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--- ft:planets:gravity [2014/03/09 22:25] – sam
+++ ft:planets:gravity [2015/04/27 18:05] (current) – sam
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 ====== Gravity ======
-The following rules are designed to model the use of planets within a Full Thrust game, both as an obstacle to navigation, and also for scenarios where the planet itself is of importance. There are rules in //More Thrust// (p. 13) for handling planets, but they are very simplistic and don't fit in well with the vector movement system introduced in the //Fleet Book//.
+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.
-{{../graphics/planet.jpg}}
+The following are values for some common planets and moons.
-All these rules assume //vectored movement// is being used. If you're using cinematic movement, then these rules won't make much sense.
+^                                ^^^ 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  |  --  |  --   |  --  |  --   |  --   |  --   |
-===== Units of Measurement =====
+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.
-Normally, Full Thrust doesn't care about real world
+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.
-measurements, and simply uses the 'turn' and the
-'movement unit' (depicted as " in the rules, and
-often taken as an inch on the table top). If we
-start using real world objects though (such as
-planets), it becomes necessary to translate these
-abstract terms into real world units.
-A turn is taken to be fifteen minutes, and 1" is
+===== Gravitational Movement =====
-assumed to represent one thousand kilometres. From
-this, we can work out that a ship thrust factor of 1
-is equivalent to an acceleration of approximately
-.125 ms-2. To keep things simple, I'll assume that
-g is equal to a thrust factor of 8.
-Unless you have a very big table, you might want to
+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.
-consider using 1" = 1cm on the table top. This provides
-a lot more room for manouevre around the planets, and
-also makes modelling planets easier.
-===== Modelling Planets =====
+  - Work out which zone the ship is currently in, and look up the gravitational acceleration.
+  - Work out the direction from the centre of the ship to the centre of the planet.
+  - Apply the gravitational acceleration to the movement counter in the same direction as in step 2.
+  - Move the ship as normal.
-The easiest way to model a planet is to cut a circle out
+==== Movement Example ====
-of a piece of cloth or paper, and simply place it on
-the table top. This also makes it very easy to place
-planetary installations on the planet, since they can be
-drawn/placed on top of the planet.
-Another easy way is to buy a polystyrene sphere from a
+=== Step One: Work out gravitational force ===
-craft shop, cut it in half to form a hemisphere and
-paint it to look planet-like. The largest spheres I've
-found though are only 10cm in diameter, so this works
-best for either dwarf planets or if you're using
-centimetres. See the picture above for an example.
-====== The Effects of Gravity ======
+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.
-Every large body, from planets to stars and black holes,
+{{ :ft:gravity_1.png?nolink |}}
-will exert gravitational attraction on nearby ships. This
-attraction will act as an acceleration directly towards
-the body, just as if the ship were thrusting towards it.
-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
+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.
-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 Two: Work out direction of 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
+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.
-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_2.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
+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.
-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 Three: Determine final vector ===
-Apply any acceleration due to the ship's thrust.
+{{ :ft:gravity_3.png?nolink |}}
-Move the ship and its marker.
-It is the distance of the centre of the ship to the
-surface of the planet that is important - the position
-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.
-^           ^                    ^ 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 |}}