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# How do you calculate the time needed to reach a celestial body?

## Question

I am trying to do a mission to a planet with life support (USI), and I would love to know how to find the time it would take to reach that planet so I could balance my habitation and resources accordingly.

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Well, the easy way is to take a craft in LKO, and plonk down a maneuver node. Pull on the handles and adjust the position of the node until your resulting Ap just touches the orbit of your destination planet, with a perfect transfer. You don't need to get an actual intercept -- just get the Ap to the right altitude.

Then check the date on the Ap.

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Posted (edited)

The harder way is to realize you're going to be traveling on an ellipse from the lower planet to the upper one. Let's say Kerbin to Duna. Kerbin is 1 KU (Kerbonomical Units, a term and measure I just made up) and Duna is 1.52 KU. Note you could use kilometers or any other accurate number but all that really matters here is the ratio so may as well use small numbers and set one of them to 1. So our ship's orbit will have a semimajor axis in the middle of those, or 1.26 KU. Also note that Duna's rather eccentric so the numbers vary a little, but that's a ballpark.

Kerbin orbits in 1 (Kerbin) year (by default). Duna orbits in 1.88 years (I got the days from the Wiki and converted, again because small numbers mean easy math) but that number isn't really necessary right now.

If you know your Kepler, in particular the square cube law, you know that the square of the orbit's period equals the cube of the orbit's semimajor axis. So 1 KU = 1 year, 1.52 KU = 1.87 years (hey rounding whatever) and your 1.26 KU orbit will take 1.41 years or 601 days. You're only going half of that to get to Duna (the other half will get you back to Kerbin so you need bare minimum 300ish days of food.

I'd pack 400 to be sure but that's me

Edited by 5thHorseman

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4 hours ago, 5thHorseman said:

If you know your Kepler, in particular the square cube law, you know that the square of the orbit's period equals the cube of the orbit's semimajor axis. So 1 KU = 1 year, 1.52 KU = 1.87 years (hey rounding whatever) and your 1.26 KU orbit will take 1.41 years or 601 days. You're only going half of that to get to Duna (the other half will get you back to Kerbin so you need bare minimum 300ish days of food.

I'd pack 400 to be sure but that's me

Of course, you CAN get to a destination faster than a Hohmann transfer, at the cost of higher delta-v, consumption, by doing a bigger injection burn, and then a bigger braking/insertion burn at the end.  I vaguely remember seeing a video from someone (maybe Scott Manley) who got to the Mun in a few minutes of in-game time by turning on infinite fuel, burning prograde halfway there, and burning retrograde for the second half to slow down.

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You will probably want food for the way back too. So you should pack 601 foods for the journey. You also need food for the dwell time at Duna. You can over-estimate and use the synodic period 1/(1/(Kerbin Year) -1/(Duna Year)) which gives 2.15 years (916 days). This is the time between transfer windows.  So you should pack about 1500 days of food. You could improve that guess by looking at when the next duna-kerbin departure window is after each kerbin-duna arrival window. I did that a while back and found that they are separated by 529 days. So you really only need 1129 days of food.

Here is the link where I work this out:

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16 hours ago, 5thHorseman said:

The harder way is to realize you're going to be traveling on an ellipse from the lower planet to the upper one. Let's say Kerbin to Duna. Kerbin is 1 KU (Kerbonomical Units, a term and measure I just made up) and Duna is 1.52 KU. Note you could use kilometers or any other accurate number but all that really matters here is the ratio so may as well use small numbers and set one of them to 1. So our ship's orbit will have a semimajor axis in the middle of those, or 1.26 KU. Also note that Duna's rather eccentric so the numbers vary a little, but that's a ballpark.

Kerbin orbits in 1 (Kerbin) year (by default). Duna orbits in 1.88 years (I got the days from the Wiki and converted, again because small numbers mean easy math) but that number isn't really necessary right now.

If you know your Kepler, in particular the square cube law, you know that the square of the orbit's period equals the cube of the orbit's semimajor axis. So 1 KU = 1 year, 1.52 KU = 1.87 years (hey rounding whatever) and your 1.26 KU orbit will take 1.41 years or 601 days. You're only going half of that to get to Duna (the other half will get you back to Kerbin so you need bare minimum 300ish days of food.

I'd pack 400 to be sure but that's me

This is highly complicated and unnecessary... I LOVE IT!!!

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On 4/13/2019 at 6:17 PM, Aegolius13 said:

Of course, you CAN get to a destination faster than a Hohmann transfer, at the cost of higher delta-v, consumption, by doing a bigger injection burn, and then a bigger braking/insertion burn at the end.

Fond memories of the time that I sent a ship from Kerbin to Eve in eight days.  (That's eight Kerbin days, i.e. 48 hours).

Of course, that was before KSP 1.0 so reentry heating wasn't a thing, thus saving a whole bunch of dV by aerobraking.  Slamming into Eve's atmosphere at over 25 km/s was... dramatic.

A bit more practically:  If you're sending a mission somewhere, and you'd like to reduce the crew time (e.g. for life support purposes or whatever) in transit, another option is to send the big / bulky / massive stuff out first, uncrewed, on a slow Hohmann transfer.  Then, later on, send your crewed transfer ship, which is stripped down to be lightweight and high-dV, so that it can make the transit in much less than Hohmann time.

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Posted (edited)
On 4/16/2019 at 1:53 AM, Nicias said:

You will probably want food for the way back too. So you should pack 601 foods for the journey. You also need food for the dwell time at Duna. You can over-estimate and use the synodic period 1/(1/(Kerbin Year) -1/(Duna Year)) which gives 2.15 years (916 days). This is the time between transfer windows.  So you should pack about 1500 days of food. You could improve that guess by looking at when the next duna-kerbin departure window is after each kerbin-duna arrival window. I did that a while back and found that they are separated by 529 days. So you really only need 1129 days of food.

Im not going to Duna though.

Edited by Rover 6428

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