RSP - Being able to land on every point of a planet/moon

[Kerbart]

[on Kerbart's comment]Well it turns out I might not need to wait so many years, just wait for the transfer window. But there are still some unresolved issues.

Just keep that on the downlow and keep charging your Kerbals a premium for the Dres Express!

I am getting a bit frustrated because my words maybe cannot really explain the problem. So I made a simple picture with all the mspaint power skills I could muster

As someone who occasionally dabbles in the arcane art of diagramming, I think the diagram would benefit from those red lines either being very flat ellipses (ellipsii?) or instead of being the orbital plane, being the planetary axis (with a 90° angle to the plane) instead. That's at least how I interpreted them, which caused me to think you got "easy" and "difficult" mixed up.

[Jackissimus]

Ah, you're right, but for the wrong reasons. Equatorial orbits are only special because they (typically) lie near the plane of the ecliptic. I wonder if you can achieve what you want this way:

- Enter the planet's SOI; your trajectory will be hyperbolic.

- Burn normal/anti-normal to adjust the periapsis so that it lies over a pole. (This should be possible for cheap, but I'm not at KSP, so can't test it.)

- Do your capture burn at periapsis, but stop the burn as soon as the orbit closes. The orbit should now be a highly elliptical orbit with periapsis over one pole and apoapsis over the other.

- Coast to apoapsis and rotate the orbit to the desired longitudinal plane.

Well yeah, I meant in KSP, where there is no axial tilt. Reaching an equatorial orbit on Uranus would prove very difficult.

There was already someone who wanted to rotate the periapsis. It seems to me that you cannot rotate the periapsis. The periapsis lies on the major axis of the ellipse (or the hyperbole), the planet is in the focus. When I want to rotate the periapsis, I have to move this axis and that means moving very large distances on the other end. Very costly. Rotating the periapsis can be done easily on a nearly circular orbit, because it's not really rotating the periapsis, but actually raising it over (or close to) the apoapsis, thus changing the periapsis position.

[Horn Brain]

I didn't get you in the beginning - how can you rotate your periapsis before the actual SOI change? Maybe a little, but not like 180 degrees, which is what I might need.

Imagine looking at the planet from your vehicle as you approach. Initially, we'll presume that you're flying straight into the center of the planet. By burning up/down/left/right you can make your trajectory miss the planet in any direction, so you can put your periapsis (Pe) anywhere you want in a circle around the planet. If you put your Pe in a location where it is in the plane of the station's orbit, that means that it will also be either the AN/DN. Since your Pe is at one node, your apoapsis (Ap) (after you get captured) will be at the other node. Usually the velocity of a ship at the edge of an SoI in a highly elliptical orbit is very, very low (like, less than 100 m/s even for Moho, I think?), so the plane change will be very cheap.

The last sentence is complete nonsense to me. It's the same dV as before. If you spend very little fuel at this stage, you still have to add a huge fuel tank at Kerbin ascent. DeltaV is the same no matter where you burn.

I wasn't under the impression that you would be designing your vehicles to have very little fuel margin. Usually these kinds of things have a little extra fuel, and you'll be replenishing it at your station anyway, so the mass used to perform the last few hundred m/s of dV is less than the mass used for any other equivalent maneuvering and it doesn't add to the initial mass of your ship (if you stay within the margins). I was just trying to make you feel better about spending a few more dozen dV sometimes.

[Jackissimus]

Imagine looking at the planet from your vehicle as you approach. Initially, we'll presume that you're flying straight into the center of the planet. By burning up/down/left/right you can make your trajectory miss the planet in any direction, so you can put your periapsis (Pe) anywhere you want in a circle around the planet. If you put your Pe in a location where it is in the plane of the station's orbit, that means that it will also be either the AN/DN. Since your Pe is at one node, your apoapsis (Ap) (after you get captured) will be at the other node. Usually the velocity of a ship at the edge of an SoI in a highly elliptical orbit is very, very low (like, less than 100 m/s even for Moho, I think?), so the plane change will be very cheap.

That doesn't solve the problem I show in the picture above. What if you are approaching the planet perpendicularly to the orbital plane of the polar station? You cannot put your periapsis there easily. The only way to do it is to speed up so much you basically fly around the planet in a straight line, then slow down again when you reach the periapsis. That's a huge amount of deltaV there.

In usual hohmann transfers, you will enter the planet's SOI from the front (the planet catches you up) and have a nice hyperbolic orbit that will throw you mostly to the front again (periapsis inside the planet), sometimes to the sides, but never ever to the rear, you need to speed up for that.

