How to Fly a Spaceship
 

          Okay, so you have downloaded Starship Pilot and tried it out.  You pointed the nose of your ship at a planet or satellite, throttled up the engines, ran up the time stasis and the next thing you knew the object went flying past on the viewscreen and shrank into the distance behind you.   Welcome to the wonderful world of space travel!  Given the large distances that need to be traversed in this simulation you may want to think about plotting a course a little more scientifically than just pointing in the desired direction and accelerating.  But how, you may ask, do you do that? 

     The answer is "astrogation."  "Astrogation" is the equivalent of "navigation" on the ocean.   "Navigation" derives from the Latin navigare ( navis="ship" +  igare= "to drive"), so by replacing navis with astro ("star") we get something like "star-driving."  Like marine navigation, astrogation will probably take many forms, however in all types of both navigation and astrogation the basic principle remains the same- figuring out the relationship of your position to that of your destination and then traversing the distance between the two. 

    There are four basic astrogational situations you will encounter within Starship Pilot. These situations are: 1) approaching and departing from jump gates; 2) traversing the space within gravitational fields (i.e. going to a planet within a star's orbit or satellite within a planet's); 3) landing on a planet or moon; 4) docking with an orbital facility.  The last mentioned, docking, is fairly straightforward and there is not much that can be added to the instructions for "rendezvous mode" contained in the program's manual.  The manual and the program itself make both landings and jump-gate maneuvers fairly easy to master as well (although I have put a few tips on both of these operations in a pair of appendices below), but the second situation listed above, that of traversing the space within orbits, is only summarily treated within the manual and the visual displays used in the Starship Pilot program almost defy any attempt to reconcile the ship's initial position with that of a destination planet or satellite.  It is with this matter of inter-orbital astrogation that the bulk of the present essay shall contend. 

     Before examining what we do have to work with, let's take a look at what it might be nice to have, but do not. First of all, by the time the human race masters interstellar travel (assuming that it ever does), we should have computers sophisticated enough to automatically make all the required observations, crunch all the necessary numbers, and then just do whatever needs to be done in the way of setting a heading and rate of acceleration. Hmph... makes one wonder if a human presence will be needed at all besides as a passenger, but I digress. At any rate, the ship's computer in Starship Pilot, although helpful, certainly does not do everything for you. Likewise, the program's displays do not give you positions in terms of three-dimensional Cartesian x,y,z coordinates. It would be pretty simple to measure distances and velocities and rates of acceleration if everything was laid out on a three-dimensional grid, but it is not.  It would also be great if the manual provided charts showing the relative positions of planets in their orbits at different times and/or graphs of such astronomical data, but we do not have that, either.

    Given the limitations just noted, the Starship Pilot manual recommends a technique dubbed "tacking" where approach to a planet or satellite is made by alternately accelerating, coasting and stopping, with the aid of a high level of time-stasis, in the general direction of the destination until its activity sphere is reached.  "Tacking" works, but it is not very efficient as the ship is required to stop repeatedly and has to travel in a zig-zag pattern as it feels its way towards the destination. For an analogy, think of "tacking" as driving through a residential neighborhood with a stop-sign on every corner and making a turn every few blocks. When covering any great distance (and the distances in space are indeed great!), most folks would prefer taking the highway.  So, where is the "highway" in space? First of all, to get on the "highway" we'd have to fully exploit the capabilities of the ship's engine. 

    The fuel-efficient "graviton engine" of the ship in Starship Pilot is capable of sustaining a hefty 50 g's of acceleration.  1 g is the abbreviation for "standard gravity"- the rate of acceleration imparted to a falling object by gravity at Earth's sea level- approximately 9.8 meters per second/ 32.2 feet per second.  The g has become a standard measure in physics for measuring acceleration and the force it exerts, and is the way acceleration is measured in Starship Pilot.  At 50 g's your ship is accelerating at a rate of 490 meters every second.  Starting from 0 m/s, after one second your ship would be traveling at 490 m/s, 980 m/s after two seconds, 1,470 m/s after three, and so on until after a little more than 600,000 seconds (7 days) when the ship would hit the speed of light (299,792,458 m/s).  To put it in automotive terms, at 50 g's (1,610 ft./s²) the ship would accelerate from 0 to 60 miles per hour (88 ft./s) in a little more than 0.05 seconds (one-twentieth of a second!).  By comparison, a really quickly-accelerating automobile can go from 0-60 m.p.h. on a level road in under 2 seconds- a rate of acceleration around 44 ft./s².  A car that can accelerate at that rate would be making the equivalent of 1.4 g's (which means my 0-60 in 10 sec. [on a good day!] '87 Jeep pulls a little less than 0.3 g's!).  It should be noted that while tests have shown that humans can briefly endure as much as 46.2 g's (in a 1954 rocket-sled experiment) and that modern jet fighter-pilots can pull 9 g's or more for sustained periods of time (with special "g-suits" to redirect blood-flow), for the extended acceleration at high g's the ship in Starship Pilot puts out it would have to be equipped with some sort of artificial gravity system.  It might also be noted that like everything else, acceleration is relative. Just as a car that can go from 0-60 m.p.h. in 2 seconds might sound swift until compared with a hypothetical spaceship that can do 50 g's, likewise that spaceship sounds mighty powerful until one encounters references such as in R.A. Heinlein's classic sci-fi novel "Citizen of The Galaxy" where a rather normal merchant space ship can accelerate at 100 g's (her captain dismisses another ship with "only" 80 g's of acceleration as being too sluggish), and a military vessel has a whopping 300 g's of thrust!  Maybe 50 g's is not so much after all... but it is what we have.

