Kerbin Semi-Synchronous Orbit altitude?

[the_pazter]

^^^^^^^^^^^^^^^

[GoSlash27]

the_pazter,

Kerbin's sidereal period is 21,549.4 seconds.

The period of a semi- synchronous orbit is 10,774.7 seconds.

The formula for radius (or SMA) based on period is

r= cuberoot(up²/4π²)

r= 2,181,745 m

This is radius from Kerbin's center, so altitude would be 1,581,745 m

Best,
-Slashy

 

[Sippitous]

I can't argue with correct math. I love it, I respect it, but maybe I am missing something.

When you are setting up a synchronous or a semi-synchronous orbit, isn't the intent to have the satellite or whatever your using, pass by the same point every orbit or 2 orbits respectively?

When I put a satellite into a circular orbit with an altitude 2,181,745 m., the satellite will slowly fall out of alignment.

Is this the difference between sidereal orbital period and a solar day?

I think I got myself confused talking about this, but I made a video showing the results of a circular orbit with an altitude of 1,581,516 m. It shows that after 10 years of time warping, the satellite remains very very very nearly in the same spot above the KSC as when it first started. Isn't this what a we want satellites to do? Isn't this what the semi-synchronous orbit altitude should be? Like I said before; I might be missing something. I would love to hear some thoughts.

Here is a link to the video:

https://www.youtube.com/watch?v=SYkJZfTGyec

 

 

[DrLicor]

@Sippitous, the heights and times you want to have your sat to orbit have to be very, very ,very precise. If your orbital time is 1sec ahead a day, it will result in a slowly fall out of alignment. In real life sats have little rockets/rcs, not only to avoid objects, but also to keep them in the right spot. (since the sphere of influence doesn't stop on 140km). 

But back to the point: the stock system a day isn't really 6hours, a bit less, it's nearly impossible to keep a orbit so precise, that will last for 10years on the same spot. Even a few 100mtrs can destroy your plans, even a 0.1 sec.

Spoiler

http://wiki.kerbalspaceprogram.com/wiki/Time

If you want to make your own math, I recently posted a kind of calculator for orbit heights/times etc., it can be used to every body, even your moms  

 

[Sippitous]

First thing first. I need to state my point. 

I BELIEVE THAT THE ALTITUDE OF A CIRCULAR SEMI-SYNCHRONOUS ORBIT AROUND KERBIN SHOULD BE: 1,581,516 M

 

@DrLicor  I understand all that. The difficulty of perfect precision is what I was sort of demonstrating. If you use the facts and numbers that all of us have accepted as true (such as the mass of kerbin, gravity at kerbin,rotational periods, etc) then the math points to an altitude height of what @GoSlash27 was saying:  1,581,745 m.  But, I am saying it should be 1,581,516 m. Not because of any math, but because when I physically (digitally) put a satellite in a circular orbit at the altitude of 1,581,516 m, it produces a semi-synchronous orbit that only shifts out of alignment 4 meters over the course of 10 years. That's very accurate. To demonstrate this accuracy I am going to digress for a bit. Time for some math.

 

A satellite in orbit around Kerbin at an altitude of 1,581,516 m  (taking into account Kerbins 600,000 equatorial radius) travels 13,706,869.27857718 meters every rotation (C=2πr).

C=2πr      13,706,869.27857718 = 2π(1,581,516 + 600,000)

 

A semi-synchronous orbit is 2 orbits per sidereal day. 

