Difference between revisions of "Orbit darkness time/ru"

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(Круговые орбиты вокруг всех планет и лун)
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[[File:Orbit darkness.svg|thumb|Orbital darkness schematic]]
 
[[File:Orbit darkness.svg|thumb|Orbital darkness schematic]]
The '''orbit darkness time''' determines the time a [[craft]] is staying in the shadow of an orbited [[Celestial body|object]]. The exact time depends on the current configuration of the orbit and the moons.
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'''Период затенения орбиты (англ. "orbit darkness time")''' определяет период времени в котором [[craft/ru|аппарат]] остается в тени [[Celestial body/ru|объекта]], вокруг которого вращается. Точное время зависит от текущей конфигурации орбиты и лун.
 
 
This page will give an expression for the worst-case scenario of how long a craft will be in darkness during an orbit. This information can be used to determine how many [[Battery|batteries]] are needed for a craft to remain powered during the dark portion of orbit.
 
 
 
== General Result ==
 
Here is the result for calculating the longest amount of time spent in darkness (in units of seconds):
 
  
 +
На этой странице дается выражение для наихудшего варианта продолжительности периода, в который [[craft/ru|аппарат]] будет в тени на орбите. Эта информация может использоваться, чтобы определить, сколько батарей необходимо для [[craft/ru|аппарата]], чтобы остаться работающим во время затененной части орбиты.
 +
== Основные вычисления ==
 +
Здесь дан результат для вычисления самого долгого промежутка времени, проводимого в тени (в единицах измерения - секундах):
 
<math>T_d = \frac{2ab}{h}\left(\text{sin}^{-1}\left(\frac{R}{b}\right) + \frac{eR}{b}\right)</math>
 
<math>T_d = \frac{2ab}{h}\left(\text{sin}^{-1}\left(\frac{R}{b}\right) + \frac{eR}{b}\right)</math>
 
+
where:
where <math>a</math> is the semi-major axis, <math>b</math> the semi-minor axis, <math>h</math> the specific angular momentum, <math>e</math> the eccentricity, and <math>R</math> the radius of the planet or moon. For reference these terms can be calculated by knowing the apoapsis (Ap), periapsis (Pe) and body to orbit:
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* <math>a</math> - [[semi-major axis/ru|главная полуось]];
 
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* <math>b</math> - [[semi-minor axis/ru|малая полуось]];
* <math>r_a = Ap + R</math>, the apoapsis measured from the center of the body
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* <math>h</math> - specific angular momentum;
* <math>r_p = Pe + R</math>, the periapsis measured from the center of the body
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* <math>e</math> - [[eccentricity/ru|эксцентриситет]];
* <math>a = \frac{r_a+r_p}{2}</math>, the semi-major axis
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* <math>R</math> - радиус [[planet/ru|планеты]] или [[moon/ru|луны]].
* <math>b = \sqrt{r_ar_p}</math>, the semi-minor axis
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Для справки, эти значения можно вычислить при известных [[apoapsis/ru|апоцентре]] (Ap), [[periapsis/ru|перицентре]] (Pe) и теле на орбите:
* <math>e = \frac{r_a-r_p}{r_a+r_p}</math>, the eccentricity
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* <math>r_a = Ap + R</math> - [[apoapsis/ru|апоцентр]], измеренный от центра тела;
 +
* <math>r_p = Pe + R</math> - [[periapsis/ru|перицентр]], измеренный от центра тела;
 +
* <math>a = \frac{r_a+r_p}{2}</math> - [[semi-major axis/ru|главная полуось]];
 +
* <math>b = \sqrt{r_ar_p}</math>[[semi-minor axis/ru|малая полуось]];
 +
* <math>e = \frac{r_a-r_p}{r_a+r_p}</math> - [[eccentricity/ru|эксцентриситет]];
 
* <math>l = \frac{2r_ar_p}{r_a+r_p}</math>, the semi-latus rectum of the orbital ellipse
 
* <math>l = \frac{2r_ar_p}{r_a+r_p}</math>, the semi-latus rectum of the orbital ellipse
 
