Introduction

Astrometrics Library
The astrometrics library extract parameterizes basic stellar and planetary classification systems for cataloguing and archiving astronomical phenomena into the stellar cartography database. Additionally, baseline information on units of measure for quantifying physical aspects of the universe are also provided to give users a rudimentary understanding of distance, mass, and time in scientific terms.

Units

Basic Units of Measure
The three fundamental units of measure are distance, mass, and time. They are considered “fundamental” because all other units of measure in the universe rely on them. The units of measure used within Starfleet and the Federation are based on the Terran metric system. They are: the meter, the gram, and the minute. When used together in various permutations, we achieve the basis for measuring the known (and unknown) universe around us. As examples, speed is distance over time, while volume is a cubic variation of distance. Additional examples include density: a fundamental measure of chemical substances that is a combination of mass and volume, while gravity is a measure of force that's determined by the distance between two objects of mass. Altogether, the fundamental units of measure permit definition of our universe, and forms the basis upon which science and mathematics are built.

Distance

Scientifically, the most efficient way to establish a unit of distance is to find a global (or universal) distance and divide it into smaller units using powers of ten (10) as a denominator or multiplier (ten represents a mathematical change in decimal place). On Earth, the original distance used for the metric system was the distance between the north pole and the equator, which was then divided into 10 million smaller units, and signified the base unit of measure: the meter. Since most life-bearing worlds that play host to a scientifically enlightened species are roughly the same size as Earth, most of them used a version the meter based on some rudimentary aspect of their home world. While a meter equates to 10 million delineations of the distance between Earth's north pole and equator, the metric system dictates the use of multiples of ten to define larger and smaller delineations in order to measure macro and micro distances, respectively. While there are limitless extrapolations of the meter via multiples of ten, the eight most common are as follows:

Mass

The fundamental unit of of mass – the gram – is based on the density of a universally known substance that is a primary component for all carbon-based life: water. Most species in the galaxy that have evolved into civilizations capable of space travel use a similar or exact water-based system of measurement. This may seem like an amazing coincidence, but cultures that attain scientific enlightenment soon learn that water, with it's special and unique properties, is required for life to exist at all. Therefore, water is often used to establish a universal measuring system early in a civilization's development, as it is a natural choice on which to base a unit of measure. It all begins with this simple mathematical formula:

Mass = Density × Volume

One aliquot of water that measures one (1) centimeter cubed equates to a density of one (1) at 1 atmosphere of pressure and a temperature of 3.98°C (the temperature of water at its largest mass-to-volume ratio). This, subsequently, equates to a mass of one (1) gram. Other substances are defined by a change in their density at a specific temperature and pressure. A lower density is dictated for substances of less mass (e.g., Helium = 0.145 grams per cubic centimeter at it's melting point), while a higher density for substances of greater mass (e.g., Lead = 10.66 grams per cubic centimeter at it's melting point). Like distance, there are nearly limitless expressions of the gram in order to express heavier and lighter masses via multiples of ten, the eight most common are as follows:

Time

The base unit of time – the minute – is established by the vibration frequency of the cesium-133 atom at a temperature of zero Kelvin (-273.15°C), which is exactly 483,495,660,575 vibrations from the ground state of the isotope to a hyperfine energy level (expressed as Δv_Cs). This is the most stable and reproducible phenomena in nature, as it is accurate over a time span of hundreds of millions of years.

Minutes form the basis of the stardate time measurement system in Starfleet and the Federation, and extensions of the minute include days (600 minutes equals one day) and years (600,000 minutes equals one year). Subsequently, a day is 290,097,396,344,952 vibrations of the Cs-133 atom, and a year 1000 times that. Seconds and hours are considered subsidiary to the minute due to the diversity of planetary dynamics between the worlds of the Federation, where some planets rotate faster or slower than others. Therefore, they are used only in the context on maintaining a circadian rhythm aboard a Starfleet vessel, allowing them to synchronize to a common standard across the fleet. For these purposes, and due to the fact that Starfleet was originally an Earth-centric organization, a second is considered one-sixtieth of a minute, and an hour sixty times that of a minute. This allows for a day to remain an easily convertible metric from hours (10 hours equals a day), and a minute to continue an Earth tradition of being sixty seconds. There are no delineations for weeks or months in the stardate time measurement system.

In Starfleet, it is very common for starships to continue utilizing a 24-hour clock for establishing daily schedules and routines, and then switch to stardates for multi-day events and log entries. Aboard a Starfleet vessel with a mostly humanoid crew, a single “day” is still colloquially referred to as a normal day/night schedule in order to maintain a circadian rhythm, which will equal to approximately 2.74 days under the stardate measure. The same can be said for weeks and months, where the 7-day week based on Hellenistic astrology from Terran history is still occasionally used by the crew to breakup the monotony of 1000-day year in the stardate system. In fact, a stardate “day” will often coincide with a shift change on starship, which happens roughly every 8.767 hours on the 24-hour Terran clock. Normally, it is up to the skipper to define whether that shift change occurs on the Terran or the stardate system. Regardless, all official ship business is required to be recorded in the stardate system.

