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# relativity

Arduino library with relativity functions.


## Description

This experimental library implements a number of functions that give an
indication of the time dilation etcetera due to relativistic speed.

Goal: Educational purposes or when one puts a cube-sat into space :)


## Interface

- **relativity()** constructor.
- **double getC()** returns speed of light.
- **double getG()** returns gravitational constant.
- **double factor(double speed)** returns sqrt(1-v2/c2).
- **double gamma(double speed)** returns 1/sqrt(1-v2/c2).
- **double relativeTime(double time, double speed)** returns the relative time for given time and speed.
- **double relativeLength(double length, double speed)** returns the relative length for given length and speed.
- **double relativeMass(double mass, double speed)** returns the relative mass for given mass and speed.
- **double EnergyMass(double mass, double speed)** returns the energyMass for given mass and speed. Think E = mc^2.


### Caching variants

These functions are the same however the math to calculate a given factor and gamma is done only once and cached. 
So these functions will perform a bit better, especially if floating point is slow.

- **void setSpeed(double speed = 0)** set the speed and calculate the factor and gamma to minimize math for next functions.
- **double getSpeed()** returns speed set.
- **double getFactor()** returns factor for speed set.
- **double getGamma()** returns gamma for speed set.
- **double relativeTime(double time)** returns the relative time for speed set with **setSpeed()**.
- **double relativeLength(double length)** returns the relative length for speed set.
- **double relativeMass(double mass)** returns the relative mass for speed set.
- **double EnergyMass(double mass)** returns the energy mass for for speed set.


### Gravity effects

- **double gravitationalTime(double time, double speed)** returns time dilation due to gravitational effects.
- **double diameterEarth(double longitude = 45)** calculates the diameter of the Earth given it is not a nice 
circle but more an ellipse, flatter on the poles and thicker on the equator.
Longitude is in degrees -90 .. 90.
- **double getPlanetMass(uint8_t n)** returns planet mass in **kg** 
where parameter n: 0 = Sun, 1 = Mercury etc.
- **double getPlanetRadius(uint8_t n)** returns planet radius in **km** 
where parameter n: 0 = Sun, 1 = Mercury etc.


## Operations

See examples for typical usage.


## Future

- test test test test
- add more functions
- fix some overflow conditions.
- add moons?
- add caching version of mass / radius;