Struggling to catch the mother of all asteroids

[TanDeeJay]

Hi all,

I have been developing my asteroid harvesting fleet and have my asteroid catching ship with just over 11k dV from 6 Nerv engines which goes out into Kerbol orbit to catch asteroids before they enter Kerbins SOI so that I can push the asteroids so that they enter Kerbin's SOI in as close to a pro-grade equatorial orbit as possible.  This has been working quite well, and I've successfully captured a 1300t class E asteroid which my mining ship is happily sucking the life out of.

Now it came to pass, that a new Class E asteroid was discovered which was on an orbit that would intercept Kerbin's SOI, so I sent my asteroid catcher out to get it.   I still had more than 8k dV just before the ship grabbed the asteroid, and when I grabbed the asteroid, I discovered that it was 3600t and my dV had dropped to 176.

This was the closest I've ever caught an asteroid at only 13 days out from entering kerbin's SOI, I've normally got 80+ days at this point.

But anyway, this asteroid was coming in low to kerbin and was on course for a polar orbit, so I set a maneuver node to change the course so that it would have close to equitorial orbit (7 degrees off), but that node needed 167 dV, and I then set another maneuver node at the kerbin PE and found I would have needed 650 dv to pull the asteroid into a high kerbin orbit.  Clearly, I am a LOOOOONG way short... even if I did not do the 1st burn and just brought the asteroid into a polar orbit, I would be short about 475dV.

I think would need to increase the ships dV by about 25k dV in order to have enough dV to spare to be able to capture asteroids of this size.

Am I thinking about this problem the right way?

Is it even possible to capture such a large asteroid?

Any ideas on how to manage a mission to capture such a beast would be greatly appreciated.

(Note: I've tried to build my asteroid mining fleet so that it is fully reusable, and able to refuel itself ready for the next asteroid)

Regards,

John

[Spricigo]

How about intercepting it with your mining rig? Maybe e a simplified smaller version just for the fuel you need to put it in a stable orbit.

[Zhetaan]

1 hour ago, TanDeeJay said:

Am I thinking about this problem the right way?

Yes and no.  As @Spricigo mentioned, you can both reduce your asteroid's mass and increase your delta-V by converting part of it into propellant.  Also, the amount that you convert will probably not add up to much of the asteroid, so expect this to be a resupply stop for a long, long time.  But from a timing perspective, it isn't going to work.  You can't convert enough in 13 days, much less whatever is left after you fast-transfer a mining rig to the asteroid.

However, from a standpoint of 'go get asteroid' you're not doing anything wrong; you've merely taken a bite of something far larger than you anticipated.

1 hour ago, TanDeeJay said:

But anyway, this asteroid was coming in low to kerbin and was on course for a polar orbit, so I set a maneuver node to change the course so that it would have close to equitorial orbit (7 degrees off), but that node needed 167 dV, and I then set another maneuver node at the kerbin PE and found I would have needed 650 dv to pull the asteroid into a high kerbin orbit.  Clearly, I am a LOOOOONG way short... even if I did not do the 1st burn and just brought the asteroid into a polar orbit, I would be short about 475dV.

You might consider an immediate manoeuvre where you are (so that it is fairly cheap) to lower your Kerbin periapsis to just outside the atmosphere (approximately 80 - 100 km), and then another manoeuvre at the periapsis to close the orbit.  That's it; just close the orbit.  That way, you can reduce the inclination at the next apoapsis and circularise afterwards at whatever altitude you like.  It may save enough propellant for you to accomplish it with the rocket you have, but should it not, it at least gives you a close Kerbin fly-by so that you can send an additional rocket with relative ease.  Send a tanker, though, if it comes to that; as I mentioned above, you don't have time to refine the propellant that you need.

1 hour ago, TanDeeJay said:

Is it even possible to capture such a large asteroid?

Any ideas on how to manage a mission to capture such a beast would be greatly appreciated.

