Request: Laythe's Roche limit around Kerbin

[Kaiser82]

If the OP doesnt appreciate what happened here, just know that I do. I freaking love you nerds. 

[Kerbart]

On 12/23/2016 at 4:29 PM, GluttonyReaper said:

https://en.m.wikipedia.org/wiki/Roche_limit

The wikipedia article on this is suprisingly detailed, as it turns out.

Detail is rarely an issue with Wikipedia. Accuracy, yes, that's always questionable. But there's usually plenty of detail.

[CrookedTube]

On 12/23/2016 at 10:08 AM, Raptor22 said:

Calling all math nerds!

So, I'm only a freshman in high school. That means that I have a pretty hard time with the equations used for orbital mechanics and things such as -  in this scenario - Roche limits. I was thinking of using Hyperedit to put Laythe in orbit around Kerbin. I want to put it as low as I can to the Roche limit, so that I can reach it easily. Could anyone help me out?

I'm giving this a like just because the OP is an admitted math nerd HS freshman. Keep on keeping on, sir.

 

CrookedTube

[Whirligig Girl]

On 12/23/2016 at 11:08 AM, Raptor22 said:

Calling all math nerds!

So, I'm only a freshman in high school. That means that I have a pretty hard time with the equations used for orbital mechanics and things such as -  in this scenario - Roche limits.

Roche Limit should be easy for a freshman if you know 8th grade math. (Especially since you ought to be a semester through 9th grade math) I encourage you to figure out similar problems on your own in the future, because it really is largely just comprehending which numbers to substitute into easy equations. (Especially if you have a calculator)

1.26 times Radius of Kerbin times ³√[Density of Kerbin / Density of Laythe]
(Note that ³√[ x ] can be written as x^1/3.)

KSP Wiki tells us the following:

Kerbin Radius = 600000 meters.

Density of Kerbin = 58.5 g/cm³.

Density of Laythe = (Laythe has .8 gee and .8 radius of Kerbin, so we expect it to be very similar density.) 56.1 g/cm³.

Note that the unit (g/cm³ or kg/m³) doesn't actually matter, because this is merely a ratio of two identical units (you can think of it as the division cancelling out the unit measurement)

Plugging this in all together gives us: 788342.246 meters, or 1.31 Kerbin Radii. Note that this is in orbital radius, not altitude. This is measured from the center of the planet, not the surface. 

HOWEVER

This will place half of Laythe within the roche limit, and part of it indeed within Kerbin's own surface. The altitude must be raised by the radius of Laythe + its atmosphere height. That is 500,000+50,000 meters. In total, the new safe semi-major axis of the orbit is 1338342.25 meters.

 

Incidentally, you might want to use a Kopernicus config instead of a temporary HyperEdit modification.

@Kopernicus:FOR[MoveLaytheToKerbinRocheLimit]
{
	@Body[Laythe]
	{
		@Orbit
		{
			@referenceBody = Kerbin
			semiMajorAxis = 1338342.25
		}
	}
}

Copy and paste this into a .cfg file anywhere in GameData, and download and install the Kopernicus plugin (make sure to install its included requirements, ModularFlightIntegrator and ModuleManager)

[Whirligig Girl]

Unrelatedly, I've seen people mention atmospheric contact and I've actually prototyped this as a replica of the Rocheworld from the novel Flight of the Dragonfly. Unfortunately if you get them close enough to engage in atmospheric contact, (which is a generous height given the thick pressure and the low gravity) the spheres of influence freak out. You definitely can not interact with the two atmospheres at a time, and the way the SOIs end up working means things either break or just don't work authentically enough to be worth it. I've not yet given up completely on the idea, but it's not likely to keep the atmospheric contact requirement alive.

The two spheroids, Roche and Eau. (Rocky and Water)

With restricted S.O.I. on Eau, you end up in the SOI in a sudden appearance of almost an atmosphere of pressure.

With unrestricted SOI, scenes in space work nicely, but if you are on the ground you will be picked up and thrown into Eau if you go to its side of Roche. Note, the planets appear black in some pictures due to lighting (I was trying to replicate Barnard's Star in Rocheworld but didn't properly set the brightness.)

Best Case Scenario happens when you are right at the closest point from Roche to Eau, and you launch. (In Restricted SOI model of course) If you are in the perfect spot, the atmosphere will have the same pressure when you exit and re-enter the SOI.

---

 

I don't think this is easily solvable, at least not for an authentic atmosphere-touching phenomenon. However, that doesn't mean we need to give up on interplanetary jet plane flight. If the planets were rescaled to kerbal size, orbital velocity would be within the realm of mildly supersonic flight. If the two planets were positioned and sized for proper game balance, it might be possible to have jet plane flight to another world, as long as you're ok with being in the vacuum of space for part of that time. Unfortunately, there would be no interplanetary waterfall.  

