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[Tutorial] Interplanetary How-To Guide


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The spreadsheet should be checked by someone other than me. However, I did correctly reproduce both examples that Kosmo-not has done. So it should be fine, unless there is something fundamentally different with a Mun-Minmus transfer.

Some things to be mindful of...

* Make sure you change the parent grav param to Kerbin.

* Make sure your using the correct units. I think everything you enter is in Km, Km/s and km3/s2.

* Note that parking orbit radius is from the center. So a 100Km high (by altitude) Kerbin orbit has a radius of 600 + 100 = 700Km.

The only thing different from a transfer between Mun and Minmus is that it uses an elliptical trajectory for exiting Mun's SOI. Other than that, it's the same.

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This is what I get... it looks right, but need to try it out.


Origin
Name Mun
Parent Grav Param 3531
Radii (km) 12000
Gravity Param 65.136
SOI Radius (km) 2430
Parking Radius (km) 220

Target
Name Minmus
Parent Grav Param 3531
Radii (km) 47000

Solution
Phase Angle 90.493 degrees
Hohmann dV 142.245 m/s
Ejection V 747.509 m/s
Ejection Angle 155.402 degrees

EDIT:

I tried this out. Seems that 747.509 Km/s is too fast. About 740 Km/s is more what it is. I think it's because the burn is not instant. So there still some guesswork. Unless you take it to the next level and do the math to factor in the ship mass, impulse, thrust in order to do a timed full thrust burn instead of hitting a target end velocity.

Edited by bsalis
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Hey Kosmo-not, I just made a .pdf out of your guide, and rewrote the equations in a more graphical way, to make it easier to read. Do you want me to post it/PM it to you so you can attach it to your first post?

Go ahead and post it.

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So, basically, these are all highly complex methods of making burns to get from one planet to another. A simpler method, though it requires two launches, involves getting one spacecraft at the target altitude, at an elliptical orbit with one apsis at the desired altitude, and the other apsis at the height you launched from, and write down the time difference between apses. Then comes the calculation.

(2piXr)^2/(T^2)=GM

Substituting the formula of the length of an arc, we get:

(θXpiXr)^2/32400T^2=GM

Now, let's imagine that the time required is around 3,058,000 seconds, and you're attempting to return from Eve (if its at 7000000km). Plugging the necessary values into the equation gets an angle of 442.4 degrees. No, there's no error, this just means that Kerbin will make at least one revolution before you reach it. The lead angle would be 82.4 degrees.

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I notice that the dV is negative when you are transferring to a lower orbit. Does this mean that you are thrusting in the opposite direction of Kerbins travel? Also, with the examples you gave at the end, what do we assume is the parking orbit for each problem?

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Is there a way to accurately measure your current angle in KSP so you know when EXACTLY to start your ejection burn or do you have to estimate that from the map view?

If you have mechjeb installed you can use it for all sorts of measurements like this

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I'm sitting with a protractor and presses that to the screen to measure the angles, must look really wierd...

But nice guide but I'll think I'll end up trying to figure out those formulas by myself, more fun that way :P

But some clarification on some of the parameters would help the uninformed a bit, like te formulas for calculating the sphere of influence etc.

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I notice that the dV is negative when you are transferring to a lower orbit. Does this mean that you are thrusting in the opposite direction of Kerbins travel? Also, with the examples you gave at the end, what do we assume is the parking orbit for each problem?

Correct. As you go from a high orbit to a lower one, you have to slow down to lower your Periapsis, and thus burn retrograde.

I'm sitting with a protractor and presses that to the screen to measure the angles, must look really wierd...

Haha, I did that yesterday when trying to get back to Kerbin from a 20,000,000 km orbit, I had to wait for a 76.4° angle...

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I'm sitting with a protractor and presses that to the screen to measure the angles, must look really wierd...

As for now, that's probably the best way to do it. But since these angles are such important parameters for precise and fuel-efficient transfer burns I'm really surprised that KSP doesn't give you this imformation directly. I also have not found any mod or plugin that shows you you're current angle.