It absolutely is possible, though the worst-case scenario is that you don't capture it this time.  Since near-Kerbin asteroids all have orbits approximately equivalent to Kerbin's orbit, setting up a subsequent encounter shouldn't be too difficult.  The question is one of timing.  If you'll recall when you learned how to rendezvous, when you had two vessels in very similar orbits, it was often better to boost one to a markedly different orbit so that you could get an intercept in something less than geologic time.  Unfortunately, that's not possible here because on the one hand, the asteroid is difficult to move, and on the other hand, Kerbin is impossible to move.  On the gripping hand, unless you're running a life-support mod, you have the time to coax this one into orbit if you put aside the idea of necessarily doing it on this orbit.

Edited July 7, 2020 by Zhetaan

[jimmymcgoochie]

Try pushing the periapsis into Kerbin's atmosphere to aerobrake and get some 'free' delta-V. You may need to unhook the capture craft and either grab on to the back of the asteroid or fly outside the atmosphere then catch up again to avoid burning up.

[peteletroll]

A Mun gravity assist can help too. Try crossing its orbit right in front of it, and if it doesn't work, try on the other side of Mun orbit.

[Spricigo]

8 hours ago, Zhetaan said:

As @Spricigo mentioned, you can... But from a timing perspective, it isn't going to work.

Oh! That is what I was missing. Thank for the clarification. (Being a while since i bothered to deal with iSRU)

[James M]

I dunno if this would work but it's what I'd try doing. Burn antinormal/normal from out of Kerbin's SOI and have the roid's trajectory pass through Kerbin's upper atmo. Then I'd launch a significantly smaller ship than your redirector equipped with like 8 airbrakes (Or more I dunno) and fly it out there and grab it's back end. Once you've gotten it in a highly elliptical orbit, you can then take a ship out there with more oomph and fuel and push it into a more desirable orbit from it's AP. Even if you have to launch a new ship specifically for this purpose, I think it'd still be worth it. 

Anyway, good luck out there and I hope you get it!

[jbdenney]

the OP said something that caught my eye.I have a standard heavy tug to grab asteroids. It has drills and converters to mine and refine fuel on the asteroid. The Tugs are a little expensive (480,000 in career mode). My original idea was to put tugs in space and then never have to re-enter the atmosphere. I planned to use existing orbital rocks to re-fuel and dock cheaper ships to change out crew.

 

The issue I found was that every new asteroid was on a different vector so in my first 4 tries I had to do do such large changes on orbital inclination to create an intercept that it became more trouble than it was worth. After topping off the tanks on the rock I would have to expend so much DeltaV to match INC that I would not have enough fuel left to make the intercept. I could launch refuel ships but that would expend more money so in the long run it was almost as cheap to launch a new tug every time.

 

Got any suggestions to make a tug fleet that never has to get back into an atmosphere worth while? 

[Zhetaan]

17 hours ago, jimmymcgoochie said:

Try pushing the periapsis into Kerbin's atmosphere to aerobrake and get some 'free' delta-V. You may need to unhook the capture craft and either grab on to the back of the asteroid or fly outside the atmosphere then catch up again to avoid burning up.

You raise a good point but for the fact that the midpoint of that manoeuvre is the perfect place to burn for capture.  The issue with burning while attached in atmosphere is that the vessel doesn't have the control that it needs:  Nervs thrust at only 60 kN--less in atmosphere--and 1,300 tonnes provide a lot of turning resistance, so if the asteroid swings to a bad direction, there isn't anything to do but wait it out and lament the lost opportunity.  That's assuming that the vessel was designed to enter the atmosphere at all, which it may not have been.  Also, asteroids, as giant, dense rocks, have reduced drag because of their mass, so aerocapture, though possible, may not be plausible.

That all being said, I think that it's worth a try, but perhaps is best considered a last-resort approach.  I won't discount the idea entirely without trying it for myself, but allow me to point out that if detaching, chasing, and reattaching are plausible ideas, then so is launching a more powerful tug equipped with Vectors or Rhinos and using that.

Also, I know that asteroids in the past have tended to be made of concentrated explodiboom when it comes to aerocapture from anything other than low orbit, but perhaps they've seen an update to their thermal tolerances.

