How can I calculate at which distance a ship is captured by the gravitational field of a planet?

[herzbube]

As long as a ship is far away from a planet the ship moves independently from the planet, however when the ship gets closer the planet will capture the ship in its gravitational field so that from now on planet and ship move together on the planet's orbit. The distance at which this capture happens can be determined experimentally for small planetary bodies that move with an orbital velocity that is greater than the minimum supercruise speed of 30 km/s.

I have made three such experimental measurements in a system that happens to have fast orbiting planets, with inconclusive results as to which factors are playing into the formula to determine the capture distance:

Planet	Gravity	Radius	Approach speed	Distance to center of orbit	Capture distance
A 1	0.14g	974 km	150 km/s	6.03 ls	4.50 Mm
A 2	0.14g	1017 km	120 km/s	8.80 ls	6.86 Mm
B 1	0.11g	761 km	62 km/s	9.39 ls	7.73 Mm

Instinctively I would have thought that gravity, or maybe planet radius would play into the capture distance, but looking at these measurements this does not seem to be the case.

Does someone know how this works?

 

[varonica]

As long as a ship is far away from a planet the ship moves independently from the planet, however when the ship gets closer the planet will capture the ship in its gravitational field so that from now on planet and ship move together on the planet's orbit. The distance at which this capture happens can be determined experimentally for small planetary bodies that move with an orbital velocity that is greater than the minimum supercruise speed of 30 km/s.

I have made three such experimental measurements in a system that happens to have fast orbiting planets, with inconclusive results as to which factors are playing into the formula to determine the capture distance:

Planet	Gravity	Radius	Approach speed	Distance to center of orbit	Capture distance
A 1	0.14g	974 km	150 km/s	6.03 ls	4.50 Mm
A 2	0.14g	1017 km	120 km/s	8.80 ls	6.86 Mm
B 1	0.11g	761 km	62 km/s	9.39 ls	7.73 Mm

Instinctively I would have thought that gravity, or maybe planet radius would play into the capture distance, but looking at these measurements this does not seem to be the case.

Does someone know how this works?

I expect it's a moving target. I think the radar has a red zone that shows influence, have you tried matching it with the red zone on the radar?

Also it should determined by mass, not gravity or radius. You would need to calculate the mass by looking at the ratio of surface gravity to radius, this will give you a value that's constant for all bodies with the same radius and surface gravity. For instance example A1 and A2 in your graph have the same gravity but different radius, therefore the mass of A1 is greater than the mass of A2 and the capture zone will be different.

It's going to be complicated! For instance the gravity figure you are using is the surface gravity, but an object with the same mass and smaller radius will have the same gravity at the same distance from the centre (not exactly the same but very close) So if a body with a mass that gives it 1g at the surface was compressed into a volume half the size the surface gravity would be greater, but if you built a tower with a platform the same distance from the centre as the previous surface level the gravity on the platform would be almost exactly 1g. In actuality there would be differences caused by the increased rotational velocity caused by compressing a body with a rotation kinetic energy to a smaller size but for this I am assuming a non-rotating perfect sphere.

So, complicated!

Sorry forgot, the capture distance also depends on the velocity of the object being captured, a faster moving object will need to be much closer than a slower moving object to be captured, so you can easily zoom by a planet within your purported capture zone without being captured. Some moons have mountains high enough that if you drive the SRV up there they drift off into space because the velocity of rotation at the top of the mountain is greater than escape velocity, in other word the capture zone is lower than the highest point of the moon!

How accurate ED physics is in this department I have no idea, let us know how you go.

 

[iain666]

Do you actually go into orbit or do you just enter a zone of the game where you get kind of sucked along? If it's the latter then it's just a game thing and there's no reason to expect actual orbital mechanics to play any part. It's probably driven by similar things but there could be additional magic numbers from the game engine. We probably need more data to work it out.

Surface gravity is a function of mass and radius, if there's real physics going on any two will do (assuming that ED has the same G).

 

[varonica]

Do you actually go into orbit or do you just enter a zone of the game where you get kind of sucked along? If it's the latter then it's just a game thing and there's no reason to expect actual orbital mechanics to play any part. It's probably driven by similar things but there could be additional magic numbers from the game engine. We probably need more data to work it out.

Surface gravity is a function of mass and radius, if there's real physics going on any two will do (assuming that ED has the same G).

You can go into orbit around bodies given that the orbital velocity is not greater than the max velocity of your ship in real space (ie not supercruise) with FA off. With FA on of course the ship will simply maintain its current height regardless of orbital mechanics, but with FA off the ship will fall towards the planet if it is to close to maintain orbit or move away if to fast. Of course it's not 100% real because the ship won't accelerate towards the surface until impact, only until max ship speed is reached, a great pity I think but that's all a big handwave to enable exciting PvP. They have a lot to answer for! I would rather proper physics than exciting PvP any day.