[Oggula]

I take roughly option 3 when landing on the Joolian moons (i.e. land from polar orbit, then wait until the station flies overhead again before I take off following its inclination). However, this necessitates a direct descent landing in a Dres scenario, without a preceding rendezvous, which is only efficient if you also land on a Kethane spot to refuel. If you can do this, I'd take option 3.

[Ralathon]

That doesn't solve the problem I show in the picture above. What if you are approaching the planet perpendicularly to the orbital plane of the polar station? You cannot put your periapsis there easily. The only way to do it is to speed up so much you basically fly around the planet in a straight line, then slow down again when you reach the periapsis. That's a huge amount of deltaV there.

In usual hohmann transfers, you will enter the planet's SOI from the front (the planet catches you up) and have a nice hyperbolic orbit that will throw you mostly to the front again (periapsis inside the planet), sometimes to the sides, but never ever to the rear, you need to speed up for that.

The trick to that problem is to do it in 2 passes. In the specific case that your incoming trajectory is perpendicular to the polar orbit you're aiming for you first get into a polar orbit (that thus will be at a 90 degree angle to your intended orbit).

BUT, you only burn enough to get into a very eccentric orbit. At the apoapsis of that orbit you change your inclination to match with the station (and since you'll be moving so slow this'll be cheap) and then you complete your burn to get down to a circular orbit.

So as you come in on trajectory 1 you preform burn A to get into orbit 2 (with the apoapsis as high as possible, not to scale here for obvious reasons). At the apoapsis you execute burn b to get into orbit 3 which matches your target orbit's inclination. From here it is a simple circularization burn © to get down to your target orbit.

[Horn Brain]

Thanks, Ralathon. That's what I'm talking about.

As for the OP, only Jool and maybe Eve have enough gravity to really turn your trajectory around when you're coming in on a Hohmann trajectory. Both of which offer aerobraking which should make the plane change problem less significant. You'll zip right by Moho, Dres, and Eeloo, and even Duna won't turn you all that much. Ralathon is right in the case of coming in facing the plane of your station's orbit: You need to move your Pe towards one of the poles.

[Ralathon]

Thanks, Ralathon. That's what I'm talking about.

As for the OP, only Jool and maybe Eve have enough gravity to really turn your trajectory around when you're coming in on a Hohmann trajectory. Both of which offer aerobraking which should make the plane change problem less significant. You'll zip right by Moho, Dres, and Eeloo, and even Duna won't turn you all that much. Ralathon is right in the case of coming in facing the plane of your station's orbit: You need to move your Pe towards one of the poles.

Well, it doesn't have to be a polar orbit. That tactic works just as well when you first go into a equatorial elliptical orbit instead. You just need to have the periapsis close to your target orbit.

[Jackissimus]

Hi again!

I completely understand what you want to say. I just don't agree. It starts with curve no. 1. That's not a real approach trajectory (and I have to admit I didn't really draw this right myself). This may seem trivial, but in fact it's crucial.

What happens during a hohmann transfer? You raise your apoapsis to the altitude of the orbiting planet. What are you doing exactly at the point when you reach the apoapsis? You are moving very slowly in the same direction the planet moves (e.g. tangential to your orbit). But the planet moves much much faster, so it catches up to you and you enter its SOI. Then what happens? You approach the planet from the front, have a periapsis somewhere on the rear and escape the SOI somewhere on the front, or maybe the side. What happens to the craft's orbit relative to Kerbol after it escapes? Depending on the gravity of the planet it changed very little or it changed a lot. But that doesn't mean that the craft's trajectory relative to the planet looks any different from what I described! It still has a periapsis somewhere near the rear of the planet and at point (a) I certainly cannot enter orbit (2). The only thing I can do at point (a) is probably reduce the eccentricity of the orbit a bit and maybe shift it a little bit sideways, that's it.

You can also imagine it from the craft's point of view. In the craft's frame of reference it was moving slowly near its apoapsis, minding its own business, when a planet whizzed by and tugged it behind it for a while. And now that I think of it, it is true that when a low gravity body whizzes fast by the craft, its orbit doesn't change much and it basically escapes the planet's SOI on the rear side. Which means that the periapsis will be on the side of the planet and I can then easily enter a polar orbit which is perpendicular to the planet's velocity vector. It leaves me in the same trouble however! It's easier to intercept this planet's orbital station when it's perpendicular to the planet's velocity vector, but it's really difficult to do that with the station's orbital plane parallel to the planet's velocity in this case.