Edit:  Apparently, given another question in this forum that involves several aerobraking passes with a class D, they've fixed the explodiboom problem.  I'm still not convinced that this is the best approach, but that particular objection, it seems, is unfounded.

14 hours ago, peteletroll said:

A Mun gravity assist can help too. Try crossing its orbit right in front of it, and if it doesn't work, try on the other side of Mun orbit.

That's a great idea for asteroids that intercept with near-zero inclination.  Unfortunately, this asteroid's polar flyby will offer precious few opportunities to attempt a gravity assist and less effect from one should the encounter actually happen.  It is possible, but there is exactly one Kerbin-Mun configuration that will work for a polar approach.  @TanDeeJay, if the asteroid will fly by the Mun in such a way that the Mun is moving directly away from it, then this is an excellent idea and may even give you a capture, since the Mun assist is worth a few hundred m/s--provided that you can get one.

 

-----

7 hours ago, jbdenney said:

The issue I found was that every new asteroid was on a different vector so in my first 4 tries I had to do do such large changes on orbital inclination to create an intercept that it became more trouble than it was worth. After topping off the tanks on the rock I would have to expend so much DeltaV to match INC that I would not have enough fuel left to make the intercept. I could launch refuel ships but that would expend more money so in the long run it was almost as cheap to launch a new tug every time.

 

Got any suggestions to make a tug fleet that never has to get back into an atmosphere worth while? 

The best suggestions that I have to offer are to pick your targets with care and to learn that patience is the key to orbital mechanics.  There are new asteroids every day; choose those that are cheap to manoeuvre.  Tugs are generally not worth the cost anyway, because propellant is rather cheap on Kerbin's surface.  You save more money by refuelling a vessel already in orbit (meaning that your entire fleet, not just the tugs, are reusable) because you also save all of cost of the launch and second stage hardware that you no longer need to build.  The main reason for ISRU is convenience, not cost:  LFO propellant costs 91.8 Funds per tonne--Liquid Fuel alone is 160 Funds per tonne if you're using only Nervs--but assuming that you're refuelling LFO rockets, you'd need to refine and transfer 5,230 tonnes of it to cover the cost of one of your tugs.  Let's call that four of @TanDeeJay's Class E asteroids--except that it's more, because asteroids are not made of 100% Ore.

You make it more worthwhile with monopropellant (300 Funds/tonne) but monopropellant is a mass loss--its density is 4 kg/L, not 5 kg/L as LFO is.  Also, you won't ever need that much monopropellant unless you're trying to waste it.

Edited July 8, 2020 by Zhetaan

[TanDeeJay]

22 hours ago, Spricigo said:

How about intercepting it with your mining rig? Maybe e a simplified smaller version just for the fuel you need to put it in a stable orbit.

I thought about that, but my question is that for this 3600T asteroid. I would need to convert enough fuel to fill my ships tanks about 4 times to get the DV I would need.  and my ship consists of 1 x Mk3 Liquid Fuel Fuselage Long, and 6 x Mk3 Liquid Fuel Fuselage Short for a total of 25000 units of liquid fuel.  that's a lot of fuel to have to generate.  Although that calculation I put in my post for required DV was to pull the asteroid into a circular orbit about half way between Mun and Minmus. so maybe that option would actually be quite viable, because once I have achieved an eliptical orbit, I then have as much time as I need to generate more fuel to circularize.

 

21 hours ago, Zhetaan said:

Yes and no.  As @Spricigo mentioned, you can both reduce your asteroid's mass and increase your delta-V by converting part of it into propellant.  Also, the amount that you convert will probably not add up to much of the asteroid, so expect this to be a resupply stop for a long, long time.  But from a timing perspective, it isn't going to work.  You can't convert enough in 13 days, much less whatever is left after you fast-transfer a mining rig to the asteroid.

However, from a standpoint of 'go get asteroid' you're not doing anything wrong; you've merely taken a bite of something far larger than you anticipated.