 

[iain666]

the ship won't accelerate towards the surface until impact, only until max ship speed is reached, a great pity I think but that's all a big handwave to enable exciting PvP. They have a lot to answer for! I would rather proper physics than exciting PvP any day.

If you had a PvP encounter where an out-gunned pilot was able to get away by having the skill and cojones to go into a steep dive towards the planet and keep control while their ship was shuddering under the strain of velocities it's not designed for and pulling out of it at the last possible second after their pursuer has had to chicken out and let them go, brushing mountain tops as they get away, how would that not be exciting and rewarding pilot skill?

Madness, I tell you. Madness.

 

[Kalpa]

There is no capture by gravity in ED. There is a distance when you are automatically pulled from supercruise. This is purely a game mechanic, though, and has nothing to do with physics simulation in game (although it may be related to relative gravity of a body)

No, I do not know how to calculate this distance. If someone knows, share. It seems to vary quite a bit (as demonstrated by OP) - I have been speculating it to be influenced by the gravity well of the body you're approaching as well as the gravity well of the parent body (ie. some kind of sphere of influence calculation) - this kind of mechanic is needed to make sure that the zones don't overlap each other. Although now that I mentioned this, someone will certainly come up with an example of dual planet / moon system which are so close to each other that you can enter the 'flight mode' of either body somewhere in the middle...

 

[Boogyman]

from my experiences in game, i do not believe the game implements quite so extensive a physics simulation. The "capture" we experience around planets it effective whether we are in supercruise or not, so supercruise is not relevant to the discussion. i believe its a matter of coordinate systems. each planet has a spherical coordinate system which is distinct and independent from the (likely rectangular) coordinate system of the star system in which it resides. The "capture" is an artifact resulting from the transition between the coordinate system that is relative to the star and the coordinate system that is relative to the planet. the planets gravity is likely implemented as an inward force relative to the center of the spherical coordinate system and would therefore be unlikely to have any effect on objects operating in a different coordinate system.

 

[Sapyx]

The "capturing" the OP is talking about is a relic of the "sphere of influence" game mechanic inherited from the previous Elite games.

The game always told you what speed you were travelling at, but obviously needed a reference point to compare that speed with. Which reference point it chose depended on where you were in the star system: if you were out in interplanetary space nowhere near a star, then the reference point was the star. If you were near a planet, then it was the planet, and so forth. I believe the game did a complicated gravitational calculation to work out which of the possible influencing objects in the system was exerting the strongest gravitational influence at that moment, and selected that object as the frame of reference.

The game also needed to know this, because the Three-Body Problem is way too complex to model in a 1990s computer game, so when it calculated the effect of gravity on your trajectory (the earlier games did not have Supercruise; all in-system travel was done using a Newtonian flight model) it was only calculated using the single object that was the frame of reference. In other words, the gravity of Jupiter did not affect your course through Sol system until and unless you got close enough to Jupiter that Jupiter's gravity became stronger than the Sun's gravity; once you entered Jupiter's "sphere of influence", your speed was measured relative to Jupiter, and it was Jupiter's gravity, rather than the Sun's gravity, that now influenced your course.

I believe something like this still exists, except for the addition of extra frames of reference such as "shipping lane" and "deep space". However, it no longer "needs" to know this to calculate gravitational course corrections, since gravity does not "pull" on a ship in Supercruise.

What it means for the OP is that there isn't going to be a simple calculation for the "capture distance", since it depends on both the gravity (mass) of the object in question, as well as whatever object it happens to be orbiting.

 

[herzbube]

A lot of interesting answers, thank you everybody for your time and insights.

I may have used some terms in a scientific incorrect way in my OP, sorry for that. I am merely a space romantic who wanted to describe an effect that is definitely observable in the game. I didn't (and still don't) really care whether this "capture" effect is based on real-world physics or some game-internal mechanic - my intent is/was only to understand things sufficiently so that I can roughly predict when the "capture" will occur for any planetary body, regardless of its size.

Specifically, the other day I found a gas giant that was on a very close orbit around the primary star (semi-major axis 0.12 AU), combined with a rather low orbital period (31.9 days). I had hoped to observe the giant trundling along its orbit (in reference to the primary star) from a distance, similar to how you can observe smaller planets speeding along in reference to their parent body (famous example: Mitterrand Hollow). No dice, though, the giant didn't want to budge. I was then thinking that maybe I had already been "sucked along" (as ian666 puts it), but I didn't know how to check at which distance this would happen.

Well, for the time being I must move along my own erratic ways, or I will never get home (or Corbin Moran will overtake me on the Sagittarius-Carina arm - and that's not something I cannot allow ).

 

[Sapyx]

You can tell which frame of reference you are in: the object named in the bottom left corner of the main game screen is the object you are curenly in the sphere of influence of. Gas giants, as I said, have larger spheres of influence than a rocky planet, but the giant's sphere will shrink because of the close proximity to the star. In cases such as this, you probably should try to fly up above one of the star's poles; that should be far enough away.