    So, how do we get the most out of the "graviton engine"?  Well, what just about every science-fiction movie or television show forgets is that spaceships do not have brakes.  Sure, some day somebody may come up with some gizmo that allows for the instant cancelling of large velocities- in fact, such a doohickey is incorporated into Starship Pilot (the SHIFT-S relative stop function), but if you really want to do space travel right then you should avoid the temptation to use it. If you want to slow the ship down, and obey the laws of physics, you will need to cancel out your forward velocity by reversing the ship and firing the engines until your speed is down to where you want it.   What this ultimately means is that the fastest and most realistic way to get from one point in space to another is to aim towards your destination and thrust towards it at the highest rate of acceleration practicable until half the distance separating your initial position from the destination has been traversed.  At the halfway point you would reverse your ship's heading and then thrust at the same rate, which will now decrease your speed, until you reach the destination.

    I suppose this maneuver could be described as a "50/50" as the ship accelerates for 50% of it and decelerates for the other half.  The trick for making it work is to know when exactly half of the total distance separating your initial starting position from your destination has been traversed.  The only positional reference Starship Pilot gives you is the distance to the center of the object creating the gravity field the ship is presently in. This by itself makes the gravity-generating object the only thing easy to plot a course for with a "50/50" maneuver... which is not exactly helpful when the object generating the gravity field is a star and/or if your destination is an orbiting satellite (the term "satellite" includes planets and moons, not just made-made orbital objects).  If you have the Orbit Pilot guide handy, however, you will also be able to get an approximate distance between each satellite and the object it orbits.  Now we have a common of point of reference for both your ship's position and that of the satellite (planet/moon/space station, etc.) which is your destination. The question now is how to make these two bits of astrogational data relate to one another. 

     Let's say you were trying to get to a planet that is orbiting a star and you are in the same star's gravitational field.  You know where you are, relative to the star (the radius display), and from the Orbit Pilot you have an idea where the planet is, relative to the star (the "average/estimated distance from" cited for each object).  In a perfect universe, you could deduce from these two bits of data the distance between your ship's position and the planet, perhaps by measuring the angle between the planet and the star and using a sine, cosine or tangent... but there really is not a workable way to measure the angle on a computer monitor.  If, like the present commentator, you are unable to come up with a straight-line distance between your ship and its destination, the best you can do is to break the trip down into two steps. 

   The first step is to place your ship at the same distance from the star as the planet.  For example, let's say you were in the Solar System, with 0 km./sec. velocity, approximately 400,000,000 kilometers from the Sun.  Let's say you want to get to the Earth.  Consulting the Orbit Pilot, you would find that the Earth orbits at an average distance of 150,000,000 km. from the Sun.  This means that you would need to first move 250,000,000 km. straight towards the Sun in order to be in the same general orbit.  You can accomplish this with a "50/50" maneuver by pointing the front end of the ship towards the Sun and, from a stop, firing your engines until exactly half of the 250,000,000 km. had been passed then, after rotating the ship backwards, decelerating for the second half until the ship has come to a stop in approximately the right location.  Let me take this opportunity to reiterate that using the relative stop (SHIFT+S) key combination is not a very authentic way to decelerate.  As space is almost entirely vacuum, there is nothing to generate friction, hence there are NO BRAKES besides your engines and the gravity fields you encounter. 