You might consider an immediate manoeuvre where you are (so that it is fairly cheap) to lower your Kerbin periapsis to just outside the atmosphere (approximately 80 - 100 km), and then another manoeuvre at the periapsis to close the orbit.  That's it; just close the orbit.  That way, you can reduce the inclination at the next apoapsis and circularise afterwards at whatever altitude you like.  It may save enough propellant for you to accomplish it with the rocket you have, but should it not, it at least gives you a close Kerbin fly-by so that you can send an additional rocket with relative ease.  Send a tanker, though, if it comes to that; as I mentioned above, you don't have time to refine the propellant that you need.

It absolutely is possible, though the worst-case scenario is that you don't capture it this time.  Since near-Kerbin asteroids all have orbits approximately equivalent to Kerbin's orbit, setting up a subsequent encounter shouldn't be too difficult.  The question is one of timing.  If you'll recall when you learned how to rendezvous, when you had two vessels in very similar orbits, it was often better to boost one to a markedly different orbit so that you could get an intercept in something less than geologic time.  Unfortunately, that's not possible here because on the one hand, the asteroid is difficult to move, and on the other hand, Kerbin is impossible to move.  On the gripping hand, unless you're running a life-support mod, you have the time to coax this one into orbit if you put aside the idea of necessarily doing it on this orbit.

from a timing perspective, I've given up hoping to capture this asteroid on this orbit.  In fact, I had totally abandoned the idea of ever capturing this particular mega-sized potato and was going to stop tracking it, however, as you mentioned its orbit might eventually bring it back within coo-ee of Kerbin,  I may check how long it will take and then consider setting an alarm to the next encounter.  I'm not running a life-support mod, so time is not of the essence, and this particular asteroid is not relevant to my planned Duna mission, I was just testing out a tweak to my asteroid catcher while waiting for the Duna transfer window  

 

 

17 hours ago, jimmymcgoochie said:

Try pushing the periapsis into Kerbin's atmosphere to aerobrake and get some 'free' delta-V. You may need to unhook the capture craft and either grab on to the back of the asteroid or fly outside the atmosphere then catch up again to avoid burning up.

I think my wording in my post is slightly misleading.  I said "this asteroid was coming in low to kerbin"  What I meant was that it was on a trajectory that would take it below the south pole of kerbin, but it was still quite a ways out, the PE was at a distance that was closer to Minmus's orbital distance than Mun's, so would still burn a lot of DV just to get the asteroid to touch the atmosphere.  how much velocity will a 3600T asteroid be able to throw off in a single aerobreak? Imagine being a kerbal on the surface of kerbin for that event

 

 

14 hours ago, peteletroll said:

A Mun gravity assist can help too. Try crossing its orbit right in front of it, and if it doesn't work, try on the other side of Mun orbit.

unfortunately this beast is coming in on a polar orbit well below Mun's orbit, so I would need to burn most of my fuel to get it near mun's orbit.

 

8 hours ago, James M said:

I dunno if this would work but it's what I'd try doing. Burn antinormal/normal from out of Kerbin's SOI and have the roid's trajectory pass through Kerbin's upper atmo. Then I'd launch a significantly smaller ship than your redirector equipped with like 8 airbrakes (Or more I dunno) and fly it out there and grab it's back end. Once you've gotten it in a highly elliptical orbit, you can then take a ship out there with more oomph and fuel and push it into a more desirable orbit from it's AP. Even if you have to launch a new ship specifically for this purpose, I think it'd still be worth it. 

Anyway, good luck out there and I hope you get it!

Will have to consider aerobreaking but I'm not sure I can pull it off for this particular rock.  how much DV is needed to change inclination by 90 degrees at the upper limit of kerbins SOI on a highly eliptical orbit? Just doing a 160ish DV burn with my current ship attached was going to burn 20000+ units of fuel 

 

 

6 hours ago, jbdenney said:

the OP said something that caught my eye.I have a standard heavy tug to grab asteroids. It has drills and converters to mine and refine fuel on the asteroid. The Tugs are a little expensive (480,000 in career mode). My original idea was to put tugs in space and then never have to re-enter the atmosphere. I planned to use existing orbital rocks to re-fuel and dock cheaper ships to change out crew.