2 * 13,706,869.27857718 = 27,416,738.55715437 meters every day

 

Kerbin orbits it's star every 426.08 days

27,416,738.55715437 * 426.08 = 11,680,445,724.43233 meters every year

 

For 10 years

11,680,445,724.43233 * 10 = 116,804,457,244.3233 meters every 10 years

 

That a lot of traveling. And to be off by only 4 meters over that much time and distance is wonderfully accurate. if I wanted to adjust my orbit so that it was 100% accurate I would have to reduce my velocity by .000074707015747 m/s, which isn't possible in this game. (also, that's assuming I was at exactly 1,581,516.000000000 meters which isn't possible to determine. ooooh. maybe it is. I can pull the orbital info from the data files):

VESSEL
        {
            pid = e5bb18b8375041ed97456799c720ded5
            name = Semi Sync
            type = Station
            sit = ORBITING
            landed = False
            landedAt = 
            splashed = False
            met = 15542565.594103955
            lct = 1266696.2960705161
            lastUT = 16809261.91017447
            root = 0
            lat = 5.042437216409775
            lon = 14.704801337842444
            alt = 1581515.6353108771
            hgt = -1
            nrm = -0.59995234,0.0479642227,0.798596621
            rot = -0.306740254,-0.287918717,-0.899826109,-0.115439601
            CoM = 0.00144628342,-0.0832113847,-0.00246789306
            stg = 1
            prst = False
            ref = 0
            ctrl = True
            cPch = -0.08799998
            cHdg = 3.43
            cMod = 0
            ORBIT
            {
                SMA = 2181515.978894108 <-----------------------------------------that's pretty close 2,181,516
                ECC = 1.6117364556775186E-07
                INC = 54.999569826795124
                LPE = 178.55552523516766
                LAN = 299.9999740444099
                MNA = -0.082294934085444207
                EPH = 16809261.890174471
                REF = 1
            }VESSEL
      

 

So, back to my point. If I understand things correctly, then the altitude at which to put an object around Kerbin with a circular semi-synchronous orbit is 1,581,516 m which will have a velocity of 1,272.1 m/s. 

 

Ideas?......Thoughts?.....Agreements?.....Disagreements?

~KSP for life!

 

[GoSlash27]

Sippitous,

 This is an interesting anomaly.

 How much error did you get with the calculated SMA? 

 I wonder what the cause of this is. Perhaps G in KSP is a little off? Maybe a result of rounding errors in warp?

Your result would require a G of 6.67172E-11. 

Best,
-Slashy

[Sippitous]

GoSlash27,

I figured it out. My experiment was done using pre-release version 1.2.0.1520. After running a similar experiment on an earlier version, that altitude was was off. I think Squad changed something somewhere.

 

Like I said above, an altitude of 1,518,516 has a velocity of 1,272.1 m/s, But in the current version (1.1.3.1289) that altitude shows a velocity of 1,272.3 m/s. So something is definitely different.

Edited September 22, 2016 by Sippitous

[Rodhern]

1 hour ago, GoSlash27 said:

 I wonder what the cause of this is. Perhaps G in KSP is a little off? Maybe a result of rounding errors in warp?

The Kerbal geeforce is updated annoyingly often (with respect to re-usability of formulas).

GoSlash27 uses 9.81 m/s². Sippitous uses 9.80665.

The formula I use to deduce this is: g = (2*pi/p)^2 * r^3/R^2, where g is the geeforce, p is the period in seconds, pi is 3.14..., R is 600E3 m, and r is the radius of the orbit in meters.

[LN400]

On 16.4.2016 at 5:49 PM, GoSlash27 said:

Kerbin's sidereal period is 21,549.4 seconds.

Doing the calculations, I get a slightly longer period. Not much, less than 0.02519s more rounded down to 25.25ms it gives me

21,549.425s.

Not much as I said but it does give a different altitude at about

1,581,763.73m.

The calulations (in case anyone wants to check)

P_year = 9,203,544.6s (per KSP Wiki)

P_solar = 21,600s (exact)

P_sidereal = P_solar* P_year/( P_solar+ P_year) = 21,549.42518... s rounded down to 21,549.425s

Punch that number in and I got 1,581,763.73m for 2 rounds per sidereal day.

Edited September 22, 2016 by LN400

[GoSlash27]

2 hours ago, Rodhern said:

 

GoSlash27 uses 9.81 m/s². Sippitous uses 9.80665.

