Difference between revisions of "Time"

Latest revision as of 12:47, 6 November 2021

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/Universal Time) elapsed since the beginning of the savegame.

MET (Mission Elapsed Time) counts up using the Kerbin Time System and shows the time since the engines were first ignited.

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
Celestial Body	Parent	Hours	Days	Months	Years	Days	Months	Years	Revolutions per Hour	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 solar day, while Kerbals usually refer to a 6 hours long 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, while Earth has many.
Noon on Kerbin always occurs on hour 0 minute 0 and second 0 where the day and year are variable. (Year ?, Day ?, 0:00:00)

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:

r={\frac {1}{p}}

Where:

$r$ is the revolutions per time unit
$p$ 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.

p_{\text{synodic}}=\left\vert {\frac {1}{{\frac {1}{p_{t}}}-{\frac {1}{p_{o}}}}}\right\vert

Where:

$p_{\text{synodic}}$ is the synodic orbital period
$p_{t}$ is the sidereal orbital period of the targeted body
$p_{o}$ 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:

r={\frac {1}{17315400s}}=5.77520589\cdot 10^{-8}Hz

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

r_{\text{relative}}=r_{\text{Duna}}-r_{\text{Kerbin}}=-5.09017\cdot 10^{-8}Hz

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.

t_{0}={\frac {\beta }{r_{\text{relative}}}}={\frac {\beta }{r_{\text{Duna}}-r_{\text{Kerbin}}}}={\frac {-0.25319}{-5.09017\cdot 10^{-8}Hz}}=4974119s

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

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 =19645709s

t_{n}=t_{0}+n\cdot p_{\text{synodic}}

@@ Line 1: / Line 1: @@
-== 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/Universal Time) elapsed since the beginning of the savegame.
+MET (Mission Elapsed Time) counts up using the Kerbin Time System and shows the time since the engines were first ignited.
+== 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"
 |-
@@ Line 40: / Line 52: @@
 | [[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 solar day], while Kerbals usually refer to a 6 hours long [https://en.wikipedia.org/wiki/Day#Stellar_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].
+* Noon on Kerbin always occurs on hour 0 minute 0 and second 0 where the day and year are variable. (Year ?, Day ?, 0:00:00)
 == Phase angles ==
-These are the phase angles of other planets, relative to Kerbin and ahead of Kerbin in the direction of rotation (taken using MechJeb2) at the beginning of the game (Year 1 day 1 00:00:00).
+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
+! Planet || Degrees || Revolutions
 |-
 | Moho || 84.92° || 0.23589
@@ Line 60: / Line 92: @@
 |-
 |}
-These starting angles will allow you to calculate what the phase angle will be at any given moment. And you don't need to use any tools such as MechJeb to tell an exact moment when the planets are aligned for a transfer orbit.
-For example the revolutions per second (RPS) for Duna is a full rotation divided by Duna's orbital period (1 / 17315400s). Then you can get the same revolutions per seconds value for Kerbin exactly the same way. To get the phase angle change per second one simply subtracts Kerbin_RPS from the target planet RPS.
-Duna_RPS - Kerbin_RPS = -5.09017e-08
-Using Kosmo-not's instructions one can calculate that the optimal phase angle for Kerbin - Duna transfer orbit is 0.12323 revolutions. We simply divide the desired change in phase angle by the angular change per second to get time until next transfer window.
-(Desired phase angle) - (Duna phase angle at game start) = Desired change in angle
-(Desired change in angle) / -5.09017e-08 = 4974119
+=== 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>
-So the first transfer window to Duna will be 4974119 seconds after game start, and will repeat every 19645699 seconds (-1 / -5.09017e-08).
+== See also ==
+* [[Time warp]]
 [[Category:Celestials]]

Difference between revisions of "Time"

Latest revision as of 12:47, 6 November 2021

Contents

Mission time

Kerbin calendar

Phase angles

Starting phase angles

Example

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