 

The issue I found was that every new asteroid was on a different vector so in my first 4 tries I had to do do such large changes on orbital inclination to create an intercept that it became more trouble than it was worth. After topping off the tanks on the rock I would have to expend so much DeltaV to match INC that I would not have enough fuel left to make the intercept. I could launch refuel ships but that would expend more money so in the long run it was almost as cheap to launch a new tug every time.

 

Got any suggestions to make a tug fleet that never has to get back into an atmosphere worth while? 

That was my plan too.  Initially I started out  with the aim to capture asteroids just after they entered kerbin's SOI, and so I started my ACM fleet (Asteroid Catcher and Miner) but soon ran into the same issue you have with each asteroid having a different inclination inside kerbins SOI, then I found that with a ship in my current configuration with 1 x Mk3 Liquid Fuel Fuselage Long, and 6 x Mk3 Liquid Fuel Fuselage Short, and 6 nerv engines, I hadaround 11k dv which was plenty to catch the asteroids well outside of kerbins SOI giving me time to push the asteroids before they hit kerbins soi, and then my mining ships could stay in an equitorial orbit, and the asteroid catcher could head out for the next after waiting for the mining ship to refuel.  I've grabbed half a dozen asteroids with my ACM fleet now, but this 3600 tonne beast has found a flaw in my system

 

6 hours ago, Zhetaan said:

You raise a good point but for the fact that the midpoint of that manoeuvre is the perfect place to burn for capture.  The issue with burning while attached in atmosphere is that the vessel doesn't have the control that it needs:  Nervs thrust at only 60 kN--less in atmosphere--and 1,300 tonnes provide a lot of turning resistance, so if the asteroid swings to a bad direction, there isn't anything to do but wait it out and lament the lost opportunity.  That's assuming that the vessel was designed to enter the atmosphere at all, which it may not have been.  Also, asteroids, as giant, dense rocks, have reduced drag because of their mass, so aerocapture, though possible, may not be plausible.

That all being said, I think that it's worth a try, but perhaps is best considered a last-resort approach.  I won't discount the idea entirely without trying it for myself, but allow me to point out that if detaching, chasing, and reattaching are plausible ideas, then so is launching a more powerful tug equipped with Vectors or Rhinos and using that.

Also, I know that asteroids in the past have tended to be made of concentrated explodiboom when it comes to aerocapture from anything other than low orbit, but perhaps they've seen an update to their thermal tolerances.

That's a great idea for asteroids that intercept with near-zero inclination.  Unfortunately, this asteroid's polar flyby will offer precious few opportunities to attempt a gravity assist and less effect from one should the encounter actually happen.  It is possible, but there is exactly one Kerbin-Mun configuration that will work for a polar approach.  @TanDeeJay, if the asteroid will fly by the Mun in such a way that the Mun is moving directly away from it, then this is an excellent idea and may even give you a capture, since the Mun assist is worth a few hundred m/s--provided that you can get one.

 

 

The best suggestions that I have to offer are to pick your targets with care and to learn that patience is the key to orbital mechanics.  There are new asteroids every day; choose those that are cheap to manoeuvre.  Tugs are generally not worth the cost anyway, because propellant is rather cheap on Kerbin's surface.  You save more money by refuelling a vessel already in orbit (meaning that your entire fleet, not just the tugs, are reusable) because you also save all of cost of the launch and second stage hardware that you no longer need to build.  The main reason for ISRU is convenience, not cost:  LFO propellant costs 91.8 Funds per tonne--Liquid Fuel alone is 160 Funds per tonne if you're using only Nervs--but assuming that you're refuelling LFO rockets, you'd need to refine and transfer 5,230 tonnes of it to cover the cost of one of your tugs.  Let's call that four of @TanDeeJay's Class E asteroids--except that it's more, because asteroids are not made of 100% Ore.

