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--- ft:planets:gravity [2015/04/26 15:44] – sam
+++ ft:planets:gravity [2015/04/27 18:05] (current) – sam
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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.
-^ Planet     ^ Diameter  ^ Surface ^ 2" ^ 4" ^ 8" ^ 16" ^ 32" ^ 64" ^
+The following are values for some common planets and moons.
-| Earth      | 12,800km  | 8T (1g) | 6T | 4T | 2T | 1T  | -   | -   |
+^                                ^^^ Acceleration at distance from surface      ^^^^^^^^
+^ Planet    ^ Diameter           ^ Gravity ^  2"  ^  4"  ^  8"  ^  16"  ^  32" ^  64"  ^  128" ^  256" ^
+| Earth     | 13" (12,700km)     |  1g     |  6T  |  4T  |  2T  |  1T   |  --  |  --   |  --   |  --   |
+| The Moon  |  3" (3,475 km)     |  0.15g  |  1T  |  --  |  --  |  --   |  --  |  --   |  --   |  --   |
+| Mars      |  7" (6,787 km)     |  0.3g   |  2T  |  2T  |  --  |  --   |  --  |  --   |  --   |  --   |
+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's a simple(ish) formulae for doing so, which will be given at the end of this page.
+===== Gravitational Movement =====
-====== The Effects of Gravity ======
+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 acceleration.
-will exert gravitational attraction on nearby ships. This
+  - Work out the direction from the centre of the ship to the centre of the planet.
-attraction will act as an acceleration directly towards
+  - Apply the gravitational acceleration to the movement counter in the same direction as in step 2.
-the body, just as if the ship were thrusting towards it.
+  - Move the ship as normal.
-Since a thrust of 8 is considered to be equivalent to 1g,
-so the force of gravity at the surface of an Earth-like
-world will cause an acceleration of 8".
-Each planet is considered to have gravity bands which reach
+==== Movement Example ====
-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 a turn within 4" of Earth will get
-dragged towards the surface by 6".
-The steps to work out the effects of gravity are as follows.
+=== Step One: Work out gravitational force ===
-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
+As an example, consider the NAC ship //Aggressor// that is performing a flyby of the Earth. At the start of its movement it is within 3" of the Earth, moving at a velocity of 8" mostly parallel to its surface.
-between the ship and the surface of the planet. If
-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
+{{ :ft:gravity_1.png?nolink |}}
-for that range. There is a table below which lists
-acceleration values for some common worlds.
-Work out the gravity vector from the ship towards the
+Since the //Aggressor// is in the 2"-4" zone, the gravitational force on it applies a thrust of 4. At no point during this example will the //Aggressor// use its own drives - all movement changes will be entirely due to the Earth.
-centre of the planet for this acceleration. This vector
-has a magnitude equal to the acceleration, and a
-direction pointing to the centre of the planet.
-Apply the gravity vector to the ship's vector marker.
+=== Step Two: Work out direction of force ===
-Apply any acceleration due to the ship's thrust.
+We next work out which direction the force of gravity applies. This is always in the direction from the ship's starting location towards the centre of the planet.
-Move the ship and its marker.
+{{ :ft:gravity_2.png?nolink |}}
-It is the distance of the centre of the ship to the
+We find the vector from the //Aggressor// to the centre of the Earth. This is the direction that the ship is being dragged towards the planet - the direction is always taken from the start of movement. Since the gravitational thrust is 4", we apply a vector of 4" to the destination point in the same direction.
-surface of the planet that is important - the position
-of the vector marker has no effect.
-===== Acceleration due to Gravity =====
+=== Step Three: Determine final vector ===
-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.
+{{ :ft:gravity_3.png?nolink |}}
-^           ^                    ^ Acceleration at distance from surface      ^^^^^^^^
-^ Planet    ^ Diameter           ^  4"  ^  8" ^ 16" ^ 32" ^ 64" ^ 128" ^ 256" ^ 512" ^
-| Earth     | 13" (12,700km)     |  6"  |  2" |  1" | --  | --  | --   | --   | --   |
-| The Moon  |  3" (3,475 km)     | 0.5" | --  | --  | --  | --  | --   | --   | --   |
-| Mercury   |  5" (4,878 km)     | 0.5" | --  | --  | --  | --  | --   | --   | --   |
-| Venus     | 12" (12,104 km)    |  4"  |  2" |  1" | --  | --  | --   | --   | --   |
-| Mars      |  7" (6,787 km)     |  1"  | 0.5"| --  | --  | --  | --   | --   | --   |
-| Jupiter   | 142" (142,200 km)  |  20" | 18" | 16" | 12" |  8" |  4"  |  2"  | 0.5" |
-| Saturn    | 119" (119,300 km)  |   9" |  8" |  6" |  5" |  3" |  1"  | 0.5" | --   |
-| Uranus    |  51" (51,200 km)   |   8" |  6" |  4" |  2" |  1" | 0.5" |  --  | --   |
-| Neptune   |  49" (49,500 km)   |   8" |  6" |  4" |  2" |  1" | --   |  --  | --   |
-| The Sun   |1392" (1,392,000 km)| 223" | 222"| 219"| 216"| 208"| 196" | 173" | 93"  |
-| Model     | 10" (10,000km)     |   4" | 2"  | 1"  | --  | --  | --   | --   | --   |
-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 of its
-own. The world is slightly smaller than the Earth,
-with statistics as follows:
-^           ^                    ^ Acceleration at distance from surface      ^^^^
-^ Planet    ^ Diameter           ^  4"  ^  8" ^ 16" ^ 32" ^
-| Model     | 10" (10,000km)     |   4" | 2"  | 1"  | --  |
-We begin the example with the //Colbert// 10,000 km (10") from the planet's surface. The //Colbert// has a current velocity of 12"/turn (as denoted by the red vector marker in the diagram).
-{{../graphics/orbits/orbit-1-1.jpg}}
-The gravitational acceleration at this point is 1"/turn, in a direction about 45 degrees to the //Colbert//'s current heading. This acceleration is applied to the vector marker (vector shown in green above).
-This moves the //Colbert// to its new location, somewhat closer to the planet but halfway around it.
-{{../graphics/orbits/orbit-1-2.jpg}}
-At the new distance of 6" (shown in red), the gravitational acceleration is 2"/turn. Again this is applied to the vector marker. Note that the marker is moved in the direction that the //Colbert// would be moved by gravity.
+=== Step Four: Move the ship ===
+{{ :ft:gravity_4.png?nolink |}}