Still, all being said, 31 days is quite a long orbital period. To put it in perspective, it's almost the same as the Earth's Moon around Earth. You can't see the Moon whizzing around the Earth, uless you're much more patient than the average computer gamer and/or you're taking timelapse video.

It is possible to see gas giants whizzing around in super-close orbit of their stars, but you'll need to find a much more extreme star system than yours. I saw one (a Class V giant around a K-class secondary star in close proximity to the primary G-class star) a few weeks back with a period of less than a day, that was visibly moving. Unfortunately, I forgot to note the system name, but I did get a screenshot:

 

[herzbube]

You can tell which frame of reference you are in: the object named in the bottom left corner of the main game screen is the object you are curenly in the sphere of influence of.

Excellent, I'll watch that next time I'm chasing a planet

Still, all being said, 31 days is quite a long orbital period. To put it in perspective, it's almost the same as the Earth's Moon around Earth. You can't see the Moon whizzing around the Earth, uless you're much more patient than the average computer gamer and/or you're taking timelapse video.

Wait. I made some - admittedly simplified - calculations which told me that the gas giant should be moving at roughly half the speed of one of its smaller siblings, which is still faster than my ship's minimal supercruise speed. In other words: Fast enough to be observable.

1 AU = 149597870.7 km
1 day = 86400 seconds
Pi = 3.1415
Orbit circumference = Semi-major axis * 2 * Pi
(assuming that the orbit is a circle and the semi-major axis is the radius)

Planet	Radius	Semi-major axis	Orbital period	Orbit circumference	Orbital velocity
A 1	974 km	0.01 AU = 1495978.707 km	1.1 days = 95040 seconds	9399234.216081 km	99 km/s
A 3	68303 km	0.12 AU = 17951744.484 km	31.9 days = 2756160 seconds	112790810.592972 km	41 km/s

Did I make a mistake here? Assuming I didn't, why shouldn't I be able to see the gas giant moving in reference to, say, it's primary star. Admittedly, the velocity is not great, but should still be observable.


Anyway, I probably did make some mistake. Knowing from your experience that they exist, I will continue to be on the lookout for fast gas-giant-shaped bullets, and take your hints into account when I find one. Again, thanks a lot for your patient explanations.

 

[varonica]

It is possible to see gas giants whizzing around in super-close orbit of their stars, but you'll need to find a much more extreme star system than yours. I saw one (a Class V giant around a K-class secondary star in close proximity to the primary G-class star) a few weeks back with a period of less than a day, that was visibly moving. Unfortunately, I forgot to note the system name, but I did get a screenshot:

I've seen quite a few small planets with a day or less orbital period, you don't realise what that means until that little planet you are just going to go in orbital cruise around suddenly starts sliding sideways across the screen and gets smaller and smaller. As soon as it gets far enough away I kick it up to about 200kps and chase it, swoop around to the leading side and slide gracefully into orbit (I say gracefully but it's usually accompanied by swearing, wrenching of the joystick and blind hope I am not going to fast to make orbital cruise)

Only come across one or two gas giants that close and I've not really bothered to have a close look.

 

[Sapyx]

OK, here's a good case study. I literally only just discovered this system, Preae Ain UR-I c23-574. It's not as good as the one I couldn't find (and I spent a couple hours this morning retracing my Visited Stars looking for it), but it's still a good example of planetary motion in action. There are three objects in the system: a G-class primary star, a K-class secondary star and a Class V gas giant orbiting real, real close to the primary, orbital period 1.4 days. Here's the system map:

...and here's a snapshot of the primary and planet, from about 30 Ls above the pole of the planet's orbital plane. As you can see, the planet is in quite an eccentric orbit, and when I took the pics, the planet was about a third of the way between aphelion and perihelion. So it wasn't as close as it could possibly be to its star, nor is it moving the fastest (remember, Kepler's laws: closer to sun = faster orbital speed).

Anyhow, here's the view from my drop-in point of the planet. Note the frame of reference down the bottom-left of the pic: "Preae Ain UR-I c23-574 A" - so my current sphere of influence is the star, not the planet. So I am (almost) motionless compared to the star, but the planet is free to move in its orbit relative to me. And it is moving, but only just barely; I couldn't actually see it move. Note the clock in the top right corner: the pics are taken six an a half minutes apart. Which makes sense; it takes an entire day and a half to make that full loop around the star. Yes, I know I should have dropped out of Supercruise and come to a complete stop, because the 30km/s idling motion is not irrelevant at such small distances; this would have exaggerated the motion a tiny bit.

For the record, in this system, for the line between star and planet, I needed to travel to a point just under 1 Ls from the planet to enter the planet's sphere of influence. In other words, I had to get this close:

Which is awfully small for a gas giant's sphere of influence, and a good example of how proximity to a star shrinks a planet's sphere of influence.