[Tutorial] Interplanetary How-To Guide

[Kosmo-not]

by Kosmo-not

Be sure to visit the Interactive illustrated interplanetary guide and calculator for KSP created by olex. It is a wonderful piece of work that does everything you see here and displays it in a visual format.

So, you want to get to another planet. It's the same as going from Mun to Minmus. However, we're dealing with vast distances and higher velocities. It will take more precision to get there. This guide addresses getting from the orbit of one planet to the intercept of another planet using a Hohmann transfer.

Assumptions:

• Planets are in circular orbits and not inclined.
• The parking orbit of the spaceship is circular and not inclined.

Section 1: Planetary Phase Angle

It doesn't do much good to your delta-v budget if you launch at the wrong time. In fact, it could be disastrous, meaning you might not have any chance at returning home. To know the right time to launch the mission, you have to calculate a phase angle the two planets should have to each other (the angle from one planet to another with the sun at the vertex).

The process of calculating this phase angle is quite simple. First, we need to determine how much time it will take to transfer from one plane's orbit around the sun to the other planet's orbit.

Remember: the radii used are of the planet's orbits around the sun and the gravitational parameter used is the sun's.

Next, we need to determine how far the other will travel (in degrees) during the time the spacecraft is in transit. We calculate the angular velocity (°/s) and multiply it by the transit time:

SQRT(μ/r₂)*t_H/r₂*180/pi

Since the spacecraft travels through 180°, we can easily get the phase angle between planets at the start of the transfer:

Phase Angle = 180°- SQRT(μ/r₂)*t_H/r₂*180/pi

For the purposes of this guide, positive values indicate the target planet starts out in front. Negative values mean the target planet starts behind.

Section 2: Velocity

To get to the other planet, you need to know what velocity you need to achieve from the planet you're currently orbiting around. This requires two steps: 1) Determine the velocity difference between the velocity needed to get to the other planet's orbit and the velocity of the current planet, and 2) The velocity needed at your current orbit to achieve the needed velocity once out of the sphere of influence.

First, we calculate the change in velocity needed for the Hohmann transfer:

We will need to be going that much faster than our planet of origin at the start of the Hohmann transfer. The value just calculated is the velocity we need to be at just prior to exiting the planet's SOI.

Using conservation of specific orbital energy, we can calculate the velocity needed at our parking orbit to exit the SOI at the correct velocity (we'll refer to this as our ejection velocity):

v₁ = SQRT((r₁*(r₂*v₂²-2*μ)+2*r₂*μ)/(r₁*r₂))

where:

r₁ = parking orbit radius

r₂ = SOI radius

v₁ = ejection velocity

v₂ = SOI exit velocity (absolute value)

µ = gravitational parameter of origin planet

Section 3: Transfer Burn Point

Exiting the sphere of influence heading in the wrong direction would screw up everything we've worked through in the last two sections. It would not only increase the delta-v needed for a transfer, but also change the transfer time. You'll either have to spend even more delta-v to salvage your situation, or suffer embarrassment as you miss the target planet. Knowing when in your parking orbit to perform your ejection burn is critical for interplanetary travel.

A lot of people will think "that's easy, just do the burn at midnight/noon." That is wrong. Your trajectory will be curved by the planet and can be off by around 30° from your intended direction of travel.

I'm going to let you loose on these equations.

r = parking orbit radius

v = ejection velocity

μ = gravitational parameter of origin planet

(have this value in degrees, not radians)

Ejection Angle = 180° - θ

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 (planet prograde is the desired direction of travel in this case):

Practice Problems:

Kerbin orbital radius: 13.5Gm (or 13,500,000 km)

μ _Kerbin: 3530.461 km3/s2

μ _Sun: 1.167922e9 km3/s2

Kerbin SOI radius: 82,000 km

A spaceship needs to get from a 700km parking orbit (100km altitude) around Kerbin to a planet that is orbiting at 3x Kerbin's orbit.

Answers:

t_H = 1.2897e7 seconds

Planetary Phase Angle = 82.0°

Hohmann Δv₁ = 2.0904 km/s

Ejection Velocity = 3.7909 km/s

Ejection Angle = 122.7°

A spaceship needs to get from a 700km parking orbit around Kerbin to a planet that is orbiting at 0.7x Kerbin's orbit.

Answers:

t_H = 3.5733e6 seconds

Planetary Phase Angle = -60.9°

Hohmann Δv₁ = -0.8605 km/s

Ejection Velocity = 3.2774 km/s

Ejection Angle = 152.3°

Edited August 26, 2016 by Kosmo-not
Fixing of characters which were translated to gibberish by forum updates.

