Ideal Insertion Method

[Raideur Ng]

I'm sure this has been asked, but I cannot find anything that specifically answers it:

Is it better to grace the edge of an SOI, and then burn down the apogee or circularize very close to the body (to presumably use a gravity assist in the process)? I've never had an ideal situation to specifically test them against each other, but the closer -seems- to work better. Thoughts?

 

 

[soulsource]

I'll just quote a posting of myself, where I quote myself:

Edit: What I didn't mention in the previous post was why one can sum energies but not velocities. That's because in a gravity field energy is a constant of motion, while the velocity obviously is not conserved. Sorry if this sounds confusing, but I'm trying to make clear that you cannot directly add a velocity change done far away from a planet to a velocity change close to the planet, as between the maneuvers your velocity will have changed due to the movement through the gravity field which requires a certain amount of work (in that case kinetic energy). The total energy - your kinetic plus your potential energy - is conserved though, as gravity is a conservative force, so you can indeed sum up energy changes done at different positions within a gravity field.

 

Edit 3: If you just want to enter orbit around a planet and stay there forever or leave again towards the same planet you came from, there are optimal altitudes:

Edit 5: I've been checking these numbers, and either the formula I derived in Edit 4 below isn't correct, or those numbers are outdated. I'd therefore recommend to recalculate them when you need them.

If however you want to land, you're better off going directly to a very low parking orbit, as it's more efficient to do that than first going to the "optimal" orbit and then decreasing your orbit's radius.

Edit 4: A few words on how those optimal altitudes are calculated:
You can just take the formula from my post I've linked to above (m*(v0+dV0)²/2-GM*m/r=m*dVh²/2), and insert the orbital velocity v0 (which can be obtained by setting the force of gravity and centrifugal force equal) and then solve for the burn's dV0. The dVh value in this formula is the first burn of a Hohmann Transfer. What you get is dV0 as a function of orbital radius. All that's left to do is to find the minimum of said function, for instance by setting the first derivative zero. The result should be given by r_ideal=2*GM/dVh² (where GM is the standard gravitational parameter of your origin body, typically Kerbin) - at least if I didn't make any typos while hacking this into my calculator...

Edited April 8, 2016 by soulsource

[Starhawk]

In my experience orbital insertion is best done directly to the altitude you want for the final orbit.

Adjusting your trajectory to change your final periapsis costs very little delta-v if done early and far from the target.

If your target has fairly large mass you also gain from Oberth by having your periapsis very low so that you are going very fast when you execute the capture burn.

If you plan to land, you will end up lowering your orbit anyway, so you may as well start with the periapsis you want for your parking orbit.

OTOH, if you just want to capture into orbit to get some science and then leave orbit, you probably want to just barely enter the SOI and capture into a very high, low energy orbit.

Happy landings!

Edited April 7, 2016 by Starhawk

[Raideur Ng]

I'll be slightly more specific, having added it up, Option 1 is nearly 200 m/s less than Option 2, I assume due to Oberth and gravity assist. Just trying to make sure I am not missing an even superior technique. Also, why doesn't the tutorials just start with teaching you the best way to intercept? Are we suppose to smile with glee when we figure it out ourselves?

vs

[nater662]

Depends what you want to do.

If you are going to land on the planet or just hang out for bit. 

If you want an orbit and then want to leave soon #1

If you want to get in close or land try to get in close on your entry. #2

Scott Manely has a video on that somewhere that explains it but Starhawk is right. Try to get your orbit where you want it from the get-go.  

 

[Plusck]

On 09/04/2016 at 7:40 PM, Raideur Ng said:

I'll be slightly more specific, having added it up, Option 1 is nearly 200 m/s less than Option 2, I assume due to Oberth and gravity assist. Just trying to make sure I am not missing an even superior technique. Also, why doesn't the tutorials just start with teaching you the best way to intercept? Are we suppose to smile with glee when we figure it out ourselves?

vs

I'm a bit lost because I don't follow what you're calling "option 1" and "option 2". Also I can't see those jpg files - did you add them in with the "insert other media" button at the bottom right of the post text box?

Oberth merely says that since E=mv², if you want to change your orbital energy then you want to do it at maximum velocity.

