Patched conics

[Pawelk198604]

In fact, I did not know in which part of the forum is put this :-)

Patched conics is what we get after upgrading of tracking station in KSP spaceport, that make interplanetary mission a lot easier.

But i wonder why is called "patched conics"

and that has to do with Conic?

[andrewas]

All 2-body orbits are conic sections - shapes that can be generated by slicing through a cone. Patched Conics is when you patch together multiple conic sections around different bodies to plan an entire mission. In reality, its a useful approximation, you can quickly put together a mission and get a rough idea of whats possible without spending too much time computing it. In KSP, its exact because KSP doesn't use N-body physics.

[sgt_flyer]

Patched conics is how KSP calculate orbits (even if it's not shown before you get the upgrade)

Instead of 'real' gravitation problems which are N-body (where every body has an influence on others) KSP uses a 2-body approximation, the patched conics (1 parent body and the ship's body) with clear spheres of influence for each body. In N body physics, there's no clear boundaries between bodies, which results in zones where several parent bodies cancels out their influences (lagrangian points)

Now, patched conic orbits are calculated from, obviously, cones the 'parent body' 'point mass' is the spike of the cone. The orbit is represented as a more or less angled truncature of the cone (the ellipse resulting from 'cutting' the cone becomes the orbit, where the point of the ellipse which is nearest from the spike becomes the periapsis, and the farthest one becomes the apoapsis, the further the ellipse is away from the 'spike', the higher the resulting orbit will be.

Now, why use cones : it's because it approximates 'real world' space time curvature (if you already saw those images were 'planets' are inside of a 'funnel'.)

Here's a simple way to visualise how 'gravity / space time curvature' works :

[Hcube]

Pretty much what they^^ said. Some examples of conic curves are paraboles, hyperboles, ellipses, and circles (wich are ellipses)...

[lajoswinkler]

Conics because of this.

[SAI Peregrinus]

sgt_flyer's video has the typical terrible rubber sheet explanation for gravity. It tries to explain gravity using a system that requires gravity, and ends up explaining nothing. The dark energy bit is totally wrong. etc.

[NFUN]

sgt_flyer's video has the typical terrible rubber sheet explanation for gravity. It tries to explain gravity using a system that requires gravity, and ends up explaining nothing. The dark energy bit is totally wrong. etc.

It's an analogy, get over it.

[sgt_flyer]

The video was just there to show why they used cones in patched conics because that's the simplest geometric approximation to the space time curvature as we know it

[B787_300]

to put it in an easily uderstanable context,

In orbital mechanics everything is a Conic section (a parabola, a hyperbola, an ellipse, or a circle) to make the orbit math easier you have what are called Spheres of Influence, which are regions in which ONE body is really providing all the gravitational force. ( F = (G*M*m)/(r^2) ). if you are doing interplanetary stuff or going to a moon you use a system called patched conics for the preliminary orbit design, so you look at the orbit of an object until you reach the edge of a SoI, then switch SoIs and look at the orbit there, until you reach your destination. then you combine (Patch) all the individual conic sections together into one overall picture. that is why it is called Patched conics.

Just as an aside when go from earth to mars (IRL) you look at 3 different SoI, the Earth, the Sun, then Mars. The math behind it is reasonably simple, but can be confusing.

If you were to look at the more complex method then you have to do n-body physics which is very hard. the Forces due to gravity only become F = (G*M*m)/(r^2) + (G*M*m)/(r^2) + (G*M*m)/(r^2) + (G*M*m)/(r^2) + ... which is very very hard to solve.

[Camacha]

sgt_flyer's video has the typical terrible rubber sheet explanation for gravity. It tries to explain gravity using a system that requires gravity, and ends up explaining nothing. The dark energy bit is totally wrong. etc.

I never got or agreed with that comparison either, until someone showed me a threedimensional version. Then it makes sense. Spacetime gets pinched by gravity (or I probably should say pinched spacetime is gravity).

[lajoswinkler]

https://imgs.xkcd.com/comics/teaching_physics.png

It's an analogy, get over it.

The problem is that usually nobody says it's an analogy, and basically no one listening to the speaker doesn't get it's an analogy.

I never got or agreed with that comparison either, until someone showed me a threedimensional version. Then it makes sense. Spacetime gets pinched by gravity (or I probably should say pinched spacetime is gravity).

http://cdn.phys.org/newman/gfx/news/hires/2011/aphotonspoin.jpg

Even that isn't good enough. Rubber sheet is a 2D object distorted into 3D space. Therefore, you need a 3D space being distorted into 4D, which is impossible to show.

But yes, it's a better analogy, however for the purposes of education, one has to use the rubber sheet if wants to roll around some massive balls. Of course, great care must be taken to make sure the people getting educated understand it's an analogy.

The same educational error, but this time with much worse consequences, is the Schrödinger's cat. That thought experiment is designed to be a real life analogy of what happens with particles only. Sadly, almost nobody understood that and people actually think such effects are normal in macroscopic world. It became a breeding ground for nutters.

[Jovus]

Instead of 'rubber sheet' say 'three-dimensional LaPlacian' if it makes you more comfortable. It's still an approximation.

[SAI Peregrinus]

The thing with the rubber sheet approximation that gets to me is that it misses the critical point: Velocity (with respect to the local geodesic) is constant unless acted upon by an outside force. Objects travel in straight lines along the geodesic, it's just that the projection of those lines into Euclidean space can create curved paths. Just as a straight line in spherical geometry is a great circle, so too are the straight lines on the geodesic "curved" when projected into Euclidean spaces. A satellite orbiting Earth is going in a straight path through space-time (ignoring air resistance, solar wind, etc). Gravity in GR isn't a real force, just like centrifugal force isn't a real force.

