ft:planets:gravity
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The following rules model gravity from the bottom up, so require a few extra measurements when a ship is manoeuvring close to a planet. Each planet will have a number of gravity zones above its surface (during the game all measurements are taken from the surface of the planet, not it's centre) which dictate the strength of the gravitational field at that point. The radius of these zones increases in a geometric progression - 2", 4", 8", 16" and beyond. | The following rules model gravity from the bottom up, so require a few extra measurements when a ship is manoeuvring close to a planet. Each planet will have a number of gravity zones above its surface (during the game all measurements are taken from the surface of the planet, not it's centre) which dictate the strength of the gravitational field at that point. The radius of these zones increases in a geometric progression - 2", 4", 8", 16" and beyond. | ||
- | ^ Planet | + | The following are values for some common planets and moons. |
- | | Earth | 12, | + | |
+ | ^ ^^^ Acceleration at distance from surface | ||
+ | ^ Planet | ||
+ | | Earth | 13" (12, | ||
+ | | The Moon | 3" (3,475 km) | ||
+ | | Mars | 7" (6,787 km) | ||
+ | According to physics, gravity will cause a ship to accelerate towards the planet. For this reason, gravitational strength is treated as thrust, as if the ship were thrusting towards the planet. A ship within 2" of the surface of the Earth will have 6 thrust towards the surface. | ||
+ | If you want to work out values for your own worlds, there there' | ||
+ | ===== Gravitational Movement ===== | ||
- | ====== | + | The rules here assume that you are using the vector movement system, and work best if you have a counter for each ship showing its vector. When a ship is moved, you apply the ships normal manoeuvring to that counter, but before you actually move the ship you need to account for gravity. |
- | Every large body, from planets to stars and black holes, | + | - Work out which zone the ship is currently in, and look up the gravitational |
- | will exert gravitational | + | - Work out the direction from the centre |
- | attraction will act as an acceleration directly towards | + | - Apply the gravitational |
- | the body, just as if the ship were thrusting towards it. | + | - Move the ship as normal. |
- | Since a thrust | + | |
- | so the force of gravity at the surface of an Earth-like | + | |
- | world will cause an acceleration | + | |
- | Each planet is considered to have gravity bands which reach | + | As an example, consider |
- | from its surface out into space. The first band is out to 4", | + | |
- | the second to 8", the third to 16" - and so on, doubling in | + | |
- | distance each time. For an Earth-like world, the gravity in | + | |
- | the first 3 bands is 6"/turn, 2"/turn and 1"/turn. This means | + | |
- | that any ship that begins | + | |
- | dragged towards the surface by 6". | + | |
- | The steps to work out the effects of gravity are as follows. | + | {{ : |
- | We assume that vectored movement is being used, and that | + | |
- | a //vector marker// is used to show each ship's position | + | |
- | at the end of the next movement. | + | |
- | At the beginning of movement, work out the distance | + | According to the table above, the ship is currently in the 2" |
- | between | + | |
- | the ship is outside any effective gravity bands for | + | |
- | that planet, then the planet has no effect (e.g., | + | |
- | outside 16" for an Earth-like world). | + | |
- | Lookup the gravitational acceleration for that planet | + | {{ : |
- | for that range. There is a table below which lists | + | |
- | acceleration values for some common worlds. | + | |
- | Work out the gravity | + | We find the vector from the // |
- | centre of the planet for this acceleration. This vector | + | |
- | has a magnitude equal to the acceleration, | + | |
- | direction | + | |
- | + | ||
- | Apply the gravity vector to the ship's vector marker. | + | |
- | + | ||
- | Apply any acceleration due to the ship's thrust. | + | |
- | + | ||
- | Move the ship and its marker. | + | |
- | + | ||
- | It is the distance of the centre of the ship to the | + | |
- | surface of the planet | + | |
- | of the vector marker has no effect. | + | |
- | + | ||
- | ===== Acceleration due to Gravity ===== | + | |
- | + | ||
- | The acceleration due to gravity on a ship depends on the size of the planet and the distance the ship is from it. For a planet of Earth size and mass, the following zones of influence are suggested. | + | |
- | + | ||
- | + | ||
- | ^ | + | |
- | ^ Planet | + | |
- | | Earth | 13" (12, | + | |
- | | The Moon | 3" (3,475 km) | 0.5" | -- | -- | -- | -- | -- | -- | -- | | + | |
- | | Mercury | + | |
- | | Venus | 12" (12,104 km) | 4" | + | |
- | | Mars | 7" (6,787 km) | + | |
- | | Jupiter | + | |
- | | Saturn | + | |
- | | Uranus | + | |
- | | Neptune | + | |
- | | The Sun | + | |
- | | Model | 10" (10, | + | |
- | + | ||
- | + | ||
- | Remember that the distances given above are the distance from the //surface// of the body. The Sun will not fit | + | |
- | into any sensible gaming area, and is given merely to show how insignificant everything else is. Even Jupiter would require at least 2.5m (at centimetre scales) to allow for manoeuvring at the edge of its gravity well. | + | |
- | + | ||
- | Where acceleration less than 1" is given, it can be ignored. However, this does mean that small worlds such as Mercury would have no effect, so it's listed anyway in case you want to use it. | + | |
- | + | ||
- | ====== Examples ====== | + | |
- | + | ||
- | + | ||
- | ===== Fast Fly-by ===== | + | |
- | + | ||
- | + | ||
- | + | ||
- | The following example shows the Light Cruiser | + | |
- | //Colbert// approaching a planet. At no point | + | |
- | does the //Colbert// apply any thrust | + | |
- | own. The world is slightly smaller than the Earth, | + | |
- | with statistics as follows: | + | |
- | + | ||
- | ^ | + | |
- | ^ Planet | + | |
- | | Model | 10" (10,000km) | + | |
- | + | ||
- | We begin the example with the //Colbert// 10,000 km (10") from the planet' | + | |
- | + | ||
- | {{../ | + | |
- | + | ||
- | The gravitational acceleration at this point is 1"/ | + | |
- | + | ||
- | This moves the //Colbert// to its new location, somewhat closer to the planet but halfway around it. | + | |
- | + | ||
- | {{../ | + | |
- | + | ||
- | At the new distance | + | |
+ | {{ : | ||
+ | {{ : | ||
ft/planets/gravity.txt · Last modified: 2015/04/27 18:05 by sam