A gravity assist, however, only happens when you use one massive body to change you velocity with respect to another massive body. So it has no influence on the question of where to arrive in any given SOI if you are not planning to leave that SOI on a new trajectory.

As people have said, above, it depends what you want to do. And as people have said, above, there are optimal altitudes for certain things. And also, as people have said above, there are issues of kinetic vs potential energy to take into account.

For example, Tylo and Laythe are both massive moons.

Tylo is bigger, obviously, but its SOI is much, much bigger. Therefore if you enter Tylo's SOI aiming for a grazing pass, it will have a long, long time to accelerate you as you fall almost vertically towards it. That means that if you want to capture, you'll benefit from the Oberth effect by aiming for a low-Pe pass but you'll have a huge amount of energy to shed. If you don't intend to land, grazing Tylo to capture might not be efficient if you enter the SOI slowly (because Tylo will have time to accelerate you massively). If you are already going fast as you enter Tylo's SOI, then it won't have time to accelerate you too much and a grazing pass is undoubtedly the cheapest way to capture.

Laythe, on the other hand, has a much smaller SOI. Therefore it makes little difference how fast you're coming in: it will always be cheap to capture and you should therefore maximise that by entering its SOI on a trajectory that comes as close as possible to its atmosphere.

 

Another way of looking at this is what soulsource was saying: there are optimal altitudes for things.

So if you had a free choice of orbit around Kerbin, and you were going to Eve or Duna, you'd want to choose something near the Mun's orbit. This is where the outward burn to Eve or Duna is the cheapest.

Since transfer orbits are entirely reversible, that means that if you are coming from Eve or Duna, and just want to get into a circular Kerbin orbit for minimum cost, you want to aim for the Mun and no lower, because a lower (circular) orbit will cost more. A lower pass around Kerbin will certainly be better just to capture into an eccentric orbit, but if you have a low TWR and can't really use those (extremely) few minutes at Kerbin Pe and want to get into a safe and stable orbit, you'd be better off circularising just inwards of the Mun, it'll cost less.

 

So now I'm wondering: was that the actual question? ; )

[MaxL_1023]

An optimal altitude that high does not make much sense - it takes only about 200 m/s more to make a Duna transfer than just the burn to put your AP at the Mun's Orbit, let alone circularizing there than making the transfer again. 

[Foxster]

Also depends if the planet/moon has an atmosphere. If it does then it is very likely your cheapest or even near-free way to achieve an orbit is with one or more aerobraking passes within the upper atmosphere. Pe being adjusted first well outside the SOI and adjusted again right after entry to the SOI to minimise the dV these adjustments require. 

This is especially easy with the new 10m heat shield available in 1.1.  

[Plusck]

5 hours ago, MaxL_1023 said:

An optimal altitude that high does not make much sense - it takes only about 200 m/s more to make a Duna transfer than just the burn to put your AP at the Mun's Orbit, let alone circularizing there than making the transfer again. 

 

This is true from a Kerbin-centric point of view, but not in absolute terms.

A "visiting" mothership from Duna, intended to provide refuelling and a meeting point for craft exploring the Kerbin system, would be able to get into a circular orbit with the least expense (and therefore the least expense when leaving Kerbin to go home again) at or around the Mun's orbit. Likewise if from Jool - the mothership would want to circularise at an altitude of 370 km.

The optimal altitude for a transfer burn measures only the pure cost of the burn to get a given surplus velocity when you get to the edge of the SOI - and obviously isn't optimal if you have to make a great expense to get there.

[MaxL_1023]

11 hours ago, Plusck said:

 

This is true from a Kerbin-centric point of view, but not in absolute terms.

A "visiting" mothership from Duna, intended to provide refuelling and a meeting point for craft exploring the Kerbin system, would be able to get into a circular orbit with the least expense (and therefore the least expense when leaving Kerbin to go home again) at or around the Mun's orbit. Likewise if from Jool - the mothership would want to circularise at an altitude of 370 km.

The optimal altitude for a transfer burn measures only the pure cost of the burn to get a given surplus velocity when you get to the edge of the SOI - and obviously isn't optimal if you have to make a great expense to get there.

Ok - I was including the cost of getting into orbit from the KSC.