Below is a table defining the stardate time measurement system in comparison to the Terran system:

Measures

Astronomical Measurements
While the meter and kilometer are useful length measures for starship and planetary scales, it becomes cumbersome for interplanetary, interstellar, and intra-galactic distance measurements. This is because the space between most celestial objects is so vast that scalars such as the kilometer easily reach to the millions even between relatively close objects such as between the Earth and the Sun. For these distances and longer, it is sometimes more preferable to utilize units of measure such as the astronomical unit (AU), light year, and parsec as defined below.

ASTRONOMICAL UNIT (AU): The average distance between the Earth (Terra, Sol III) and the sun (Sol). 1 AU = 144 million kilometers

LIGHT YEAR: The distance that light travels in a vacuum in one Earth year 1 Light Year = 9.46 trillion kilometers

PARSEC: The distance at which 1 AU perpendicular to the observers line of site substended at an angle of 1 arc second (see diagram at left). 1 parsec = 30.8396 trillion kilometers

Star Classes

Stellar Classification System
A star radiates not only visual light, but an entire spectrum of electromagnetic radiation separated in space with different wavelengths ranging from short (gamma rays) to long (radio waves). The spectrogram of a star reveals spectral lines that identify the chemical substances within it. For the most part, stars contain hydrogen and helium, with a very small percentage of other substances such as metals. Stars, under the force of gravity, convert hydrogen into helium in a process called nuclear fusion, resulting in the electromagnetic radiation mentioned above. This includes infrared radiation (heat), and the actual surface temperature of a star can be determined by the color of the visual light it radiates. Colors, ranging from blue to red, culminate the SPECTRAL CLASS of a star and are scientifically delineated into 70 separate units as outlined below. Temperatures are reported in KELVIN (K), which is a version of the Celsius scale (1 Kelvin = -273° Celsius).

O0 to O9 = Blue (Surface Temperature: 28,000 K to 50,000 K)
B0 to B9 = Light Blue (Surface Temperature: 10,000 K to 28,000 K)
A0 to A9 = White (Surface Temperature: 7,500 K to 10,000 K)
F0 to F9 = Light Yellow (Surface Temperature: 6,000 K to 7,500 K)
G0 to G9 = Yellow (Surface Temperature: 5,000 K to 6,000 K)
K0 to K9 = Orange (Surface Temperature: 3,500 K to 5,000 K)
M0 to M9 = Red (Surface Temperature: 2,500 K to 3,500 K)


Luminosity Class and Energy
A star's luminosity is a measure of the rate at which electromagnetic radiation is emitted from it's surface. This a function of how much hydrogen is converted into helium in the process of nuclear fusion, which is in turn, a function of it's size. Although, because of surface temperature, luminosity and size are not perfectly proportional to one another. Therefore, the LUMINOSITY CLASS categorizes stars according to both size and energy output in the following classifications:

Luminosity Class I = Supergiants
Luminosity Class II = Bright Giants
Luminosity Class III = Giants
Luminosity Class IV = Subgiants
Luminosity Class V = Main Sequence Stars

Other objects that are the remnants of stars; such as white dwarfs, red dwarfs, and brown dwarfs; have luminosity classes of VI and VII, but are no longer fully functioning stars. Likewise, though very rare, stars greater in size than supergiant (Luminosity Class I), are far and few between, and classified as “hypergiants” (Luminosity Class 0). There are only a handful of known hypergiants, and are technically classified as variable stars (stars with energy outputs that fluctuate), and occassionally register with energy outputs that fall into the supergiant category, and recorded as such.

The H-R Diagram
The Hertzsprung-Russell Diagram, or H-R Diagram, was first invented on 20th century Earth and incorporates both Spectral Class and Luminosity Class to classify any particular star according to the properties mentioned above. Sol is identified near the center of the diagram, and shows an example of the final stellar classification notation using Spectral Class (Sol = G2) and Luminosity Class (Sol = V) in combination. Note that a Luminosity (L) of 1 is equal to the energy of Earth's sun (390,000,000,000,000,000,000,000,000 watts), and is stepped up or down by a factor of “powers” (e.g., 2 L is second power, 4 L is fourth power, 6 L is sixth power, and so forth). Similarly, a Radius (R) of 1 is equal to the radius of Earth's sun (260,000,000 kilometers).

Planet Classes

Planetary Classification System
There are far too many varieties of planets in the galaxy for one classification system to accurately represent all of them. However, when a Starfleet vessel encounters a new one, a preliminary notation is assigned to it that supplies general information. Later, after a full survey is completed (if possible), more specific data and information is entered into the Starfleet Planetary Database including indigenous names if sentient life exists in the system. Below is the general planetary classification system used by Starfleet.