Edited December 26, 2016 by GregroxMun

[tseitsei89]

8 hours ago, GregroxMun said:

Unrelatedly, I've seen people mention atmospheric contact and I've actually prototyped this as a replica of the Rocheworld from the novel Flight of the Dragonfly. Unfortunately if you get them close enough to engage in atmospheric contact, (which is a generous height given the thick pressure and the low gravity) the spheres of influence freak out. You definitely can not interact with the two atmospheres at a time, and the way the SOIs end up working means things either break or just don't work authentically enough to be worth it. I've not yet given up completely on the idea, but it's not likely to keep the atmospheric contact requirement alive.

The two spheroids, Roche and Eau. (Rocky and Water)

With restricted S.O.I. on Eau, you end up in the SOI in a sudden appearance of almost an atmosphere of pressure.

With unrestricted SOI, scenes in space work nicely, but if you are on the ground you will be picked up and thrown into Eau if you go to its side of Roche. Note, the planets appear black in some pictures due to lighting (I was trying to replicate Barnard's Star in Rocheworld but didn't properly set the brightness.)

Best Case Scenario happens when you are right at the closest point from Roche to Eau, and you launch. (In Restricted SOI model of course) If you are in the perfect spot, the atmosphere will have the same pressure when you exit and re-enter the SOI.

---

 

I don't think this is easily solvable, at least not for an authentic atmosphere-touching phenomenon. However, that doesn't mean we need to give up on interplanetary jet plane flight. If the planets were rescaled to kerbal size, orbital velocity would be within the realm of mildly supersonic flight. If the two planets were positioned and sized for proper game balance, it might be possible to have jet plane flight to another world, as long as you're ok with being in the vacuum of space for part of that time. Unfortunately, there would be no interplanetary waterfall.  

Yes in the challenge for "Highest altitude achieved with jet engines only" we have already achieved 140+km apoapsis so as long as the SOI change happens before that altitude the flight is doable. Too lazy to calculate distance needed for this right now since I'm on my phone right now. But tje calculation is very simple.

[swjr-swis]

1 hour ago, tseitsei89 said:

in the challenge for "Highest altitude achieved with jet engines only" we have already achieved 140+km apoapsis

You meant 240+ km, yes?

[tseitsei89]

1 hour ago, swjr-swis said:

You meant 240+ km, yes?

Oh yes sorry forgot the numbers. But my point was that if you set the planets so that the SOI change happens in vacuum you won't have that "sudden pressure change" @GregroxMun was talking about and it is still very much possible to reach that altitude with only jet engines.

EDIT: math was wrong. Will be back soon...

EDIT2: turns out that SOI sizes work a little differently from what I thought they would so I'm not sure what is the best way to approach this right now  Sorry I'm stupid...

EDIT3: Okay so weird things would happen....

Let's assume that we put Laythe to a circular orbit around Kerbin that has let's say 2600km semi-major axis (that means that from surface to surface the distance is 200km).

http://wiki.kerbalspaceprogram.com/wiki/Sphere_of_influence

From that wiki page I got the equation that says that the radius of a body's SOI orbiting another body is R(SOI) = a*(mass(orbiting body) / mass(central body))^(2/5) where a is  semi-major axis.

So for our orbit Laythe's R(SOI) would be 2600km*(2.94/5.29)^(2/5) = 2056km.

So, Laythe is orbiting 2600km / 2 = 1300km from kerbin (measured from center to center) and it's SOI radius is 2056km. That means that if we launch our craft wen Laythe is above us we should already be in it's SOI and we would just "drop" directly to its surface since we are in Laythe's SOI Kerbin's gravity shouldn't affect us anymore

Now I don't know if the game models Kerbin's atmosphere if we are not in its SOI but it's not a problem. If the game doesn't model it we are just in freefall until we arrive at Laythe's SOI (so that would be 1300km - radius(kerbin) - radius(laythe) - atmospheric height(laythe) = 1300 - 600 - 500 - 50 = 150km of freefall). And if the game still models Kerbin's atmosphere that would just slow down our speed once we are in it but we would still "fall" to Laythe... And there shouldn't even be any SOI changes along the way and we never enter 2 atmospheres simultaneously so we shouldn't have these "pressure difference" problems either.  This way it would be possible to "travel" to Laythe without any engines at all  Only chutes and maybe some airbrakes needed...

Now I don't know if this would actually work in game since putting two planets so close to each other might break it badly  but that is how it should work if that wiki page for SOI gives me a correct equation... 

Edited December 26, 2016 by tseitsei89

[swjr-swis]

3 minutes ago, tseitsei89 said:

if we assume that laythe and kerbin are rigid bodies

Not sure why there is so much assuming going on in these threads.

Yes, both Kerbin and Laythe have oceans, and yes, Laythe more so than Kerbin appears to be almost entirely covered by water. But those oceans are what, 1.4km deep on Kerbin, on average less than 1km, and 2.7km deep on Laythe, average about 1.5km? In either case just a very thin layer of liquid around otherwise rocky bodies, considering that their density is 10-11x as high as the rockiest planet we know in the terrestial system. Even if their hyperdense cores are still molten (of which we have no evidence, as there is nothing indicating plate tectonics or volcanism on either planet), they would still act very rigidly.