* <math>\mu = GM</math>, the [[w:Standard gravitational parameter|gravitational parameter]]
 
* <math>\mu = GM</math>, the [[w:Standard gravitational parameter|gravitational parameter]]
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When using kilometer for the orbital parameters the gravitational parameter needs to be divided by 1000<sup>3</sup>. For example [[Kerbin]] has an equatorial radius 600&#8239;000 m or 600&nbsp;km. Its gravitational parameter is 3.5316000×10<sup>12</sup> m<sup>3</sup>/s<sup>2</sup> or 3.5316000×10<sup>3</sup> km<sup>3</sup>/s<sup>2</sup>.
 
When using kilometer for the orbital parameters the gravitational parameter needs to be divided by 1000<sup>3</sup>. For example [[Kerbin]] has an equatorial radius 600&#8239;000 m or 600&nbsp;km. Its gravitational parameter is 3.5316000×10<sup>12</sup> m<sup>3</sup>/s<sup>2</sup> or 3.5316000×10<sup>3</sup> km<sup>3</sup>/s<sup>2</sup>.
  
=== Simplified Result ===
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=== Упрощенное вычисление ===
  
 
For (almost) circular orbits where the eccentricity <math>e</math> is very small this equation becomes rather simple:
 
For (almost) circular orbits where the eccentricity <math>e</math> is very small this equation becomes rather simple:
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This simpler result only works when the apoapsis and periapsis are very close to the same altitude.
 
This simpler result only works when the apoapsis and periapsis are very close to the same altitude.
  
== Limitations ==
+
== Ограничения ==
  
 
This method assumes the orbit is an ellipse/circle which is not changing or being altered by other bodies. It also assumes the sun's rays are parallel across the orbiting planet, although all bodies are small enough and far enough from the sun for this to be nearly true. The method does not take into account darkness caused by eclipses of a different body than the orbited body, for example, orbiting [[Laythe]] but [[Jool]] blocks the sun.
 
This method assumes the orbit is an ellipse/circle which is not changing or being altered by other bodies. It also assumes the sun's rays are parallel across the orbiting planet, although all bodies are small enough and far enough from the sun for this to be nearly true. The method does not take into account darkness caused by eclipses of a different body than the orbited body, for example, orbiting [[Laythe]] but [[Jool]] blocks the sun.
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The method gives the longest amount of time spent in darkness, which for some orbits (e.g. polar orbits), will only be experienced periodically (see [[w:Beta_angle|beta angle]]). However, it is a good idea to plan on the worst-case amount of time in darkness.
 
The method gives the longest amount of time spent in darkness, which for some orbits (e.g. polar orbits), will only be experienced periodically (see [[w:Beta_angle|beta angle]]). However, it is a good idea to plan on the worst-case amount of time in darkness.
  
== Application ==
+
== Применение ==
  
 
By entering the equations into a program such as Microsoft Excel or going to [http://www.prism.gatech.edu/~bnichols8/projects/kspdarkness/main.shtml this calculator page], the darkness time can be calculated for various orbits around any planet or moon. Knowing the amount of time spent in darkness and the energy drain, the battery storage can be calculated by
 
By entering the equations into a program such as Microsoft Excel or going to [http://www.prism.gatech.edu/~bnichols8/projects/kspdarkness/main.shtml this calculator page], the darkness time can be calculated for various orbits around any planet or moon. Knowing the amount of time spent in darkness and the energy drain, the battery storage can be calculated by
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The darkness time along with the total [[w:Orbital period|orbital period]] can also be used to calculate how many solar panels are needed to recharge the batteries before the next cycle of darkness. However, the time spent in sunlight is usually quite long, and even a single small solar panel will recharge most any craft's batteries before the next darkness cycle.
 
The darkness time along with the total [[w:Orbital period|orbital period]] can also be used to calculate how many solar panels are needed to recharge the batteries before the next cycle of darkness. However, the time spent in sunlight is usually quite long, and even a single small solar panel will recharge most any craft's batteries before the next darkness cycle.
  
