Request: Laythe's Roche limit around Kerbin

[Raptor22]

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?

[Rocket In My Pocket]

Afaik Roche limits are not modeled in KSP.

All the planets are "on rails" pretty much, actual n body physics and gravitational pull is not calculated.

That said, not really sure what the closest distance you could place it would be without the game freaking out. I'd imagine 70km up so it's outside the atmosphere. (If you are doing something for school and youre interested in fooling around with Roche limits and actual n body physics, try Universe Simulator 2.)

 

Edited December 23, 2016 by Rocket In My Pocket

[linuxgurugamer]

I've accidentally hyperedit edited the mun to an orbit 70km high.  Game was fine, it looked rather funny.

[MinimalMinmus]

Then again, keep this in mind: Kerbin and Laythe are approximately as massive, so if Laythe is within Kerbin's RL, then Kerbin is probably in Laythe's RL. So, the two bodies would probably be somewhat both torn open before fusing, cracking tectonic plates and causing mayhem on both bodies. Ouch.

[JadeOfMaar]

Physics aside, I'm expecting the game to go nuts concerning SOI. Ships could end up in orbital hop-scotch around these practically mirror-mirror bodies.

Spoiler

Someone should actually do this and add a Sigma Binary node to Laythe. That'd be all kinds of sweet. Their barycenter would be right between them.

 

18 minutes ago, linuxgurugamer said:

I've accidentally hyperedit edited the mun to an orbit 70km high.  Game was fine, it looked rather funny.

A guru does not "accident" But I believe you.

[steuben]

Funny no. Sci-fi awesome, yes. The tricky part is finding the distance such that you can fly from one to the other with an atmospheric craft.

[linuxgurugamer]

53 minutes ago, steuben said:

Funny no. Sci-fi awesome, yes. The tricky part is finding the distance such that you can fly from one to the other with an atmospheric craft.

That would be interesting 

[GluttonyReaper]

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

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

[septemberWaves]

3 hours ago, steuben said:

Funny no. Sci-fi awesome, yes. The tricky part is finding the distance such that you can fly from one to the other with an atmospheric craft.

Kerbin has a radius of 600km and an atmosphere height of 70km. Laythe has a radius of 500km and an atmosphere height of 50km. To get their atmospheres to touch, Laythe would have to be in a 620km orbit of Kerbin. In order to actually fly from one to the other though, that would require probably about a 570km orbit of Kerbin, giving their atmospheres 50km of overlap at the closest point, and putting sea level on Laythe right at the top of Kerbin's atmosphere. I'd be interested to see somebody try to fly a plane between them in this configuration.

To clarify, I am going by orbital altitude rather than semi-major axis.

Edited December 23, 2016 by eloquentJane

[Raptor22]

I know that the roche limit isn't in the game, but I just want to make it realistic. But if I could fly from one to another, then that would be pretty awesome. Or perhaps I could make a plane using the ramjet engines that will allow me to jump out of the atmosphere of one planet and into the atmosphere of the other.

[TheEpicSquared]

2 hours ago, eloquentJane said:

Kerbin has a radius of 600km and an atmosphere height of 70km. Laythe has a radius of 500km and an atmosphere height of 50km. To get their atmospheres to touch, Laythe would have to be in a 620km orbit of Kerbin. In order to actually fly from one to the other though, that would require probably about a 570km orbit of Kerbin, giving their atmospheres 50km of overlap at the closest point, and putting sea level on Laythe right at the top of Kerbin's atmosphere. I'd be interested to see somebody try to fly a plane between them in this configuration.

To clarify, I am going by orbital altitude rather than semi-major axis.

I'm going to try that tomorrow. I wonder what'll happen  

[MDZhB]

2 hours ago, eloquentJane said:

Kerbin has a radius of 600km and an atmosphere height of 70km. Laythe has a radius of 500km and an atmosphere height of 50km. To get their atmospheres to touch, Laythe would have to be in a 620km orbit of Kerbin. In order to actually fly from one to the other though, that would require probably about a 570km orbit of Kerbin, giving their atmospheres 50km of overlap at the closest point, and putting sea level on Laythe right at the top of Kerbin's atmosphere. I'd be interested to see somebody try to fly a plane between them in this configuration.

To clarify, I am going by orbital altitude rather than semi-major axis.

6 hours ago, steuben said:

Funny no. Sci-fi awesome, yes. The tricky part is finding the distance such that you can fly from one to the other with an atmospheric craft.

Trying this right now. Building the plane, should work.