Well anyway, I have to test this myself I think, but it involves a lot of time to set everything up and I am also afraid it involves a bit more complicated thinking than "burn prograde, burn anti-normal" etc...

EDIT: I thought about it even a bit more and now I think it really depends on a planet and it's gravity what trajectory I will have relative to it. Even then I can probably do different things like some strange swing-bys etc. But I am really just dodging the issue that for a Hohmann transfer I will approach from the front, that's a given, and that means I will always be limited in the positions my periapsis can have. There is no getting around it.

EDIT2: Yeah and I can always try to really fine tune my approach so that I barely scrape the SOI. That way I will have my periapsis almost perpendicularly to the planet's velocity. It was basically discussed earlier in the thread. Yeah now I think I understand it well. I can enter all the polar orbits, it's just really difficult, especially the scraping of the SOI.

Edited August 13, 2013 by Jackissimus

[SRV Ron]

The retrograde slingshots or captures, difficult to set up, can place you in any orbital plane desired, either around the target body, or, as you can see by the slingshot around Laythe, to a close in orbit of Jool saving tons of fuel. The slingshot went 180* around Laythe pulling tons of speed off the Jool orbit.

Slightly closer and aero braking could have reduced the orbit further

[Mr Shifty]

I completely understand what you want to say. I just don't agree. It starts with curve no. 1. That's not a real approach trajectory (and I have to admit I didn't really draw this right myself). This may seem trivial, but in fact it's crucial.

Curve 1 should be a hyperbola that curves toward the planet instead of away, but is otherwise totally plausible.

What happens during a hohmann transfer? You raise your apoapsis to the altitude of the orbiting planet. What are you doing exactly at the point when you reach the apoapsis? You are moving very slowly in the same direction the planet moves (e.g. tangential to your orbit). But the planet moves much much faster, so it catches up to you and you enter its SOI. Then what happens? You approach the planet from the front, have a periapsis somewhere on the rear and escape the SOI somewhere on the front, or maybe the side.

With a perfect Hohmann transfer, you would enter the planet's SOI with a velocity vector that pointed straight toward the planet's center. If you're doing Hohmann transfers to Duna or Eve, you're going to enter the planet's SOI with a relative velocity of 800-850 m/s. Let's say you're going to Eve, which can bend your path considerably because it's massive. If you set your hypberbolic periapsis at about 4Mm from Eve, your orbital trajectory will change by about 90 degrees due to Eve's gravity. (The formula for that is here.) Which means that your periapsis will be 90 degrees around the planet from your approach trajectory. Since you're initially pointing directly at the planet, you can change your trajectory in any direction. Hyperbolas are basically straight-line paths that far out, so you can use simple trignonometry to figure out the delta-V necessary to change your periapsis from the center of Eve to 4Mm if you do it at the SOI edge:

The angle you need to change by is approximately:

sin^-1(desired_periapsis_radius/SOI_radius)=sin^-1((4Mm+0.7Mm)/85.1Mm)=3.2 degrees

To change your velocity vector by this much, the forumula is:

2 * current_velocity * sin (desired_angle_change/2) = 2 * 845m/s * sin(3.2/2) = 47 m/s

And you can change the vector to put your periapsis at any point around the circumference of Eve that is facing your approach vector.

Edited August 13, 2013 by Mr Shifty

[AmpsterMan]

I like option 2. It is actually the main reason I have my statioms be in a relatively high Orbit around their bodies. It makes inclination shifts very simple

[Ralathon]

Hi again!

I completely understand what you want to say. I just don't agree. It starts with curve no. 1. That's not a real approach trajectory (and I have to admit I didn't really draw this right myself). This may seem trivial, but in fact it's crucial.

What happens during a hohmann transfer? You raise your apoapsis to the altitude of the orbiting planet. What are you doing exactly at the point when you reach the apoapsis? You are moving very slowly in the same direction the planet moves (e.g. tangential to your orbit). But the planet moves much much faster, so it catches up to you and you enter its SOI. Then what happens? You approach the planet from the front, have a periapsis somewhere on the rear and escape the SOI somewhere on the front, or maybe the side. What happens to the craft's orbit relative to Kerbol after it escapes? Depending on the gravity of the planet it changed very little or it changed a lot. But that doesn't mean that the craft's trajectory relative to the planet looks any different from what I described! It still has a periapsis somewhere near the rear of the planet and at point (a) I certainly cannot enter orbit (2). The only thing I can do at point (a) is probably reduce the eccentricity of the orbit a bit and maybe shift it a little bit sideways, that's it.

