Vector movement

Traveller has always had the rule that hyperspace jumps should be made beyond 100 diameters of the planet, gasgiant, ship, star or nearby massive object. When some kind of reason for this is mentioned it goes along the lines of  ‘too deep within the gravity well’ or other reference to gravity. Can ships jump inside nebulae (they’d certainly be inside 100 diameters of the nebula)? How can ships jump at all when they are always inside 100 diameters of the milky way galaxy? What about jumping near black holes or neutron stars (shouldn’t the density of objects be accounted for at all)?

We all know the real reason is to force ships to actually travel in space before jumping, without such a limit the ships could just as well jump directly from the ground and not much space travelling would occur. So let us all agree that wa want some kind of rule that forces ships to fly away from planets before jumping, preferrable such a rule should behave as the 100 diameter rule for planets yet still make some scientific sense. The rule should also dismiss the cases of nebulae and galaxies so ships can jump inside these while still abiding to the rule. If the rule is based on gravity instead of some weird new invented force all the better.

Gravity then, is proportional to the mass of the object and inversely proportional to the square of the distance. Gravitational force is not the only measure of gravity, we have gravitational potential and tidal force as well. These two are effects derived out of gravity but they behave differently range wise:

• Gravitational potential falls off as M/R, where M is the mass of the planet and R is the distance from the planet. It is a measure of the energy needed to reach the distance R.
• Gravitational acceleration falls off as M/R^2, where M is the mass of the planet and R is the distance from the planet. It is a measure of the gravitational acceleration exerted on an object at the distance R.
• Gravitational tidal force falls off as  M/R^3, where M is the mass of the planet and R is the distance from the planet. It measures the fall-off rate of gravitational acceleration. It is the force that causes ebb and flood on Earth as well as what causes the moon to always show the same face towards Earth.

The mass of a planet is proportional to its volume (given the same density), that means that it rises with D^3. Twice the diameter and the planet becomes 2^3 = 8 times as massive. The 100 diameter rules states that a planet twice as large must be jumped from twice as far away and as mass scales with D^3 we need something that scales as 1/R^3 and the only gravity effect that fit the bill is tidal force. Using tidal force as a limiter for when a safe jump can be performed makes a lot of sense; it is a measure of fast gravity changes near the ship. If jumdrives need a uniform gravity field to work properly the tidal force tells us how much gravity differs in different parts of the ship. If jumpdrives need to know the exact gravity pull when jumping the tidal force tell us how much error we get from our positional error. 

Safe jump distance (taught to Imperial school children to be 100 x the diameter of the object) is really calculated like this (x^(1/3) means the cubic root of x):

• Planet safe jump Rj = 1 000 000 km x (Traveller Size / 8 ), multiply by the cube root of Earth density if you want that level of detail (Earth has density 1.0)
• Planet safe jump Rj = 1 000 000 km x (M) ^(1/3), M is measured in Earth masses (Earth has a mass of 1.0)
• Star safe jump Rj = 0.5 AU x (M) ^(1/3), M is the stars mass in Solar masses (Sol has a mass of 1.0)

What does all this give us? The referee can tell its players that they must travel out 100 diameters from a planet to “where the tidal force is weak enough to safely engage the jump drive”. If one wants the detail one can calculate the actual safe jump distance from any object. When scientifically versed players asked how one can jump inside the 100 diameters of the milky way the referee can tell them it is because the tidal force from the galactic centre is way too weak to cause any problems, the same goes for jumping inside nebulae.

Note: I have taken the liberty to round off figures in the formulae above, it should really be 1 280 000 km but I find one million kilometers easier to remember.

Relativistic rock? Is that a sub-genre of Space rock? You know, Hawkwind, Ufomammut and the like?

This entry was posted on May 30, 2010 at 15:25 and is filed under Rules, Science, Science fiction, Traveller. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.