 

Actually, that's incorrect. I use the same surface g as sippitous for precision calculations. We're referring to the universal gravitational constant "G", not surface gravity "g".

"Best,

-Slashy 

[Rodhern]

1 minute ago, GoSlash27 said:

Actually, that's incorrect. I use the same surface g as sippitous for precision calculations. We're referring to the universal gravitational constant "G", not surface gravity "g".

"Best,

-Slashy 

Given a fixed radius of Kerbin of 600 km, how do you propose that "G" and "g" is not really the same parameter, except for artistic license?

[icedown]

12 minutes ago, Rodhern said:

Given a fixed radius of Kerbin of 600 km, how do you propose that "G" and "g" is not really the same parameter, except for artistic license?

G is the standard abbreviation for Gravitational constant, it is what is used in calculations to figure out the gravitational force that is being applied to a body based on their mass and distance. g is the current force on the body proportional to gravity while at rest on the surface.

Edited September 22, 2016 by icedown
Clarify my definition before I get jumped

[Rodhern]

1 hour ago, icedown said:

G is the standard abbreviation for Gravitational constant, it is what is used in calculations to figure out the gravitational force that is being applied to a body based on their mass and distance [ed: bolded]. g is the current force on the body proportional to gravity while at rest on the surface.

Fair enough. Your "G" is a universal constant. It needs the mass of Kerbin to calculate gravity with respect to Kerbin. That is the key, the mass (and distance).

GoSlash27 seems to use a local "G", roughly equivalent of the in-game Kerbin "GM" parameter. Otherwise we end up either 1) with two parameters ("G" and "M") that (locally) do almost the same thing or 2) having to doubt the mass parameter of Kerbin or 3) with artistic license (KSP is a game so obviously we can invent any formula that we like - but then it may turn out dissimilar to classic real world models).

To make a long story short. The Kerbin surface geeforce (at sea level) is probably the gravitational acceleration experienced by a small object (much much less heavy than Kerbin) at a distance of 600 km from the center of Kerbin.

Edited September 22, 2016 by Rodhern
trying to make the statement more precise

[GoSlash27]

1 hour ago, Rodhern said:

Fair enough. Your "G" is a universal constant. It needs the mass of Kerbin to calculate gravity with respect to Kerbin. That is the key, the mass (and distance).

GoSlash27 seems to use a local "G", roughly equivalent of the in-game Kerbin "GM" parameter. Otherwise we end up either 1) with two parameters ("G" and "M") that (locally) do almost the same thing or 2) having to doubt the mass parameter of Kerbin or 3) with artistic license (KSP is a game so obviously we can invent any formula that we like - but then it may turn out dissimilar to classic real world models).

To make a long story short. The Kerbin surface geeforce (at sea level) is probably the gravitational acceleration experienced by a small object (much much less heavy than Kerbin) at a distance of 600 km from the center of Kerbin.

Rodhern,

 I often use the short-hand "9.81 m/sec²" when discussing processes or doing quick back of the envelope estimates, but I do not use that value for precision calculations. In fact, surface "g" is calculated from the body's mass M, the universal gravitational constant G, and the body's radius r. I'm using the same values that @Sippitous is using, which is why our math agrees.

 What is at issue is that something is slightly off in this latest build. They've either altered the value of G itself, Kerbin's mass, or radius. Could also be that time warping is introducing some rounding error.

 I'm curious to find out what's been changed.

Sippitous,

 Your SMA value and altitude figures agree that Kerbin's radius is still 600 km. That leaves a change in either Kerbin's mass or G. I propose checking Dunasynchronous orbit and seeing if it is similarly affected. If so, either G is altered or warping is handling it incorrectly.

Best,
-Slashy

 

[Rodhern]

42 minutes ago, GoSlash27 said:

They've either altered the value of G itself, Kerbin's mass, or radius.

Yes!