You make it more worthwhile with monopropellant (300 Funds/tonne) but monopropellant is a mass loss--its density is 4 kg/L, not 5 kg/L as LFO is.  Also, you won't ever need that much monopropellant unless you're trying to waste it.

this particular asteroid I latched onto not very many days out from kerbins SOI.  I guess if I detected it a lot sooner, I might have been able to catch it earlier, and affect its orbit with much less DV?  still doesn't leave much DV to get even an eliptical orbit though.

 

 

[Zhetaan]

23 hours ago, TanDeeJay said:

Will have to consider aerobreaking but I'm not sure I can pull it off for this particular rock.  how much DV is needed to change inclination by 90 degrees at the upper limit of kerbins SOI on a highly eliptical orbit? Just doing a 160ish DV burn with my current ship attached was going to burn 20000+ units of fuel 

For the most extreme of stable elliptical orbits in Kerbin's sphere of influence, where the periapsis is at 670 km and the apoapsis is at 84,000 km (those are centre-based radii, not surface altitudes), the orbital velocity at apoapsis is 25.8 m/s, so the delta-V to change the inclination by 90° is 36.5 m/s.  For a circular orbit at 84,000 km near the sphere of influence edge, the orbital velocity is 205 m/s, so the delta-V to change inclination by 90° is 290 m/s.

[TanDeeJay]

On 7/9/2020 at 11:58 PM, Zhetaan said:

For the most extreme of stable elliptical orbits in Kerbin's sphere of influence, where the periapsis is at 670 km and the apoapsis is at 84,000 km (those are centre-based radii, not surface altitudes), the orbital velocity at apoapsis is 25.8 m/s, so the delta-V to change the inclination by 90° is 36.5 m/s.  For a circular orbit at 84,000 km near the sphere of influence edge, the orbital velocity is 205 m/s, so the delta-V to change inclination by 90° is 290 m/s.

that's a small delta-V for a 90° inclination change.   But how much DV would I need to get my asteroid to that initial eliptical orbit?  For that to be effective, the periapsis/apoapsis, would need to be on an equatorial plain.  But the 3600 tonne asteroid was coming in well below kerbin with a periapsis below the south pole.  An apoapsis burn would just rotate the polar orbit, and not get me that equitorial orbit?

[Zhetaan]

2 hours ago, TanDeeJay said:

that's a small delta-V for a 90° inclination change.

It is, but there are good reasons for that.  Changes to inclination are changes in the direction of the velocity, not changes to the magnitude, but since changing the direction of a velocity in a practical sense means cancelling the velocity in one direction while adding an equivalent in another direction, the most advantageous time to do it is when the magnitude is as small as possible.  An extremely elliptical orbit has an extremely small velocity at apoapsis, so it is the most efficient to make the change there.

Spoiler

 

It is best to calculate the change by use of vector addition:  if you superimpose the initial and final vectors tail-to-tail, then the vector to change from one to the other is the one that runs from the head of the initial to the head of the final.  Since we're trying to change the direction and not the speed, the initial and final vectors will have the same length, and since it is a 90° change in direction, the resulting construction is similar to an isosceles right triangle.  The length of the hypotenuse of an isosceles right triangle is always the leg length multiplied by √2, and the direction is that of its rotation away from the positive x-axis.  In this case, that is 135°--in other words, exactly half-way between retrograde and normal.

As to why the magnitude is so small at extreme apoapsides, consider what it would mean to make the magnitude exactly zero at apoapsis:  with no velocity at all, the vessel would stop there and, having stopped, would not return.  Of course, for that to work in a gravitational field, the apoapsis would have to be where the gravity is also zero, which is to say at infinite distance from the gravitational source.  This is not realistically achievable, but mathematically it is equivalent to an escape on a parabolic orbit, which leads to an alternative definition of a parabola:  a parabola is an ellipse with one focus at infinity, and a parabolic orbit is one with zero velocity at apoapsis.  We are working with something less extreme, so the situation scales accordingly:  apoapsis is at a long--but finite--distance, and the velocity there is nearly--but not quite--zero.

 

 

3 hours ago, TanDeeJay said:

But how much DV would I need to get my asteroid to that initial eliptical orbit?