Mechjeb does give you a LOT of information, but as far as I know it doesn't include infos on angles.

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What is radius one and two, are they simply my orbit and the target orbits radius (for example, 150km orbit 75km radius)? "tH = 1.2897e7 seconds" "Planetary Phase Angle = 82.0°" "Hohmann ÃŽâ€v1 = 2.0904 km/s" what does any of this data mean?

"This is the angle from your travel direction as your get farther from the planet to your ejection burn point. Here is a picture to illustrate (for the case of a positive Hohmann delta-v):"

Which data is my ejection burn point? The Planetary Phase Angle? If it's 82 degrees where is that burn point in my circular orbit?

What do I use with the hohmann transfer v1 data? I only need to know the ejection velocity if I want to intercept the Mun or Murs for example don't I?

What am I supposed to do with the tH data, are the seconds relevant to something or did I only need to know if in order to figure out the phase angle?

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Isn't 14 the prime time in life to learn math? This math can't be far from what you do in school at that age (I know I did at 15). It looks scary, but it is just fractions, squareroots and some trigonometry (I started learning about the latter around 15).

Math is awesome!

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This is what I get... it looks right, but need to try it out.


Origin
Name Mun
Parent Grav Param 3531
Radii (km) 12000
Gravity Param 65.136
SOI Radius (km) 2430
Parking Radius (km) 220

Target
Name Minmus
Parent Grav Param 3531
Radii (km) 47000

Solution
Phase Angle 90.493 degrees
Hohmann dV 142.245 m/s
Ejection V 747.509 m/s
Ejection Angle 155.402 degrees

EDIT:

I tried this out. Seems that 747.509 Km/s is too fast. About 740 Km/s is more what it is. I think it's because the burn is not instant. So there still some guesswork. Unless you take it to the next level and do the math to factor in the ship mass, impulse, thrust in order to do a timed full thrust burn instead of hitting a target end velocity.

I have the numbers in exactly like that. I still get a #NUM! error for the ejection angle. I never use excel, so I have no idea what that means.

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I still get a #NUM! error for the ejection angle. I never use excel, so I have no idea what that means.

I changed the ACOS to COS for the Ejection Angle since the value going into it was >1. No idea if that is correct or not. As I said before, someone else should confirm the numbers.

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I have the numbers in exactly like that. I still get a #NUM! error for the ejection angle. I never use excel, so I have no idea what that means.

The ejection trajectory for going to minmus from the mun is elliptical and not hyperbolic. I might look into solving for that. But for interplanetary travel, the ejection trajectory will be hyperbolic.

In other news, the guide has been updated to include the missing parking orbit radii and Kerbin's SOI radius for the practice problems.

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I changed the ACOS to COS for the Ejection Angle since the value going into it was >1. No idea if that is correct or not. As I said before, someone else should confirm the numbers.

As Kosmo-Not implies, but I thought someone should explicitly state, you got really lucky here, and hit a mathematical coincidence.

You can't generally substitute cos(x) for cos-1(x). They're inverse functions of one another, and it's analagous to deciding to take the square root of a number instead of squaring it. For certain values of x, you'll get close enough to the right answer, but for most values of x, the answer you'll get will be very, very wrong.

Edited by maltesh
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As Kosmo-Not implies, but I thought someone should explicitly state, you got really lucky here, and hit a mathematical coincidence.

I was channeling Jebediah :cool:

Though it would be nice to know if my implementation for hyperbolic transfer is correct.

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I don't understand what I'm doing wrong. I'm trying to calculate tH first, but every time I put the numbers in, I don't get the same numbers that you do! I thought it was tH = 3.14 (sqrt(13500000+40500000)^3/8(1.167922e9)) but I keep getting the wrong answer. Then I put it into a calculator proper and I get an entirely different answer, which is also wrong! It's not jsut that either, I keep getting wrong answers for all of them! Help!!! If I can't figure this out, I'm going to have to rely on MechJeb to do my transfers. This is impossible for me.

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