And the real objection was to the bit about dark energy. What he represented was simply negative mass, which has no relation to dark energy.

[NFUN]

The thing with the rubber sheet approximation that gets to me is that it misses the critical point: Velocity (with respect to the local geodesic) is constant unless acted upon by an outside force. Objects travel in straight lines along the geodesic, it's just that the projection of those lines into Euclidean space can create curved paths. Just as a straight line in spherical geometry is a great circle, so too are the straight lines on the geodesic "curved" when projected into Euclidean spaces. A satellite orbiting Earth is going in a straight path through space-time (ignoring air resistance, solar wind, etc). Gravity in GR isn't a real force, just like centrifugal force isn't a real force.

And the real objection was to the bit about dark energy. What he represented was simply negative mass, which has no relation to dark energy.

I didn't watch the video, but if he said that he is mistaken. Sorry for the oversight.

[Kerbart]

The thing with the rubber sheet approximation that gets to me is that it misses the critical point: Velocity (with respect to the local geodesic) is constant unless acted upon by an outside force. Objects travel in straight lines along the geodesic, it's just that the projection of those lines into Euclidean space can create curved paths. Just as a straight line in spherical geometry is a great circle, so too are the straight lines on the geodesic "curved" when projected into Euclidean spaces. A satellite orbiting Earth is going in a straight path through space-time (ignoring air resistance, solar wind, etc). Gravity in GR isn't a real force, just like centrifugal force isn't a real force.

What I never get with that... Suppose your satellite is in a 100km orbit. Wouldn't you see that satellite than roughly 40,000km ahead of you? Because the light would be travelling in the same straight line, right? Why don't we see earth ahead and back of us if we're really moving in a straight line that's curved in such a way that it forms a circle?

I'm not denying Einstein's theory. It's just that I don't understand why it applies to mass but not to the same extend to light, apparently. Unless, obviously, I am missing something. What is it?

[SargeRho]

Orbits are determined by velocity. c is much, much faster than orbital velocity. Light's path is still affected by gravity, but it's not enough to bend it into an orbit around Earth.

[YNM]

- (1st) Patched because the trajectory is determined by the energy and momentum at that particular instance, assuming a simple limited two-body orbit.

- Conics because the trajectory results in conic sections, which is either a circle, ellipse, parabole or hyperbole.

- (2nd) Patched because the orbit is limited to SOIs. So you can't get a transfer to Mun using trajectory akin to GRAIL's trajectory, or you can escape mun in an elliptical orbit (eccentricity less than 1), for example. Also explains why a few near-Kerbin asteroid can get itself to orbit Kerbin, while lacking perturbations.

There's no link between patched conics method and GR at any rate, because trajectory in GR are always spiral.

Edited June 22, 2015 by YNM

[Pawelk198604]

- (1st) Patched because the trajectory is determined by the energy and momentum at that particular instance, assuming a simple limited two-body orbit.

- Conics because the trajectory results in conic sections, which is either a circle, ellipse, parabole or hyperbole.

- (2nd) Patched because the orbit is limited to SOIs. So you can't get a transfer to Mun using trajectory akin to GRAIL's trajectory, or you can escape mun in an elliptical orbit (eccentricity less than 1), for example. Also explains why a few near-Kerbin asteroid can get itself to orbit Kerbin, while lacking perturbations.

There's no link between patched conics method and GR at any rate, because trajectory in GR are always spiral.

Mathematics is very cool just a pity that I have a problem to understand it

Truth be told through KSP learned me more about mathematics than throughout the elementary school, middle school and high school

[hirschhornsalz]

Now, why use cones : it's because it approximates 'real world' space time curvature

Conic sections are the exact solutions for the 2-body problem, and the two body model is what KSP is using. It has nothing to do with general relativity.

[Superfluous J]

The problem is that usually nobody says it's an analogy, and basically no one listening to the speaker doesn't get it's an analogy.

I don't remember if it was stated to me that it was an analogy, but even at fairly young (12 maybe?) I got that it was one. And it helped me immensely in imagining 4 dimensional spacetime curvatures.

Anybody who thinks it's not an analogy just isn't thinking it through. It's not like people seeing this think that Earth is rolling around on a big rubber sheet.

[lajoswinkler]

I don't remember if it was stated to me that it was an analogy, but even at fairly young (12 maybe?) I got that it was one. And it helped me immensely in imagining 4 dimensional spacetime curvatures.

Anybody who thinks it's not an analogy just isn't thinking it through. It's not like people seeing this think that Earth is rolling around on a big rubber sheet.

Trust me, they do. Just because you're at least reasonably intelligent doesn't mean others are, too.

[Kerbart]

Orbits are determined by velocity. c is much, much faster than orbital velocity. Light's path is still affected by gravity, but it's not enough to bend it into an orbit around Earth.

Aaaah. To use the rubber sheet analogy (pre-emptive snark: yes we know it's not the right model. It's an ANALOGY ) -- if I toss a marble really quick through a depression in the sheet it will go nearly straight, where if I release it slowly it will turn significantly?

[TythosEternal]

Conic sections are the exact solutions for the 2-body problem, and the two body model is what KSP is using. It has nothing to do with general relativity.

This.

Kepler's first law--"all orbits are conic sections"--can be directly derived from Newton's law of gravity and conservation of angular momentum. No relativity knowledge is required.