Difference between revisions of "Time"

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(*table more compact; +highlight moons; -double/tripple… links to the planets/Kerbol;)
(Kerbin calendar)
 
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== Kerbin Calendar ==
+
{{Stub||
The following table outlines the orbital period and frequency of each [[Celestials|Celestial Body]] in the [[Kerbol]] system. The MET lists time based on an Earth Year - 365 days - the following table calculates Earth Months as 365/12 ≈ 30.4 days. A sidereal Kerbin day is 6 hours long, the [[Mun]] has an orbital period of 38.60 hours which defines a Kerbin Month, and [[Kerbin]] has an orbital period of 2556.50 hours which defines a Kerbin Year.
+
* Outdated. This is based on pre-1.0 Kerbin rotation, and so assumes the wrong sidereal period.
 +
* Needs to consider multiple timescales available
 +
* Should consider contracts and deadlines?}}
 +
{{Outdated}}
 +
 
 +
The measurement of '''time''' in [[KSP]] is kept according to both Earth and [[Kerbin]]-specific units. Hours, minutes, and seconds progress exactly as they would on Earth, whereas days are defined by Kerbin's rotation, resulting in a solar day of six hours (sunset occurring three hours after sunrise). Prior to version [[0.23.5]], the game relied on a timeline which measured days in Earth-time (1 day = 24 hours) meaning a single day included four sunrises.
 +
 
 +
== Mission time ==
 +
During a mission, the time elapsed since launch is called [[w:Mission Elapsed Time|Mission Elapsed Time]] or MET for short. When clicking on the mission clock in the top left of GUI, it switches between MET and Kerbin time (also called UT) elapsed since the beginning of the savegame.
 +
 
 +
== Kerbin calendar ==
 +
The following table outlines the orbital period and frequency of each [[celestial body]] in the [[Kerbol System]]. The following table calculates Earth Months as 365 days/12 months/year ≈ 30.4 days. A solar Kerbin day is 6 hours long, the [[Mun]] has an orbital period of 38.6 hours which defines a Kerbin month, and [[Kerbin]] has an orbital period of 2556.5 hours which defines a Kerbin year.
 
{| class="wikitable"
 
{| class="wikitable"
 
|-
 
|-
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| [[Eeloo]] || Kerbol || 43608.90 || 7268.15 || 1129.76 || 17.06 || 1817.04 || 59.74 || 4.98 || 0.00 || 0.00 || 0.00 || 0.06 || 0.00 || 0.02 || 0.20
 
| [[Eeloo]] || Kerbol || 43608.90 || 7268.15 || 1129.76 || 17.06 || 1817.04 || 59.74 || 4.98 || 0.00 || 0.00 || 0.00 || 0.06 || 0.00 || 0.02 || 0.20
 
