis is a. For this scenario I want v to be the orbital speed of the Moon, which I'll round off to 1,000 m/s. In units of km, this is 1 km/s. We also said we want r to be about 320,000 km. Then plugging these values into the formula we get: a = 267,000 km. Now the Earth is well off-set from the center so that the perigee is only 400 km. The apogee is nearly then twice the semi-major axis, which I'll round off to 534,000 km. If we let e be the eccentricity then the perigee distance is rp = a(1 - e) and the apogee distance is ra = a(1 + e). Since rp is 400 km, and a is 267,000 km, we calculate e to be .998502. A highly eccentric ellipse. Another factor I need to check though is if direction of the velocity vector for the spacecraft at this point is at least close to the direction of the velocity vector of the Moon when the spacecraft reaches the Rsoi. Bob Clark Last edited by RGClark; 09-20-2012 at 07:28 PM.
 09-20-2012, 07:44 PM #13 dgatsoulis Orbinaut So, if I got this correctly, you are going for a transfer orbit that will have a ~1km/s velocity at altitude X, and altitude X will be inside (or at the edge) of the moon's SOI. Correct?
 09-20-2012, 08:03 PM #14 RGClark Mathematician Quote: Originally Posted by dgatsoulis  So, if I got this correctly, you are going for a transfer orbit that will have a ~1km/s velocity at altitude X, and altitude X will be inside (or at the edge) of the moon's SOI. Correct? Yes. Bob Clark
 09-20-2012, 11:45 PM #15 dgatsoulis Orbinaut Here is a pic of the characteristics of a 400km x 534000km orbit: (the Moon is in yellow) LeftMFD distances are measured from the Earth's center. RightMFD distances are measured from the Earth's surface. I'll do the simulation and let you know at which altitude the velocity is 1km/s. But there is no way that the direction of the velocity vector is going to be anything than close to perpendicular to that of the moon. EDIT: As expected, that kind of transfer orbit ends up with a high velocity Moon encounter. After transfer burn: At ALT 320000 km the velocity was 1022m/s. Relative to the Moon the velocity was already 1200m/s at that point. 1000km above the moon's surface the velocity was already at 2200 m/s ---------- Post added at 11:19 PM ---------- Previous post was at 10:13 PM ---------- I remembered something about a japanese sattelitte that was on a course to the moon but failed and I found these: http://adsabs.harvard.edu/abs/1993JGCD...16..770B http://www.marspapers.org/papers/MAR98076.pdf The last one is for Mars, but it also mentions the Belbruno-Miller transfer, which seems very interesting. I'll try to find more information and see if this can be simulated in Orbiter. The downside is that it takes 5 months instead of 3 days to get to the Moon, but it saves up to 18% of Δv relative to a Hohmann transfer (according to the abstract of the paper). I have flown similar missions in Orbiter, using the Moon to get from a polar LEO to a GEO with minimum Δv, so this should be similar to that, just the PeA is going to be much higher. ---------- Post added 09-21-12 at 01:45 AM ---------- Previous post was 09-20-12 at 11:19 PM ---------- The initial setup of the B-M transfer looks very promising. Unfortunately, it's getting too late here to try the flight now. I'll give it a go sometime tomorrow. Last edited by dgatsoulis; 09-20-2012 at 09:24 PM.
 Thanked by:

 Posting Rules BB code is On Smilies are On [IMG] code is On HTML code is Off You may not post new threads You may not post replies You may not post attachments You may not edit your posts
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Orbiter-Forum.com     Announcements     Meets & Greets Orbiter Space Flight Simulator     Orbiter Web Forum         OFMM         Orbiter Forum Space Station III         Simpit Forum     General Questions & Help     MFD Questions & Help     Hardware & Software Help     Tutorials & Challenges     Orbiter SDK     Orbiter Visualization Project » Orbiter Project Orbiter Addons     OrbitHangar Addons & Comments     Addons     Addon Development     Addon Requests     Addon Support & Bugs         Addon Developer Forums Far Side of the Moon     Spaceflight News     Math & Physics     Astronomy & the Night Sky     Backyard Rocketry     Brighton Lounge     International Forum

All times are GMT. The time now is 11:56 AM.