Arduino library with relativity functions.

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 :)

#include "relativity.h"

• 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.

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.

• 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.

See examples for typical usage.

• documentation

• test test test test

• Split .h into .h and .cpp
• add more functions
  • Schwarzschild horizon etc
• fix some overflow conditions.
• add moons?
  • need a database :)
• add caching version of mass / radius;
• move code to .cpp

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Thank you,