EDIT:

Apparently, KSP automagically determines you to be in Laythe's SOI, and doesn't even count the atmosphere of Kerbin.

Also, as for the Roche Limit for Laythe around Kerbin, it should be about 2 1/2 times the radius of Kerbin away, from center to center. From center to center, that translates to about 1500km distance. So, from surface to surface, it should be roughly at least 400km away.

Edited December 24, 2016 by MDZhB

[something]

As soon as you are closer to Laythe than you are to Kerbin, the SOI should change*. Do the atmospheres overlap at all? I'd say no because the game basically only pays regard to one celestial body per time meaning you'd insta-switch atmospheric pressure. Fascinating...

*i.e. their gravitational acceleration is bigger...

 

 

 

[pincushionman]

2 hours ago, MDZhB said:

…Apparently, KSP automagically determines you to be in Laythe's SOI, and doesn't even count the atmosphere of Kerbin.

What did you set Laythe's SOI to be? If you use Laythe's default SOI radius, it overlaps all of Kerbin, and the inner SOI takes precedence.

[DrunkenKerbalnaut]

For extra points, just dupe Kerbin into orbit of it's self. Like Evil Kerbin. With yellow Kerbals. 

[Raptor22]

...

I just want to know Laythe's Roche limit if put around Kerbin... I didn't ask for all of this atmosphere overlapping stuff.

[DrunkenKerbalnaut]

Just now, Raptor22 said:

...

I just want to know Laythe's Roche limit if put around Kerbin... I didn't ask for all of this atmosphere overlapping stuff.

That has been answered. Not modeled in game. 

[Raptor22]

I know that it's not modeled. I just want to know so that I can make it somewhat realistic! If someone can give me the information, I'll just figure out the equations myself!

[brdavis]

It's not even remotely possibly realistic… so asking for "the right value" doesn't make sense. It's like asking "what color is middle C?"

Generally, the Roche limit is about 2.5 times the radius of the primary body… if you want to be more precise, there's a factor of ratio of the densities of the two objects in there as well. And then there's the deformation into a triable ellipsoid that both Laythe and Kerbin would suffer given their rotation rates, not to mention the tidal distortion as you approach the Roche limit. And you could use the classical "touching spheres" limit or the "homogeneous fluid body" approximation… which do you prefer? And all of this assumes one object is much much smaller than the other… which isn't the case here.

If you want wild fun Roche limit problems… grab a copy of Forward's "Rocheworld", and read up (and yes, it includes trying to take an airplane of sorts on a trip between two worlds that just about share their Roche lobe… and the plane has to start as a raft falling down a waterfall between the worlds, before gaining enough speed to have enough lift to fly). But here… there's no realism to be had at that level.

A lot of fun "wow I wonder what happens to a model when I break nearly all the assumptions it's built on" sort of questions… but realism, here, isn't any of them.

[steuben]

16 hours ago, brdavis said:

 It's like asking what color is middle c?"  

green.

16 hours ago, Raptor22 said:

I just want to know Laythe's Roche limit if put around Kerbin... I didn't ask for all of this atmosphere overlapping stuff.

Welcome to science and KSP. If anytime you ask a question and don't get at least a couple more questions and a few related but unasked answers, you're asking the wrong question.

Edited December 24, 2016 by steuben

[Kerbal Fried Chicken]

that KSP movie person...   Nassault?   needs to use this to make the KSP version of the movie Upside Down.

[steuben]

Laythe in orbit as viewed from the KSC. Looks like the mun is there just to the right.

Edited December 24, 2016 by steuben

[tseitsei89]

On 23.12.2016 at 6:08 PM, 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?

There are equations directly in the Roche limit wikipedia article.... Just throw the numbers in there and you'll get the answer very easily.

No need to understand where those equations come from. Although I found it quite interesting to read and actually see how you get those equations 

Physics and maths student from Finland here

[Mastikator]

Kerbin: 600km radius, 5.3x10^22 kg mass

Laythe: 500km radius, 2.9x10^22 kg mass

roche limit: d = 1.26 x 500km x ((5.3x10^22)/(2.9x10^22))^(1/3) = 770 km

[MDZhB]

Ayay, just answer the question guys:

For the Roche Limit for Laythe around Kerbin, it should be about 1500km distance from center to center. So, from surface to surface, its roughly at least 400km away. The 2 1/2 trick goes for any two bodies with the same density: R = 2.5 times the radius of the main body. Kerbin's radius is 600km, 600*2.5=1500. Of course, this changes with bodies with different densities; higher satellite density means it can get closer, and lower means it has to be further.