    Getting back to our scenario, the "50/50" maneuver outlined in the preceding paragraph can be performed from a stop at a distance of 400,000,000 km. from the Sun in the following manner:  First- line the front cross hairs up with the Sun, then fire the engines at three quarters power (37.5 g's) and carefully use the time stasis until the ship's radius from the Sun is equal to the initial radius minus one half of the distance to be traveled (400,000,000 - [250,000,000/2])= 275,000,000 km.).  Once you have reached 275,000,000 km. you would then set the time stasis to 0, rotate the craft so that the back end was pointing towards the Sun, reset the time stasis and keep thrusting until the ship's velocity was down (approximately) to 0 km./sec.  At this point the ship should be about 150,000,000 km. from the Sun (if your initial position is closer to the central star than your destination [i.e., when traveling from Earth to Saturn for example], you may want to get closer to the star before heading for your target's orbit.  Back-tracking the few million kilometers until you reach a few times the star's diameter will ensure that you are closely lined up with the destination and sure beats slogging through a billion or more kilometers later, which you may have to do if the destination planet is on the far side of its orbit from your final position.)

      So now what?  Well, although it is true that bodies in space actually move in more or less elliptical orbits and that the objects they orbit are not necessarily in the exact center of said orbits, for rough calculations we can assume that that now both our ship and the planet we are trying to reach are located on a sphere that encompasses the planet's circular orbit around a centrally located star.  Hmmm... I had better diagram this... 

     Even though we do not know what the measurement of line 1. is, we can still figure out its midpoint by using a little geometry. Assuming that the planet describes a perfectly circular orbit and the star is located exactly in the center of the orbit, then both the ship's position at A. and the planet's at B. will be equidistant from the star at C. (lines 2. and 3.).  Therefore 1., the direct line between A. and B., will be bisected by line 4. from C.  The point where line 4. intercepts line 1. would also be the closest line 1. would come to C.  So, we will know we are at line 1.'s half-way point when the distance between our ship and star C. stops decreasing, as shown by the radius display in the program (the distance to the star will stop going down, and start going up).  The halfway point can also be found by using the program's orbit screen (F3 key). When a gravity-generating object is being passed with a "50/50" manuver the orbit screen will indicate that your ship is at its closest point to the object by displaying your orbit as a straight line, as follows:  

     Needless to say, it does not really work out this smoothly.  As I already pointed out, natural orbits are really elliptical, not circular, and the object being orbited is often not exactly in the center of the orbit.  Another problem is that planets do not sit still, but are rather hurtling along their orbits (in some cases at as much as 50-100 km./sec.).  Oh, and I should probably note that the distances from the Sun given in the Orbit Pilot are mean distances taken from astronomical tables, meaning that the targeted planet could be either closer or farther from the star; and the data for other systems was taken with the computer clock set to 7/01/1990, so it may not be very accurate at all for other dates.  Below are two examples of what would happen if you were to use the above approach on a planet with a highly elliptical orbit: 

      In the example at right you can see that line 2. is much longer than line 3.  If  you accelerate from A. on line 1. until it intersects with line 4. and then reverse, you will go clear past (or possibly collide with) the planet at B. and not come to a stop until you reach point D., leaving a sizable amount of space to backtrack over in order to reach B.. 

      As can be seen above, you may find yourself in a situation where you will want to slow down faster than you originally intended.  For this reason, I would recommend accelerating towards a target planet at 50% to two thirds power (25-33.33 g's) in order to leave some extra boost.  When decelerating you will want to keep an eye on the "xv" course indicator (on the sensor screens) and adjust your course by changing the angle of your thrust to ensure that you are heading straight for the target.  If you overshoot or undershoot a planet, then I would recommend accelerating straight at it until you achieve a velocity of 500 or 1000 km./second, and use the time stasis until you hit its gravity field.  Then reverse course and decelerate to 0 km./sec.  Keep in mind that at full throttle (50 g's) it takes approximately 1 million kilometers of space to go from 1000 to 0 km./sec. and 250,000 km. to go from 500 to 0 km./sec. 

      For more on the distances required for accelerating to/from different velocities, see the appendix on acceleration rates below. 

      Once you have arrived in the destination planet's orbit, you can use the "50/50" to either head for the planet itself, a moon, or an orbital facility such as a space station or dock.  If you are headed for a moon or orbital facility, you would use the "50/50" method just as outlined above- first positioning the ship in the same orbital radius and from there burning for the target until the radius to the planet is no longer decreasing, then reversing the ship and decelerating until the same orbit is achieved again, adjusting for the actual position by further acceleration and deceleration as needed.  You would do the same thing if you needed to go to a moon, but would land as described below. 