[bsalis]

I see what you did there. You solved the problem using maths!

Awesome work. I don't understand the details of the math but it all makes sense me. I might create a spreadsheet and plug those formulas into it.

[maltesh]

A potential simplification; Since both departure planet and target planet are orbiting the same body, you can use Kepler's third law to find the ratio of the transfer time to the period of the destination planet without calculating the periods explicitly, or using the gravitational parameter in that particular step.

[Kosmo-not]

A potential simplification; Since both departure planet and target planet are orbiting the same body, you can use Kepler's third law to find the ratio of the transfer time to the period of the destination planet without calculating the periods explicitly, or using the gravitational parameter in that particular step.

Yeah, that's what you get when you combine the two equations. That's what I did for my rendezvous work.

[AncientAstronaut]

Kosmo-not, someone here mentioned they wanted to make a spreadsheet. You made one, right?

You should post it.

[Kosmo-not]

Kosmo-not, someone here mentioned they wanted to make a spreadsheet. You made one, right?

You should post it.

I would have to tidy up the spreadsheet before releasing it. There's plenty of time to do so and add features before 0.17 comes out.

[bsalis]

I posted a speadsheet attachment with the calcs in the following post...

http://kerbalspaceprogram.com/forum/showthread.php/15796-A-Guide-to-Basic-Kerbal-Rocket-Design-Through-Rocket-Science?p=231289&viewfull=1#post231289

[Olsson]

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?

Edited August 9, 2012 by Olsson

[Sbowyer28]

Math is too hard, Especially if your 14 and dont know much, Ill find my own method if I have too.

[simplemunrockets]

Yeah, most likely I'll just burn into a transfer orbit, set MechJeb to "Warp until SOI Switch", and go have lunch.

[Cepheus]

Interesting. I'd like to try this out later. Would you mind specifying what the grav. parameter is? I know it's the gravational constant times mass, but I don't know what the mass of the sun is (or whether the value on the wiki is even correct).

[AncientAstronaut]

Interesting. I'd like to try this out later. Would you mind specifying what the grav. parameter is? I know it's the gravational constant times mass, but I don't know what the mass of the sun is (or whether the value on the wiki is even correct).

The Gravitational Parameter figures on the KSP wiki are right. Just use those.

[Cykyrios]

Very interesting and well-written guide!

Incidentally, I was practicing interplanetary mission a few hours ago, but hadn't seen your guide. I didn't bother with deltaV though, and only went through Hohmann transfer time and phase angle to get back to Kerbin from a higher orbit.

Section 3 is actually what I was missing when researching the subject, so I'll be sure to study that in more detail.

[hunter558]

you could just escape kerbin orbit and then push out your kerbol orbit like you do to get to the mun except with another planet. Its not efficient but it works and requires little precision, just some patience in having to warp at 100,000 until you get within the influence of the planet. The problem is returning of course although i except space stations to make this a much simpler(though still extremely difficult) process.

[silent_prtoagonist]

Lol, I was just about to work this out myself, then you beat me to it, Kosmo-not. I'm going to have to give this a try...

Math is too hard, Especially if your 14 and dont know much, Ill find my own method if I have too.

Being 14 doesn't have to stop you. I know these formulae look horrible, but they're really not that complicated. You don't even need to do any algebra to use them, just plug in numbers in place of the variables, and work out the answers step-by-step with a calculator. And trust me, the feeling of accomplishment from getting somewhere, knowing that you crunched the numbers yourself, rather than letting mechjeb or some other program do it for you, is well worth the effort; you should give it a try

[duckunlimited2]

you could just escape kerbin orbit and then push out your kerbol orbit like you do to get to the mun except with another planet. Its not efficient but it works and requires little precision, just some patience in having to warp at 100,000 until you get within the influence of the planet. The problem is returning of course although i except space stations to make this a much simpler(though still extremely difficult) process.

Hunter its not all that easy. with the vast distances that exist outside kerbin's sphere of influence, you would actually find it extremely difficult to get back to kerbin without any sort of precision. You see, Kerbin's sphere of influence is actually extremely tiny when compared to these vast distances, which makes it extremely easy to miss. It feels like your trying to hit a target the size of a pinhead when you actually try. Trust me, I've gotten to a kerbol orbit around 7-8 billion in altitude and returned back to kerbin.