|}
 
|}
 +
 +
While on Earth, Calendar were created and are used to predict sun related event, Kerbal Calendar is purely astronomical and describe its motion relative to a fixed external frame :
 +
* On Earth, noon will always occur at about 12 hours. On Kerbin, from the KSC, the first sunrise occurs at 4h13 on day 1, and the 209th occurs at 1h08. This is because humans usally refer at a 24 hours long [https://en.wikipedia.org/wiki/Day#Apparent_and_mean_solar_day], while Kerbals usually refer to a 6 hours long [https://en.wikipedia.org/wiki/Day#Stellar_day].
 +
* Kerbin having a perfect circular equatorial orbit, and its rotation axis being not tilted, there are no seasons : every days are the same, night has the same duration (~3h25) as days, anywhere on kerbin, and the position of the Sun in the sky solely depends on latitude. That's why orbital period was the only choice of year, [https://en.wikipedia.org/wiki/Year#Astronomical_years while Earth has many].
 +
 +
== Phase angles ==
 +
The phase angle determine the angular distance between two bodies around the same object. The phase angle of a body exactly on the other side of the central body is 180°. If the central body is on one side, and the two compared bodies are in line, the phase angle is 0°.
 +
 +
With the starting phase angles listed below it is possible to calculate the phase angle at any given moment. This information can be used to determine if both bodies are aligned for a transfer orbit. To calculate this value, the revolutions per second (RPS) for both bodies is required. This is the inverse of the orbital period:
 +
{{Formula|math=r = \frac{1}{p}|where=* <math>r</math> is the revolutions per time unit
 +
* <math>p</math> is the orbital period in the time unit
 +
<small>Both time units are ''second'' for RPS</small>}}
 +
The phase angle change per second is then simply the subtraction of the origin from the target's planet RPS. This also tells when the current alignment repeat again, by inverting the phase angle change again. This time is called synodic orbital period.
 +
{{Formula|math=p_\text{synodic} = \left\vert\frac{1}{\frac{1}{p_t} - \frac{1}{p_o} }\right\vert|where=* <math>p_\text{synodic}</math> is the synodic orbital period
 +
* <math>p_t</math> is the sidereal orbital period of the targeted body
 +
* <math>p_o</math> is the sidereal orbital period of the original body}}
 +
 +
There are [[calculation tools]] available online which tell which is the best phase angle for an efficient transfer. Knowing this, the first alignment date can be calculated by first subtracting the starting phase angle from the desired phase angle. This gives the required first change with needs to be divided by the the phase angle change to determine how long it takes to get the first alignment.
 +
 +
=== Starting phase angles ===
 +
The following table shows the phase angle in degrees and revolutions of each planet at the beginning of each game (UT = 0s).
 +
 +
{| class="wikitable"
 +
|-
 +
! Planet || Degrees || Revolutions
 +
|-
 +
| Moho || 84.92° || 0.23589
 +
|-
 +
| Eve || 15.00° || 0.04167
 +
|-
 +
| Duna || 135.51° || 0.37642
 +
|-
 +
| Jool || 238.43° || 0.66231
 +
|-
 +
| Dres || 10.02° || 0.02783
 +
|-
 +
| Eeloo || 309.98° || 0.86106
 +
|-
 +
|}
 +
 +
=== Example ===
 +
The revolutions per second for Duna is:
 +
:<math>r = \frac{1}{17315400 s} = 5.77520589 \cdot 10^{-8} Hz</math>
 +
The phase angle change per second relative to Kerbin is then:
 +
:<math>r_\text{relative} = r_\text{Duna} - r_\text{Kerbin} = -5.09017 \cdot 10^{-8} Hz</math>
 +
The optimal phase angle for a transfer from Kerbin to Duna is 0.12323 revolutions or 44.3628°. The starting phase angle is 0.37642 revolutions so the first time change required is -0.25319 revolutions.
 +
:<math>t_0 = \frac{\beta}{r_\text{relative} } = \frac{\beta}{r_\text{Duna} - r_\text{Kerbin} } = \frac{-0.25319}{-5.09017 \cdot 10^{-8} Hz} = 4974119 s</math>
 +
The transfer windows will then repeat periodically using the synodic period between both bodies:
 +
:<math>p_\text{synodic} = \left\vert\frac{1}{\frac{1}{p_\text{Duna} } - \frac{1}{p_\text{Kerbin} } }\right\vert = \left\vert\frac{1}{-5.09017 \cdot 10^{-8} Hz}\right\vert = 19645709 s</math>
 +
:<math>t_n = t_0 + n \cdot p_\text{synodic}</math>
 +
 +
== See also ==
 +
* [[Time warp]]
  
 
[[Category:Celestials]]
 
[[Category:Celestials]]

Latest revision as of 00:07, 25 June 2019

This is a stub. You can help KSP Wiki by expanding or discussing it.

  • Outdated. This is based on pre-1.0 Kerbin rotation, and so assumes the wrong sidereal period.
  • Needs to consider multiple timescales available
  • Should consider contracts and deadlines?


The measurement of time in KSP is kept according to both Earth and Kerbin-specific units. Hours, minutes, and seconds progress exactly as they would on Earth, whereas days are defined by Kerbin's rotation, resulting in a solar day of six hours (sunset occurring three hours after sunrise). Prior to version 0.23.5, the game relied on a timeline which measured days in Earth-time (1 day = 24 hours) meaning a single day included four sunrises.

Mission time

During a mission, the time elapsed since launch is called Mission Elapsed Time or MET for short. When clicking on the mission clock in the top left of GUI, it switches between MET and Kerbin time (also called UT) elapsed since the beginning of the savegame.

Kerbin calendar

The following table outlines the orbital period and frequency of each celestial body in the Kerbol System. The following table calculates Earth Months as 365 days/12 months/year ≈ 30.4 days. A solar Kerbin day is 6 hours long, the Mun has an orbital period of 38.6 hours which defines a Kerbin month, and Kerbin has an orbital period of 2556.5 hours which defines a Kerbin year.

