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# relativity

Arduino library with relativity functions.


## Description

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

Goal: Educational purposes or when one puts a cubesat 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 function will perform a bit better, especially if floating point is slow.

- **void setSpeed(double speed = 0)** set the speed once and calculate the factor and gamma to minimize math for next functions. Think caching.
- **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(uint8_t 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 (absolute) degrees.
- **double getPlanetMass(uint8_t n)** returns planet mass in **kg** 
where param n: 0 = Sun, 1 = Mercury etc
- **double getPlanetRadius(uint8_t n)** returns planet radius in **km** 
where param 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;