     If you wanted to land on a planet's surface, I'd recommend first doing a "50/50" in order to reach a point twice the radius of the planet.  Let's say we were located 750,000 km. from Earth with a velocity of 0 km./sec. and wanted to land at Cape Canaveral.  First we would aim the ship at Earth and calculate the distance.  As Earth has a radius of about 6,400 km., our destination will be a radius of 12,800 km. (remember: Starship Pilot gives radii from the center of the object- aiming for a point with a radius of 12,800 km. from the Earth actually puts you 6,400 km. above the surface).  The distance to accelerate will equal twice the radius of the planet subtracted from the initial radius (your starting position), the result in turn will be divided by two and subtracted from the initial radius.  Expressed mathematically it looks something like this: 750,000 - [(750,000-12,800)/2]= 381,400.  So, you would need to accelerate (I'd recommend no more than 2/3 thrust [33.33 g's]) until you reach a radius of 381,400 km. from the Earth and then flip the ship and decelerate until you arrive at the desired point approximately 12,800 km. from the Earth's center and with a velocity around 0 km./sec. 

    Now kill the engines (F6) and go into a circular orbit (using the thrusters or SHIFT+C) until you can see Cape Canaveral on the short range screen (F4).  Now 0 the time stasis and your veloicity and use the thruster keys (numeric keypad) and orbit screen (F3) to shape an orbit that will allow you to descend towards Cape Canaveral with the goal of reaching a point directly over the port and approximately 100 km. above the planet's surface (6,500 km. radius).  To make adjustments to your path you should frequently 0 the time stasis, consult the orbit screen, and use the thrusters to change your path of descent as needed.  Once you are about 100 km. from the surface you should, hit the landing mode (F7) and use the main engine and thruster keys to bring the ship in for a landing.

      To make a jump to another star system, you can just follow the manual's instructions (Chapter 2.5.3, "Jump Mode" & Chapter 3.3, "Starflight").  On emerging from the jump, 0 the time stasis and adjust the engines to the deceleration rate recommended by the computer in the message box.  Once your ship's speed is down near a halt, then you can either line up for another jump or, using the "50/50" method, set course for a planet or secondary star's orbital distance from the primary star, and then use another "50/50" to reach the planet/secondary star itself. 

      The way the manual tells you to do a jump is alright, if you are not in a hurry, but if you want to shave days off of your interstellar travel time, however, there are a few things you can do a little differently.  The manuvers described below are demanding, so make sure you are fully familiar with the ship's controls in Starship Pilot before attempting them. For starters, you can get to the gate much faster if you start your jump by accelerating towards the gate at full-throttle until your speed is 90 or 95% of light speed and only then reducing your acceleration so that you will reach the speed of light right at the jump gate. What this means is that when beginning your jump you should ignore the computer's recommended rate of acceleration and the "in - track error indicator" and, assuming you can get the "lateral error indicator" lined up, set your acceleration for full throttle (50 g's). If you are unable to get the "lateral error indicator" lined up properly then you should get the indicator's red dot as close to the green circle as you can and set your speed so that the "in - track error indicator" is as closely aligned as possible. Accelerate at this rate (using time-stasis) until you are able to get the "lateral error indicator" aligned- then and only then should you increase your acceleration to 50 g's. With the "lateral error indicator" aligned and your throttle up to 50 g's, you would then run up the time-stasis and wait for your speed to hit either .90 or, if you are feeling cocky, .95 of the speed of light (c). Once you are at .90c or .95c, turn the time-stasis down and then line up on the "in - track error indicator" (make sure you get lined up before you hit .982c, because at that point the ship's computer will start bombarding you with an "abort jump" message and an alarm tone- you can continue your jump, but the constantly-repeating message and sound is a bit annoying).

      As soon as you jump into hyperspace, 0 the time- stasis. You have two options when emerging from a jump- either you can (if you have enough fuel) head for another jump gate or you can set your course for a planet or secondary star in the system. Either way, if you want to get to your destination as fast as possible you will ignore the program's recommended rate of deceleration. If it is your intent to head for another jump gate, following the program's recommended rate of deceleration will lead you on an unnecessarily long detour into the center of the star-system. When you intend to make another jump it will take less time and distance if you fire the engines at a full 50 g's immediately after you emerge from the jump gate and, over the course of a week, bring your velocity down to zero km./sec. (the only exception to this would be if you just emerged into the Asgard system from the BS3607 gate and are headed for Solsys [because of the way the Solsys and BS3607 gates are aligned], in this case you will want to set your thrust to 0 g's and coast at light-speed until your ship is 115 billion kilometers from Alkab A and then decelerate to 0 km./sec. at 50 g's). Once your speed is canceled out you can then line up your heading for another jump and accelerate for it at 50 g's (assuming you are able to get the "lateral error indicator" to line up, if not, do as described in the preceding paragraph) and then repeat the process of lining up the "in - track error indicator" once you reach .90/.95c. When using this method for passing through a star system, you must keep in mind that the green crosshair "visual gate" for the destination jump gate will be quite a bit off from your actual heading to the gate. This is because the "visual gate" is lined up with the center of the star system (the primary star itself) and not your ship's position, so the "visual gate" only appears to line up with the jump gate if you are relatively close to the primary star. When performing this maneuver depend on the "lateral error indicator," and not the "visual gate" for a true bearing to the destination jump gate!