Celestial Body Parent Hours Kerbin Earth Revolutions
per Hour
Revolutions per Kerbin Revolutions per Earth
Days Months Years Days Months Years Day Month Year Day Month Year
Moho Kerbol 615.49 102.58 15.95 0.24 25.65 0.84 0.07 0.00 0.01 0.06 4.15 0.04 1.19 14.23
Eve Kerbol 1571.7 261.95 40.72 0.61 65.49 2.15 0.18 0.00 0.00 0.02 1.63 0.02 0.46 5.57
Gilly Eve 107.9 17.98 2.80 0.04 4.50 0.15 0.01 0.01 0.06 0.36 23.69 0.22 6.77 81.19
Kerbin Kerbol 2556.50 426.08 66.23 1.00 106.52 3.50 0.29 0.00 0.00 0.02 1.00 0.01 0.29 3.43
Mun Kerbin 38.60 6.43 1.00 0.02 1.61 0.05 0.00 0.03 0.16 1.00 66.23 0.62 18.91 226.94
Minmus Kerbin 299.50 49.92 7.76 0.12 12.48 0.41 0.03 0.00 0.02 0.13 8.54 0.08 2.44 29.25
Duna Kerbol 4809.80 801.63 124.61 1.88 200.41 6.59 0.55 0.00 0.00 0.01 0.53 0.00 0.15 1.82
Ike Duna 18.20 3.03 0.47 0.01 0.76 0.02 0.00 0.05 0.33 2.12 140.47 1.32 40.11 481.32
Dres Kerbol 13303.60 2217.27 344.65 5.20 554.32 18.22 1.52 0.00 0.00 0.00 0.19 0.00 0.05 0.66
Jool Kerbol 29072.60 4845.43 753.18 11.37 1211.36 39.83 3.32 0.00 0.00 0.00 0.09 0.00 0.03 0.30
Laythe Jool 14.70 2.45 0.38 0.01 0.61 0.02 0.00 0.07 0.41 2.63 173.91 1.63 49.66 595.92
Vall Jool 29.43 4.91 0.76 0.01 1.23 0.04 0.00 0.03 0.20 1.31 86.87 0.82 24.80 297.66
Tylo Jool 58.87 9.81 1.53 0.02 2.45 0.08 0.01 0.02 0.10 0.66 43.43 0.41 12.40 148.80
Bop Jool 110.92 18.49 2.87 0.04 4.62 0.15 0.01 0.01 0.05 0.35 23.05 0.22 6.58 78.98
Pol Jool 153.70 25.62 3.98 0.06 6.40 0.21 0.02 0.01 0.04 0.25 16.63 0.16 4.75 56.99
Eeloo Kerbol 43608.90 7268.15 1129.76 17.06 1817.04 59.74 4.98 0.00 0.00 0.00 0.06 0.00 0.02 0.20

While on Earth, Calendar were created and are used to predict sun related event, Kerbal Calendar is purely astronomical and describe its motion relative to a fixed external frame :

  • On Earth, noon will always occur at about 12 hours. On Kerbin, from the KSC, the first sunrise occurs at 4h13 on day 1, and the 209th occurs at 1h08. This is because humans usally refer at a 24 hours long [1], while Kerbals usually refer to a 6 hours long [2].
  • Kerbin having a perfect circular equatorial orbit, and its rotation axis being not tilted, there are no seasons : every days are the same, night has the same duration (~3h25) as days, anywhere on kerbin, and the position of the Sun in the sky solely depends on latitude. That's why orbital period was the only choice of year, while Earth has many.

Phase angles

The phase angle determine the angular distance between two bodies around the same object. The phase angle of a body exactly on the other side of the central body is 180°. If the central body is on one side, and the two compared bodies are in line, the phase angle is 0°.

With the starting phase angles listed below it is possible to calculate the phase angle at any given moment. This information can be used to determine if both bodies are aligned for a transfer orbit. To calculate this value, the revolutions per second (RPS) for both bodies is required. This is the inverse of the orbital period:

Where:
  • is the revolutions per time unit
  • is the orbital period in the time unit
Both time units are second for RPS

The phase angle change per second is then simply the subtraction of the origin from the target's planet RPS. This also tells when the current alignment repeat again, by inverting the phase angle change again. This time is called synodic orbital period.

Where:
  • is the synodic orbital period
  • is the sidereal orbital period of the targeted body
  • is the sidereal orbital period of the original body

There are calculation tools available online which tell which is the best phase angle for an efficient transfer. Knowing this, the first alignment date can be calculated by first subtracting the starting phase angle from the desired phase angle. This gives the required first change with needs to be divided by the the phase angle change to determine how long it takes to get the first alignment.

Starting phase angles

The following table shows the phase angle in degrees and revolutions of each planet at the beginning of each game (UT = 0s).

Planet Degrees Revolutions
Moho 84.92° 0.23589
Eve 15.00° 0.04167
Duna 135.51° 0.37642
Jool 238.43° 0.66231
Dres 10.02° 0.02783
Eeloo 309.98° 0.86106

Example

The revolutions per second for Duna is:

The phase angle change per second relative to Kerbin is then:

The optimal phase angle for a transfer from Kerbin to Duna is 0.12323 revolutions or 44.3628°. The starting phase angle is 0.37642 revolutions so the first time change required is -0.25319 revolutions.

The transfer windows will then repeat periodically using the synodic period between both bodies:

See also