[maltesh]

you could just escape kerbin orbit and then push out your kerbol orbit like you do to get to the mun except with another planet. Its not efficient but it works and requires little precision, just some patience in having to warp at 100,000 until you get within the influence of the planet. The problem is returning of course although i except space stations to make this a much simpler(though still extremely difficult) process.

Most players do aim a launch window when heading for the Mun or Minmus, using the Munrise/Minmusrise burn method.

The reason why looking for launch windows is so important is because the "launch at any old time, push my apoapsis out to the planet's distance, circularize there and wait to catch up" method can easily take hours at 100,000x for planets as close as 20 million km from Kerbol, because you're attempting to catch up to an object dozens of millions of kilometers ahead at a relative velocity of maybe 20 meters/second.

And then once you get there, you still have to find the planetary SOI.

At the very least, eyeballing the proper position for the launch window determined by the equations will put you a heck of a lot closer to your eventual target.

[silent_prtoagonist]

Just gave parts 1 and 2 a try, and they work like a charm. I took a ship out to a Mars-analogue circular orbit (i.e. 20e+6 km or so) and then calculated a phase angle of -68 deg for a return to Kerbin. Even eyeballing the phase angle, the Kerbin intercept popped up at periapsis just as it was passing Kerbin's orbit, as expected. The calculated dV was approximately correct too. After 7 years of Orbiter and 1 of KSP, 0.17 has finally convinced me to start learning to do this by the maths instead of relying on IMFD/Transx/MechJeb

I think my next goal is going to be a solar-orbit rendezvous with a ship marked in Mars-analogue orbit, so that I can give part 3 a try.

[SunJumper]

I plan on describing how this can be done a simpler way...

[Endeavour]

So that spreadsheet Bsalis posted works like a charm for the delta-V, but I can't figure out the interplanetary stuff. I tried using it to figure things out for a Mun-to-Minmus mission, but I couldn't get it. Does it take more than switching out all the numbers?

[2008dragon]

Thanks for the guide, but could someone answer some questions for me?

What do you use all of this info for? I got kind of confused lol...

Would it be like this?:

A spaceship needs to get from Kerbin to a planet that is orbiting at 3x Kerbin’s orbit.

Answers:

tH = 1.2897e7 seconds------------Time it takes ship to get to planet, used to find phase angle

Planetary Phase Angle = 82.0°-----Angle between planet-sun-planet when you do the injection burn

Hohmann ÃŽâ€v1 = 2.0904 km/s------Required ÃŽâ€v needed in addition to "host" planets ÃŽâ€v (I don't know what to call it)

Ejection Velocity = 3.7909 km/s---Speed at end of injection burn

Ejection Angle = 122.7°-----------Angle between ship-planet-sun

That is my understanding of it... If anything is horribly off could someone please clarify for me?

Once I understand what the math means I can figure out how to do it

[Kosmo-not]

I plan on describing how this can be done a simpler way...

Are you talking about doing it in a simpler way, or describing it in a simpler way?

[Kosmo-not]

Thanks for the guide, but could someone answer some questions for me?

What do you use all of this info for? I got kind of confused lol...

Would it be like this?:

A spaceship needs to get from Kerbin to a planet that is orbiting at 3x Kerbin’s orbit.

Answers:

tH = 1.2897e7 seconds------------Time it takes ship to get to planet, used to find phase angle

Planetary Phase Angle = 82.0°-----Angle between planet-sun-planet when you do the injection burn

Hohmann ÃŽâ€v1 = 2.0904 km/s------Required ÃŽâ€v needed in addition to "host" planets ÃŽâ€v (I don't know what to call it)

Ejection Velocity = 3.7909 km/s---Speed at end of injection burn

Ejection Angle = 122.7°-----------Angle between ship-planet-sun

That is my understanding of it... If anything is horribly off could someone please clarify for me?

Once I understand what the math means I can figure out how to do it

The ejection angle is from hyperbolic trajectory direction to the ejection point with the planet at the vertex.

Speed at end of ejection burn will be a little lower than that value, since you can't change velocity instantly and will gain altitude during the burn.

Edited August 10, 2012 by Kosmo-not

[2008dragon]

Ok thanks, I guess the rest is close to correct?

Anyway thanks for the guide(s) and help!

[bsalis]

So that spreadsheet Bsalis posted works like a charm for the delta-V, but I can't figure out the interplanetary stuff. I tried using it to figure things out for a Mun-to-Minmus mission, but I couldn't get it. Does it take more than switching out all the numbers?

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.