      If you have emerged from a jump and intend to head for a planet or secondary star, you can get there the fastest by coasting at light-speed for as long as possible instead of following the program's recommended rate of deceleration. To do this you would set your thrust to 0 g's and coast (using time-stasis) at light-speed until you are 92 billion kilometers from the orbit of your destination planet/star. This is because at 50 g's it takes a little less than 92 billion km. to decelerate from light-speed to 0 km./sec. Using this technique when inbound from a jump gate for a planet or secondary star you would add the planet/star's distance from the primary star (taken from the Orbit Pilot) to 92 billion km. and wait until your ship reaches that point before engaging the engines at full-50 g's-power. After upping the time-stasis you would watch your speed decrease before making a thrust-correction at a lower speed, such as 1 percent of light-speed (3,000 km./sec.). To make such a thrust-correction, you would 0 the time-stasis when your velocity indicator displayed 3,000 km./sec. and then subtract the distance from the orbit of your destination planet/star from your present position. If you take the result (in millions of kilometers) and divide the number 459 by it, the end result will be the approximate number of g's you will need to decelerate at to be close to your desired destination by the time your velocity reaches 0 km./sec.

     For example, if you had just emerged in the Solar System from the BS2943 jump gate (located 126.321 billion km. from the Sun) and had Earth as your destination, you would shut down the engine (F6) right after emerging from the gate. You would then coast along until you reached Earth's distance from the Sun plus 92 bill. km. As Earth orbits the Sun at a mean distance of 150 million kilometers (= 0.15 billion km.), the point where you would begin your deceleration (at 50 g's) would be at 92.15 bill. km. from the Sun. You would continue to decelerate at 50 g's until your speed reached 3,000 km./sec. After setting the time-stasis to 0 at 3,000 km./sec., you would find that you were now positioned something like 175.341 million kilometers from the Sun. Next you would subtract from this the distance between Earth and the Sun, 150 mill. km., which would give you 25.341 mill. km. Dividing 459 by 25.341 produces the result of 18.11, the number of g's you need to decelerate at in order to end up with a velocity of 0 km./sec. at a point 150 mill. km. from the Sun. The closest the program will let you come to setting 18.11 g's is 18.09. After setting your thrust to 18.09 g's and turning the time-stasis back up, you will find that you will overshoot the mark a little bit, so you will come to a halt at 149.895 mill. km. from the Sun. This is close enough to Earth's orbit to make a "50/50" straight for Earth practical. For more on calculating rates of deceleration, see the appendix below.

     As the workings of Starship Pilot are based on real-life physics, the motion of everything can be calculated with real-life formulas. The most useful textbook formula is that used for calculating linear acceleration:

      Depending on which variables you have information for, the formula can be used to solve for either a rate of acceleration, the distance it will take to go from one velocity to another, or how fast an object will be traveling either before or after accelerating at a given rate over a given distance.

      For example, say you were on a course straight for Mars at a distance of 424,210 km. with a velocity of 300 km./sec. You want to reach a point 6,800 km. from Mars' center, but do not know how many g's to decelerate at. First, you would subtract 6,800 km. (your destination) from 424,210 km. (your starting point), giving you 417,410 km. Now we use the formula:

      Here is another example, where we want to know how much distance will be needed to decelerate from 500 km./sec. to 0 km./sec. at 50 g's. In this case the final velocity (v_f) = 0 km./sec., initial velocity (v_i) = 500 km./sec., acceleration (a) = -0.49 km./sec.² (50 g = 490 m./sec.² = 0.49 km./sec.²) and the distance (d) is the unknown we are trying to solve for.  Plugging these values into the formula we get:

      For ease-of-reference, listed below are a few pre-figured factors for calculating decelerating/acceleration and the distances required to come to a halt at 50 g's from given velocities. For the following, "c" = the speed of light, "d" = distance and "a" equals the rate of acceleration, in g's. Unless otherwise indicated, "d" is for the distance in billions of kilometers.