The classes above are identified with an alphabetic notation, and each fall into one of four generic superclasses: Lithic, Biotic, Aeric, Xenic. Lithic planets are the most common, and their most notable attributes deal with their geologic features as they most often lack any atmosphere, surface water, or biological organisms. Biotic planets are characterized by their ability to harbor carbon-based life, and as such, host some sort of hydrosphere and atmosphere. Aeric planets encompass all gas giants, and are the most common planets next to Lithic; they always lack a solid surface and liquid water. Xenic planets are the “catch-all” planetary superclass, as their major features are either undetectable without a detailed survey, or their features are so dynamic that they change drastically on a random basis.

System Position
A planet's position in a star system is indicative of whether or not the planet is habitable for carbon-based life. This varies according to the energy output of the star, or stars, of which the system is based. The sphere of habitation, or “Ecosphere”, dictates the boundary for the “Hot Zone” (the area closest to the star where temperatures are too hot for planets to sustain life) and the “Cold Zone” (the area of the system beyond the ecosphere where it is too cold for planets to sustain life).

Atmosphere: A true planetary atmosphere relies on gravity, their distance from their star, and a defense against solar wind such as a magnetic field. There are some planets that have an intermittent atmosphere due to orbital variances. The general rule of thumb for the common astrometrics officer is that if a planet retains elements or compounds in gaseous form close to its surface for more than half of it's solar year, it is considered to have an atmosphere.

Hydrosphere: Normally found only on biotic worlds, the hydrosphere refers to the amount of surface water in liquid form, or sometimes solid form (ice) depending upon the abundance. In general, if a normally lithic planet has only a few scarce pockets of solid ice, it is not considered a true hydrosphere (eg: Luna). However, if solid ice consists more than a fourth of it's surface, it is categorized as having a hydrosphere (eg: Europa).

Biosphere: This refers to the ability of a planet to sustain carbon-based life. Water is a key ingredient for this, and so, Biotic planets tend to have some sort of hydrosphere. A planet's biosphere is described by the number of different climatic biomes it has, the species diversity in those biomes, and whether those species are of a high complexity (eg: birds, mammals, etc.), or of simple lifeforms (eg: non-vascular plants and microbes). This can vary to some degree for classification purposes.

Lithosphere: This refers to the solid structure of the planet and it's composition. For the most part, lithospheres are composed of iron and/or silicates. Iron is more common among planets without life, while silicon is found most often on biotic planets. Granite and basalt are the normal forms of iron and silicate, and depending upon the atmosphere (assuming it has one), these minerals may be partially oxidized. Volcanically active planets may have a partial or fully molten lithosphere, but a lithosphere nonetheless. Gas giants generally do not have a lithosphere.

Interstellar Travel

Interstellar Travel Times
Without the influence of gravity, the speed of light through the vacuum of outer space is a constant 300,000 kilometers per second. Although there are energies and sub-nuclear particles that can exceed this, the speed of light is considered a universal axiom. However, gravity has control over not just speed, but also the vector of a light particle (also called a “photon”). There are very few natural phenomena that can move faster than this, unless there is an enormous amount of matter (gravitational mass) affecting it. Some phenomena, such as black holes (the result of a supergiant star collapsing in on itself) exert so much gravitational influence, that light is only absorbed and cannot be reflected away, hence the name.

Today, with the advent of warp drive, it is possible to artificially exceed the speed of light. By using the energy produced by a dilithium-mediated matter/antimatter reaction, the fabric of space can be bent, or warped, forcing it to act like an artificial gravity well for matter and energy. In this way, a vessel can use a standard fusion engine or ion-propulsion system to cross this “warped” space resulting in travel time vastly shorter than if it occurred in “unwarped” space. Depending upon how carefully the matter/antimatter reaction is controlled, the amount of warped space can be increased resulting in even shorter travel times. However, there is an upper limit of how much space can be artificially warped. This is known as the “warp barrier.”

Below is a listing of travel times under the different possible warp speeds that space vessels may travel. The lightspeed multiplier refers to how many times the speed of light that that particular warp speed is. Warp factor 0.5 is approximately twice that of full impulse speed. Warp factor 9.9999 is approximately the speed of subspace radio. Until recently, warp factor 10 was considered impossible due to the Theory of Infinite Velocity, as a starship traveling at such as speed would mathematically exist in every location of the universe at once. However, it is now known that this speed is technically achievable, but has deleterious effects on all biological lifeforms. Regardless, warp 10 is included as a reference.

It should be noted the calculations of “warp factor” changed during the last two decades of the 23rd century to take into account the advent of transwarp theory and adjustments necessitated by the realization that there was a mathematical upper limit to standard warp speed calculations. By the start of the 24th century, warp field calculations had been refined to such a degree that the old warp factor scale (known as the “Cochrane Scale”) had been rendered obsolete, and the new warp factor scale became the accepted standard. While the differences are minor at low warp speeds (warp 1 through 4), the scales diverge moderately between warp 5 and 9, and become completely incomparable beyond warp 9.