You can also imagine it from the craft's point of view. In the craft's frame of reference it was moving slowly near its apoapsis, minding its own business, when a planet whizzed by and tugged it behind it for a while. And now that I think of it, it is true that when a low gravity body whizzes fast by the craft, its orbit doesn't change much and it basically escapes the planet's SOI on the rear side. Which means that the periapsis will be on the side of the planet and I can then easily enter a polar orbit which is perpendicular to the planet's velocity vector. It leaves me in the same trouble however! It's easier to intercept this planet's orbital station when it's perpendicular to the planet's velocity vector, but it's really difficult to do that with the station's orbital plane parallel to the planet's velocity in this case.

Well anyway, I have to test this myself I think, but it involves a lot of time to set everything up and I am also afraid it involves a bit more complicated thinking than "burn prograde, burn anti-normal" etc...

EDIT: I thought about it even a bit more and now I think it really depends on a planet and it's gravity what trajectory I will have relative to it. Even then I can probably do different things like some strange swing-bys etc. But I am really just dodging the issue that for a Hohmann transfer I will approach from the front, that's a given, and that means I will always be limited in the positions my periapsis can have. There is no getting around it.

EDIT2: Yeah and I can always try to really fine tune my approach so that I barely scrape the SOI. That way I will have my periapsis almost perpendicularly to the planet's velocity. It was basically discussed earlier in the thread. Yeah now I think I understand it well. I can enter all the polar orbits, it's just really difficult, especially the scraping of the SOI.

Oh boy we're going to have to dig into orbital equations aren't we... Remember, the safe word is banana.

So this is our situation when we enter the SoI if we simplify to a 2d picture (Justified since you can always adjust your FoR to coincide with your orbital inclination):

We wonder if we can adjust the location of the periapsis. If we take a look at the equations we can see that the periapsis can be adjusted to any angle between 90 and 180 degrees relative to the line drawn by your SoI entry and the parent body, simply by manipulating your orbital velocity(retro/prograde) and angular velocity(any direction 90 degrees to the velocity vector). After all, you can mirror a hyperbola through the periapsis, so this means the angle between periapsis and both asymptotes must be equal. Since the asymptotes can vary between 0 and 180 degrees the periapsis can vary between 90 and 180.

This means you're still limited to a certain area. BUT, you can also adjust the point where you enter the SoI relative to the rest of the solar system. You have to make this adjustment a lot earlier, but it allows you to essentially rotate the entire picture. This means it should theoretically be possible to always have your periapsis over a pole if you want to.

Edited August 13, 2013 by Ralathon

[Jackissimus]

Curve 1 should be a hyperbola that curves toward the planet instead of away, but is otherwise totally plausible.

Well yeah, it is, but the periapsis doesn't lie at point (a). Burning at point (a) doesn't put you in orbit (2).

With a perfect Hohmann transfer, you would enter the planet's SOI with a velocity vector that pointed straight toward the planet's center. If you're doing Hohmann transfers to Duna or Eve, you're going to enter the planet's SOI with a relative velocity of 800-850 m/s. Let's say you're going to Eve, which can bend your path considerably because it's massive. If you set your hypberbolic periapsis at about 4Mm from Eve, your orbital trajectory will change by about 90 degrees due to Eve's gravity. (The formula for that is here.) Which means that your periapsis will be 90 degrees around the planet from your approach trajectory. Since you're initially pointing directly at the planet, you can change your trajectory in any direction. Hyperbolas are basically straight-line paths that far out, so you can use simple trignonometry to figure out the delta-V necessary to change your periapsis from the center of Eve to 4Mm if you do it at the SOI edge:

The angle you need to change by is approximately:

sin-1(desired_periapsis_radius/SOI_radius)=sin-1((4Mm+0.7Mm)/85.1Mm)=3.2 degrees

To change your velocity vector by this much, the forumula is:

2 * current_velocity * sin (desired_angle_change/2) = 2 * 845m/s * sin(3.2/2) = 47 m/s

And you can change the vector to put your periapsis at any point around the circumference of Eve that is facing your approach vector.

The last sentence is not correct. That would mean that I have to speed up significantly to have almost a straight path around Eve. But actually my path will bend around Eve, maybe by those 90 degrees or something, and that will put the periapsis at roughly 45 degrees behind the planet. I still cannot easily reach my orbital station with the orbital plane perpendicular to the velocity of the planet.

[Jackissimus]

Oh boy we're going to have to dig into orbital equations aren't we... Remember, the safe word is banana.

LOL!

Anyway, do you know how much dV it will cost you to increase phi to 180deg? The question is not if we can, the question is whether we should.

[Ralathon]

LOL!