The values from KSP version 1.1.3 are:

• Kerbin GM = 3'531'600'000'000
• Kerbin M(ass) = 52'915'792'628'109'100'000'000 kg
• Kerbin R(adius) = 600'000 m

From those three you can get a classic Kerbin gravity acceleration at the radius distance to the center. It is exactly (GM/R^2 = ) 9.81000 m/s² in ver. 1.1.3. (not 9.80665).

That is why you are getting two different results.

Edited September 22, 2016 by Rodhern
9.80655 changed to 9.80665

[GoSlash27]

45 minutes ago, Rodhern said:

Yes!

The values from KSP version 1.1.3 are:

• Kerbin GM = 3'531'600'000'000
• Kerbin M(ass) = 52'915'792'628'109'100'000'000 kg
• Kerbin R(adius) = 600'000 m

From those three you can get a classic Kerbin gravity acceleration at the radius distance to the center. It is exactly (GM/R^2 = ) 9.81000 m/s² in ver. 1.1.3. (not 9.80655).

That is why you are getting two different results.

 

Ah! That would explain why the calculations are off; it appears they've altered Kerbin's mass slightly. Running with full allowable precision, I get a g0 of 9.810118 m/sec². I wonder why they changed it.

 Where did you get that value for Kerbin's mass?

Best,
-Slashy

 

Edited September 22, 2016 by GoSlash27

[GoSlash27]

Readjusting the values in my spreadsheet, something must still be off.

Using M=5.2915793E+12
         r=6E+5
        G=6.67408E-11

I get a predicted semisynchronous orbit at 1,581,772 meters, but in 1.2 prerelease it happens at 1,581,516.

I have to assume that either Kerbin's mass has changed or they've altered G.

haha "I have altered G. Pray that I do not alter it any further"...

Best,
-Slashy

[Rodhern]

20 minutes ago, GoSlash27 said:

Readjusting the values in my spreadsheet, something must still be off.

Using M=5.2915793E+12
         r=6E+5
        G=6.67408E-11

Best,

-Slashy

We have to be reasonably precise about the KSP version that we are referring to. I am referring to version 1.1.3. It uses the numbers I already quoted. In particular if you want to have your 'universal' G, you should take GM and divide by M. You get G = 6.674E-11 (not the 08-part). They say you do get the 08-part in version 1.2; but I don't play that version yet.

edit: If you are putting (small) things in orbit of Kerbin, the interesting parameter is 9.81 for version 1.1.3. And it will likely be 9.80665 for version 1.2.

Edited September 23, 2016 by Rodhern
added info

[GoSlash27]

19 minutes ago, Rodhern said:

We have to be reasonably precise about the KSP version that we are referring to. I am referring to version 1.1.3. It uses the numbers I already quoted. In particular if you want to have your 'universal' G, you should take GM and divide by M. You get G = 6.674E-11 (not the 08-part). They say you do get the 08-part in version 1.2; but I don't play that version yet.

edit: If you are putting (small) things in orbit of Kerbin, the interesting parameter is 9.81 for version 1.1.3. And it will likely be 9.80665 for version 1.2.

Rodhern,

 I use 6.67408 because that's the established universal G to the maximum precision it is known. It is assumed on my part that Squad uses this value in all versions to avoid small errors like this mucking up precision maneuvers... but I don't know that.

 I think we'll need to get a clarification from Squad about exactly what values they are using.

Best,
-Slashy

[Rodhern]

1 minute ago, GoSlash27 said:

Rodhern,

 I use 6.67408 because that's the established universal G to the maximum precision it is known. It is assumed on my part that Squad uses this value in all versions to avoid small errors like this mucking up precision maneuvers... but I don't know that.

 I think we'll need to get a clarification from Squad about exactly what values they are using.

Best,
-Slashy

Ok, you are of course welcome to use any value you see fit in your Kerbal universe. I (implicitly) use 6.674 in my version 1.1.3 games. Don't you think It is a bit cavalier to call the different parameter choices for errors; the orbital mechanics are equally consistent regardless of your choice (assuming we don't go several magnitudes overboard).

