## Why Use the Calculators?

Science fiction (especially hard scifi) can include ships and other objects maneuvering or just traveling through space. These objects might be involved in a complicated battle scene or just there waiting to be hit by something else. If you try to rely on your common sense, you’re bound to screw things up and someone more versed in the science of high-speed moving objects is going to call you out on your mistake. The calculators are used to keep the science in your stories as close to reality as possible.

I do all my calculations in the metric system primarily because I write for an international audience and because I fervently hope that the American system of measurement will eventually be replaced with the more scientific metric system used by the rest of the world. All scientists these days use the metric system for all their calculations. The mixing of metric and American systems of measurement resulted in the destruction of the \$125 million Mars Climate Orbiter.

## Units of Measurement

Most people confuse energy and power, thinking they are equivalent--they are not!

ENERGY
Energy is a measure of the ability to do work. There are several types of energy that can be measured. Some well known examples are: Potential (the energy of an object at rest at a specific height); Kinetic (the energy associated with an object in motion); Mass (the amount of energy contained in the mass of an object). Energy is measured in joules in the metric system.

POWER
Power is the amount of energy expended per unit of time. A single watt of power, for example, is one Joule of energy being expended every second.

## Distance in Kilometers given a constant acceleration in Gs

One of the things a ship must do to maneuver is accelerate. The equation I’ve provided for this not only gives you the distance that will be traveled at the end of the specified period of acceleration, but it also calculates the ship’s final velocity in kilometers per second and as a fraction of the speed of light. This is a non-relativistic equation and it does not take into account any of the effects of relativity. As such, it will be accurate enough for use in your book as long as you keep the final speed at something under 50% light speed.

One good use I’ve found for this equation is to calculate the final velocity of a high-speed missile that’s capable of accelerations of 3,000 Gs (a hypervelocity missile). With only 30 seconds of fuel, the missile can achieve a final speed of 882 Km/sec and it will have run out of fuel at a distance of 13,230 kilometers from its point of origin.

Distance in light years traveled given speed in C and time

This is an essential equation if the ships in your story are capable of faster than light travel. Simply plug in the ship’s speed as a multiple of the speed of light and how long the ship is moving at that speed. If you fill in the time in hours, the code will convert this into the equivalent days and vice-versa. The distance traveled in light years is shown as the result.

## Time required to travel x light years given speed in C

You can use this equation if you want to know how long it will take a ship traveling at a specific multiple of light speed to reach a destination that is light-years away. The result is presented in human-understandable terms. Another use for this equation is showing people just how vast space really is. For example; The nearest star is 4.3 light-years away. If we could build a ship that could achieve a speed of 25 times the speed of light it would take us about 62 days 18 hours to get there.

## Time required to travel x kilometers given a constant acceleration in Gs assuming no deceleration

This is a non-relativistic equation and should only be used for final speeds that do not approach a significant fraction of the speed of light. This equation is designed to be used to assist the author in calculating in-system maneuvers. The result is presented in human-understandable terms.

## Relativistic time to travel x light-years at constant acceleration in Gs

This is an incredibly interesting calculation that can be used to calculate ship time and point of origin time for a ship that never exceeds the speed of light. The important point to remember when using this equation is that the amount of acceleration is what is felt by the passengers of the ship, not what is measured by the people left behind. One prime use of this equation would be in calculating how long it takes for a generation ship to travel to another star system as measured both by the people who built it and the people who are on board.

## Time dilation given fractional speed in C

If you do have a situation where a ship is traveling at a good fraction of the speed of light, you can use this equation to determine how the speed affects the clocks on the ship. The effects are minimal until you get very close to the speed of light. For example, at 50% light speed, and hour becomes about 52 minutes.

## Power required to accelerate a given mass

Unless you are using some type of exotic propulsion system (or you want to flagrantly violate the laws of physics) it takes a lot of power to start a large mass moving. A 90,000 ton battleship would require the expenditure of 3.9 gigawatts of power to provide the crew with a constant 1G of acceleration. If your spaceships are huge and they are maneuvering in a battle, they’ll be consuming vast amounts of energy.

## Equivalent kinetic energy of a moving object in kilotons

What happens if the International Space Station were to hit a stationary object? Well, that depends on how you define stationary. Kinetic energy is a relative measurement. The ISS orbits the earth at 7.66 kilometers per second. If it were to hit the Earth at that relative speed it would be equivalent to a 2.9 kiloton bomb minus all the radiation. Kinetic energy is converted to heat during a collision. But it can also transfer that kinetic energy in other forms. One prime example is an object slamming into a force field. A large enough impact should tear the shield generator off its mounts.

## Round trip time of a light-speed signal

If the characters in your story are sending messages via laser beams, microwaves, or any other light-speed communications, there’s going to be a noticeable time lag between asking a question and receiving an answer if the distance is too great. To ensure you get it right, plug the distance into this calculator.

## Distance between two stars

It’s not difficult to look up the distance from Earth to a nearby star. But how do you calculate the distance between two such stars? The answer is a three-dimensional distance calculator. Since our point of reference is Earth, the calculator must be able to compute the distance between two stars given their coordinate in space from Earth. These coordinate are given using right ascension, declination, and distance. After plugging all this data (as accurately as possible) into the calculator, the distance between the two stars can be determined.