That is dependent on the periapsis of its present hyperbolic orbit and a value called its hyperbolic excess velocity.  The essence of it is that the hyperbolic excess velocity is the velocity that it has beyond escape velocity, and the periapsis distance affects the eccentricity of the orbit.  Because the asteroid started in a solar orbit very nearly identical to that of Kerbin, the hyperbolic excess will be close to zero; however, whatever it is, you will need to shed a corresponding amount of velocity in order to effect a capture.  The periapsis distance will determine how effective your burn is to make that capture; the closer you can get to Kerbin, the better, but given the size of the asteroid, you may well need to make use of what you have and hope that it is enough.  However, you are probably in a very good position to change your periapsis; it isn't the best possible, but you might want to see what you can do with a small normal/radial burn just inside Kerbin's sphere.  Normally, radial burns are wasteful, but this is one time that they can be useful.

3 hours ago, TanDeeJay said:

For that to be effective, the periapsis/apoapsis, would need to be on an equatorial plain.  But the 3600 tonne asteroid was coming in well below kerbin with a periapsis below the south pole.  An apoapsis burn would just rotate the polar orbit, and not get me that equitorial orbit?

You are correct in that a rotation about the line of apsides (which is the 'apoapsis burn' you referred to) will not necessarily change the inclination.  Changes to inclination are absolutely dependent on the line of nodes (that is the line connecting the ascending and descending nodes, the axis of rotation about which inclination is measured, and thus the reason why inclination changes are best made there), and burns at any other point will only change the inclination to the extent that the line of nodes projects to the point of the burn.  In a more intuitive sense, it means that if the apsides are located above the poles of the planet, then no burn at those apsides can change the inclination, because rotating a polar orbit about the poles will naturally result in an orbit that still goes through the poles--i.e., it will still be polar.

To fix that, you need to rotate the apsides of the orbit to the equatorial plane (the specific orbital parameter that you need to change is called the argument of periapsis).  There are a few ways to do this:  one is to burn at the periapsis to capture, burn again at the periapsis to circularise (this doesn't need to take two burns but it may be necessary to keep the burn from being too long), burn to raise the apoapsis from the equator, burn at the apoapsis to change the inclination, and finally, burn at the periapsis to circularise (or burn for the first part of a transfer to a different orbit).  There are ways to increase the efficiency; for example, burning for as low a periapsis as possible as early as you can will save a lot of delta-V on later manoeuvres.  You may also be able to influence the location of the periapsis with a few creative burns very close to the sphere edge, and that can save propellant later by reducing the adjustment.  For another example, the really important thing is capture; once you have that, you can rendezvous with the asteroid at your leisure with whatever equipment you think you might need.  For yet another, you may be able to get a lot of free delta-V from Mun gravity assists once you have an equatorial orbit, though that can be tricky.

Because the initial orbit and the first stage intermediate orbit (the orbit immediately post-capture and the orbit with the apoapsis at the equator) have the same size and shape (semi-major axis and eccentricity) and share the same orbital plane (they have the same inclination and longitude of ascending node), they necessarily must intersect at two points.  It is possible to get a single-burn solution to change the argument of periapsis at one of these points, but it is expensive.  I do not know how expensive it is, but it involves radial velocity, so the answer is 'too expensive for your rocket'.  From my limited research on the subject, it appears that the delta-V cost is the same at either intersection point, which is a bad sign; I expect that the single-burn manoeuvre has a cost well into the thousands.

There is also a two-burn solution involving tangential ellipses; the idea is that for any two distinct coplanar elliptical orbits, there is at least one other orbit that is tangent to both of them, and the elegance of that is that moving from one orbit to a tangent orbit requires only prograde/retrograde burns.  You may also recognise this as a generalisation of the Homann transfer orbit.  For this reason, I suspect that it is potentially the cheapest of the alternatives, but I must confess to only passing familiarity with the theory; I have never attempted it for myself.

To reiterate, the first priority is to capture the asteroid because you can then take the time to equip it properly before attempting further refinements to its motion.