Imperial Metric and Astronomical Lengths

The Imperial, Metric and Astronomical Lengths function evaluates an input length of any units and returns the comparable value in largest possible units that are not fractions in Imperial Units, Metric Units and Astronomical Units.

INSTRUCTIONS: Choose units and enter the following:

• (LD) Length or Distance

Imperial and Metric Units (IMU):  The calculator returns the length in the largest non-fractional Imperial and Metric units, and if large enough, astronomical units (see below).

The Math / Science

This function returns a list with the equivalent value of LD in both Imperial and Metric units where the output unit is the smallest unit that is not a fraction.  If L is great enough, larger than a light minute, the calculator also returns L in astronomical units.  

Metric Units

• nm - nanometer
• mm - millimeter
• cm - centimeter
• m - meter
• km - kilometer

Imperial Units

• mil - mils are 1/1000th of an inch
• in - inch
• ft - feet
• yd - yards
• mi - miles

Astronomy Distance Units

Astronomical Unit (au): Within our solar system, a common measure of distance is au, which stands for astronomical units.  A single astronomical unit is the mean distance from the Sun's center to the center of the Earth. The following picture is NOT to scale.

Light Travel in Time: Light is a primary observable when studying celestial bodies.  For this reason, the distance to these objects are measured in the amount of time it would take light to travel from there to the Earth.  We can say that an object is one light-year away, and that means that the object is at a distance where it took an entire year for light from the object to travel to Earth.  Since the speed of light is 299,792,458.0 meters per second, one can compute the distance equal to a light year as follows:

1 light year = 299,792,458.0 (meters / second) x 31,536,000 (seconds / year) = 9,460,528,405,000,000 meters

The same exercise can be used for light traveling shorter periods of times, light seconds, light minutes, light hours and light days.  Since even these units are not enough when computing distances across the universe, there is also a light relative distance of kilo-light years (1000 light years), or the distance light travels in a thousand years!

Angle Shift Seen from Earth: Because the Earth goes around the Sun, our observation of distant objects such as stars results in an angular shift when observed at opposite sides of the elliptical orbit.  This shift is used as the basis of a unit knows as a parsec.  A parsec was traditionally defined as the distance where one astronomical unit subtends an angle of one arcsecond.  A parsec was redefined in 2015 to 648000/π astronomical units.  Proxima Centauri, is the nearest star to the Sun and is approximately 1.3 parsecs (4.2 light-years) from the Sun. A mega-parsec is a million parsecs.

Sub Routine Methodology

To use this function to provide the optimal outputs, use the following code structure:

def IMAL = []
IMAL = execEquation("627da9b2-66b3-11ee-b65f-bc764e203090",L) //Imperial, Metric and Astronomical Lengths

IMAL.each{
  oP << it
  }