Anyway, do you know how much dV it will cost you to increase phi to 180deg? The question is not if we can, the question is whether we should.

I'll assume you mean 90 degrees. That way your periapsis is over one of the poles (180 is opposite to the planet, which is a rather useless position to have it if you're aiming for a polar orbit).

And the answer is: Arbitrarily small depending on how good you are at executing precision burns:

[Mr Shifty]

The last sentence is not correct. That would mean that I have to speed up significantly to have almost a straight path around Eve. But actually my path will bend around Eve, maybe by those 90 degrees or something, and that will put the periapsis at roughly 45 degrees behind the planet. I still cannot easily reach my orbital station with the orbital plane perpendicular to the velocity of the planet.

Here's the situation I'm talking about:

Note that it's totally symmetrical around the original velocity vector; you can rotate it 360 degrees and put your periapsis anywhere on that circle and though the drawing is fairly awful and doesn't show it clearly, it's possible to get that periapsis very close to 90 degrees from your original approach vector. You don't have to speed up at all, you just have to change your velocity vector angle so that you pass farther from the planet.

Edited August 13, 2013 by Mr Shifty

[Jackissimus]

OMG, how do you make those diagrams, is this still mspaint?

OK Ralathon, I think we talk about different things again. I never said it's not possible to enter a polar orbit very cheaply. Again, I am just saying there are 360degrees worth of polar orbits and I have to enter the right one.

Shifty, that's a great idea. A few posts back I finally realized even better way, when I was talking about "barely scraping" the SOI.

[Horn Brain]

OMG, how do you make those diagrams, is this still mspaint?

OK Ralathon, I think we talk about different things again. I never said it's not possible to enter a polar orbit very cheaply. Again, I am just saying there are 360degrees worth of polar orbits and I have to enter the right one.

Shifty, that's a great idea. A few posts back I finally realized even better way, when I was talking about "barely scraping" the SOI.

-snip-

NO! This is the worst way to get captured that you can possibly attempt in terms of dV requirements.

If you would just go and try it you would see we're right. I have DONE this and it works (best on low gravity worlds and high velocities). If you do your correction burns early enough you can put the periapsis over/near the pole and then all you have to do is do the inclination change at/near the Ap of your highly elliptical orbit and then circularize at Pe again. Done. Moving on.

[Jackissimus]

NO! This is the worst way to get captured that you can possibly attempt in terms of dV requirements.

Because of the Oberth effect? Yeah, that's very possible.

If you would just go and try it you would see we're right. I have DONE this and it works (best on low gravity worlds and high velocities).

Yeah I agreed it's the best way to do it on low gravity worlds and high velocities. Unfortunately you cannot do this on high gravity worlds or low velocities. As a test, you can try putting your Pe over the pole when transferring to the Mun. Can't be done, sorry.

If you do your correction burns early enough ...

Why do people keep mantioning this? Do I appear so dumb to not know this? This is called the Duke's Advice in my country.

Service engineer: Boss, I tried to fix your computer and it can't be done. I've worked with computers for the past 10 years and I've seen everything. I can tell you, you can throw that PC in the trash.

Boss: Have you tried turning it off and on again?

[Horn Brain]

Do your transfer at a slight inclination, and then when you come in, you'll be coming in from above or below the planet/moon and your Pe will be closer to the pole once you do the final corrections. This is what I mean by early enough in the worst cases. You don't have to get it right on the pole, you just have to get it "close" and you can do the majority of your corrections at/near Ap. If that doesn't work for you, there is no way to do it and you have to wait years and years for transfer windows to align with your particular orbits. You will have to try and figure out if the dV required to do the early inclination is worth the savings in the plane change at the destination. Here's a hint: if you need to turn your orbit 90 degrees at Jool or Eve, it will be. It will also ALWAYS be better than your scraping the SoI suggestion.

Here's another idea: Don't use a station at all. Just use the lander itself to ferry fuel directly to your spacecraft. That way, you can get into any polar orbit you like (trivial) and the lander can be launched to match it.

[pokeman]

Because of As a test, you can try putting your PE over the pole when transferring to the Mun. Can't be done, sorry.

Yes it can, it simply requires a 2nd course correction burn to get to.

1st burn for injection to equatorial mun orbit, a 2nd burn half way to the Muns SOI to put the PE over one of the poles, a 3rd burn at the PE to capture (with a high AP), a 4th burn at AP to change to whatever polar orbit you want (eg: to dock with a polar station) and finally burn 5 to circularize.

If executed correctly the 2 extra burns (2 and 4) will require minuscule amounts of fuel.