== Examples ==
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== Примеры ==
  
=== Orbiting Kerbin with 100 km circular orbit ===
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=== Круговая орбита вокруг [[Kerbin/ru|Кербина]] на высоте в 100 км. ===
  
 
<math>T_d = 642 \text{ seconds (10m 42s)}</math>
 
<math>T_d = 642 \text{ seconds (10m 42s)}</math>
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So at least 57.8 e of electricity is needed in storage to make it through the darkness for this orbit around Kerbin, using 0.09&nbsp;e per second. The battery with the next largest amount of storage (as of {{Check version|0.21.1}}) is the [[Z-100 Rechargable Battery Pack|Z-100]] with 100&nbsp;e of storage. The RC-001S can also store 30&nbsp;e so in theory only 27.8&nbsp;e are required.
 
So at least 57.8 e of electricity is needed in storage to make it through the darkness for this orbit around Kerbin, using 0.09&nbsp;e per second. The battery with the next largest amount of storage (as of {{Check version|0.21.1}}) is the [[Z-100 Rechargable Battery Pack|Z-100]] with 100&nbsp;e of storage. The RC-001S can also store 30&nbsp;e so in theory only 27.8&nbsp;e are required.
  
=== Orbiting Jool with apoapsis 700 km and periapsis 200 km ===
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=== Орбита вокруг [[Jool/ru|Джула]] с [[apoapsis/ru|апоцентром]] в 700 км. и [[periapsis/ru|перицентром]] в 200 км. ===
  
 
<math>T_d = 2403\text{ seconds (40m 3s)}</math>
 
<math>T_d = 2403\text{ seconds (40m 3s)}</math>

Revision as of 13:24, 16 September 2014

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Orbital darkness schematic

Период затенения орбиты (англ. "orbit darkness time") определяет период времени в котором аппарат остается в тени объекта, вокруг которого вращается. Точное время зависит от текущей конфигурации орбиты и лун.

На этой странице дается выражение для наихудшего варианта продолжительности периода, в который аппарат будет в тени на орбите. Эта информация может использоваться, чтобы определить, сколько батарей необходимо для аппарата, чтобы остаться работающим во время затененной части орбиты.

Основные вычисления

Здесь дан результат для вычисления самого долгого промежутка времени, проводимого в тени (в единицах измерения - секундах): where:

Для справки, эти значения можно вычислить при известных апоцентре (Ap), перицентре (Pe) и теле на орбите:

  • - апоцентр, измеренный от центра тела;
  • - перицентр, измеренный от центра тела;
  • - главная полуось;
  • малая полуось;
  • - эксцентриситет;
  • , the semi-latus rectum of the orbital ellipse
  • , the gravitational parameter
  • , the specific angular momentum

The following parameters are the minimum requirements to calculate the values from above:

  • , planned apoapsis of the craft's orbit from the surface of the body
  • : planned periapsis of the craft's orbit from the surface of the body
  • : radius of body to orbit (a.k.a. equatorial radius)
  • : mass of body to orbit

The radius and mass of a body can be obtained by visiting the page of the body (e.g. Kerbin) or by visiting Kerbol System/Table which contain the mass and radius of all celestial bodies. The actual page of a body also shows the gravitational parameter directly so it doesn't need to be multiplied by G.

When using kilometer for the orbital parameters the gravitational parameter needs to be divided by 10003. For example Kerbin has an equatorial radius 600 000 m or 600 km. Its gravitational parameter is 3.5316000×1012 m3/s2 or 3.5316000×103 km3/s2.

Упрощенное вычисление

For (almost) circular orbits where the eccentricity is very small this equation becomes rather simple:

This simpler result only works when the apoapsis and periapsis are very close to the same altitude.

Ограничения

This method assumes the orbit is an ellipse/circle which is not changing or being altered by other bodies. It also assumes the sun's rays are parallel across the orbiting planet, although all bodies are small enough and far enough from the sun for this to be nearly true. The method does not take into account darkness caused by eclipses of a different body than the orbited body, for example, orbiting Laythe but Jool blocks the sun.