 Anyway, I think Squad is going to adjust the G 'constant' to 6.67408 in version 1.2; in that case we probably end up using the same parameters at some point.

[Rodhern]

13 hours ago, GoSlash27 said:

Where did you get that value for Kerbin's mass?

Hey @GoSlash27

Admit you were using 9.81, you just didn't know it at the time, and I will reveal my source.

Spoiler

I can get the mass of Kerbin from a running version 1.1.3 game by the (F#) command

let M = Planetarium.fetch.Home.Mass

(I compiled it to a plugin dll)

 

Btw. you are in luck, mad scientist Rodbob Kerman just finished his lecture on the universality of G in ver. 1.1.3.

And there is even a list with the mass for all the Kerbal Celestial bodies! Some people have all the luck, aeh?

Happy orbiting,

- Rodhern

[GoSlash27]

2 hours ago, Rodhern said:

Hey @GoSlash27

Admit you were using 9.81, you just didn't know it at the time, and I will reveal my source.

  Reveal hidden contents

I can get the mass of Kerbin from a running version 1.1.3 game by the (F#) command

let M = Planetarium.fetch.Home.Mass

(I compiled it to a plugin dll)

 

Btw. you are in luck, mad scientist Rodbob Kerman just finished his lecture on the universality of G in ver. 1.1.3.

And there is even a list with the mass for all the Kerbal Celestial bodies! Some people have all the luck, aeh?

Happy orbiting,

- Rodhern

Rodhern,

 It seems to me that you are dabbling in circular logic.

 How do you *know* that the programmers used precisely 9.81 m/sec²? Why not 9.810017, or 9.806, or some other value? You have assumed values for g0 and G, and attempted to use them to prove each other.

 We need to know precisely what values they are using, and what has changed between 1.1.3 and 1.2 (beta), not an arrogant and logically fallacious "lesson" in kinematics 101 from a guy who didn't even know what the universal gravitational constant *was* yesterday.

 If you have a way of looking into the code for the values like you do for the mass, *that* would be helpful.

 Thanks,
-Slashy

 

Edited September 23, 2016 by GoSlash27

[Rodhern]

7 minutes ago, GoSlash27 said:

 We need to know precisely what values they are using, and what has changed between 1.1.3 and 1.2 (beta), not an arrogant and logically fallacious "lesson" in kinematics 101 from a guy who didn't even know what the universal gravitational constant *was* yesterday.

I see you didn't find it quite as entertaining as it was meant. Sorry about that; it was meant to be just fun. Btw. I still don't subscribe to a universal gravitational constant for my KSP universe. But I don't object to you doing it for yours. And the intial g₀ explanation was actually meant as being helpful too.

[Rodhern]

25 minutes ago, GoSlash27 said:

Rodhern,

 It seems to me that you are dabbling in circular logic.

How do you *know* that the programmers used precisely 9.81 m/sec²? Why not 9.810017, or 9.806, or some other value? You have assumed values for g0 and G, and attempted to use them to prove each other.

That part, believe or not, was intended as helpful as well. [Obviously failed, but still]. The idea is that it seemed to me that you and @Sippitous were making some good experiments in the two relevant version of KSP (ver 1.1.3 and prerelase 1.2) to check gravitaional parameters at Kerbin. If I could give a guess for each of the version (in this case in the form of g₀), you would be able to dispel or confirm that as a good guess. Can that be done? Or, is it maybe simply not worth the effort?

[GoSlash27]

1 hour ago, Rodhern said:

I see you didn't find it quite as entertaining as it was meant. Sorry about that; it was meant to be just fun. Btw. I still don't subscribe to a universal gravitational constant for my KSP universe. But I don't object to you doing it for yours. And the intial g₀ explanation was actually meant as being helpful too.

 Rodbern,

 My humblest apologies. I totally misinterpreteed what you were trying to do!

Sorry,

-Slashy