The method gives the longest amount of time spent in darkness, which for some orbits (e.g. polar orbits), will only be experienced periodically (see beta angle). However, it is a good idea to plan on the worst-case amount of time in darkness.

Применение

By entering the equations into a program such as Microsoft Excel or going to this calculator page, the darkness time can be calculated for various orbits around any planet or moon. Knowing the amount of time spent in darkness and the energy drain, the battery storage can be calculated by

where is the battery storage required in the electricity unit e, is the rate of energy use in units of e/sec, and is the darkness time in seconds.

The darkness time along with the total orbital period can also be used to calculate how many solar panels are needed to recharge the batteries before the next cycle of darkness. However, the time spent in sunlight is usually quite long, and even a single small solar panel will recharge most any craft's batteries before the next darkness cycle.

Примеры

Круговая орбита вокруг Кербина на высоте в 100 км.

Using 0.05 e/s for the RC-001S and 0.04 e/s for the Illuminator Mk1 for a total drain of 0.09 e/s:

So at least 57.8 e of electricity is needed in storage to make it through the darkness for this orbit around Kerbin, using 0.09 e per second. The battery with the next largest amount of storage (as of 0.21.1[outdated]) is the Z-100 with 100 e of storage. The RC-001S can also store 30 e so in theory only 27.8 e are required.

Орбита вокруг Джула с апоцентром в 700 км. и перицентром в 200 км.

Using 0.05 e/s for the RC-001S and 0.16 e/s for 4x Illuminator Mk1 for a total drain of 0.21 e/s:

So at least 505 e of electricity is needed in storage to make it through the darkness for this orbit around Jool, using 0.21 e per second.

Круговые орбиты вокруг всех планет и лун

Следующая таблица содержит в себе периоды затенения для планет и лун. Все орбиты - круговые, на высоте 20% радиуса небесного тела.

Небесное тело Период затенения Период обращения орбиты Высота над уровнем моря (м)
TinyMoho.png Мохо (Moho) 788 s 13 минут 8.4 секунд 41 минут 54.3 секунд 50 000 m
TinyEve.png Ив (Eve) 531 s 8 минут 50.6 секунд 28 минут 12.2 секунд 140 000 m
TinyGilly.png Джилли (Gilly) 1 333 s 22 минут 13.3 секунд 1 часов 10 минут 52.1 секунд 2 600 m
TinyKerbin.png Кербин (Kerbin) 641 s 10 минут 40.5 секунд 34 минут 2.6 секунд 120 000 m
TinyMun.png Мун (Mun) 908 s 15 минут 7.6 секунд 48 минут 14.5 секунд 40 000 m
TinyMinmus.png Минмус (Minmus) 906 s 15 минут 5.8 секунд 48 минут 8.7 секунд 12 000 m
TinyDuna.png Дюна (Duna) 854 s 14 минут 14 секунд 45 минут 23.5 секунд 64 000 m
TinyIke.png Айк (Ike) 891 s 14 минут 50.9 секунд 47 минут 21.1 секунд 26 000 m
TinyDres.png Дрес (Dres) 906 s 15 минут 5.8 секунд 48 минут 8.7 секунд 27 600 m
TinyJool.png Джул (Jool) 2 265 s 37 минут 44.6 секунд 2 часов 0 минут 21.8 секунд 1 200 000 m
TinyLaythe.png Лейт (Laythe) 654 s 10 минут 53.7 секунд 34 минут 44.8 секунд 100 000 m
TinyVall.png Валл (Vall) 934 s 15 минут 34.3 секунд 49 минут 39.5 секунд 60 000 m
TinyTylo.png Тило (Tylo) 716 s 11 минут 56.1 секунд 38 минут 3.7 секунд 120 000 m
TinyPol.png Пол (Pol) 890 s 14 минут 49.8 секунд 47 минут 17.6 секунд 8 800 m
TinyBop.png Боп (Bop) 861 s 14 минут 20.7 секунд 45 минут 44.7 секунд 13 000 m
TinyEeloo.png Иилу (Eeloo) 914 s 15 минут 13.7 секунд 48 минут 33.8 секунд 42 000 m