/// <summary>
/// This calculates the downward force(Weight that you feel) due to Acceleration due to "pushing forward" in your own time gradient
/// This assumes the massBody is not in any other Time Gradients except for the one produced by acceleration
/// Where? At the Center of Mass?
/// </summary>
/// <param name="massBody">This is the "inertial mass"</param>
/// <param name="accelerationMetersPerSecondSquared"></param>
/// <returns></returns>
public static double WeightForceDueToAcceleration(this MassBody massBody, double accelerationMetersPerSecondSquared = 0, double initialVelocity_ms = 0)
{
var lorentzFactor = LorentzFormula.IncreaseDueToVelocity_LorentzFactor_Gamma(initialVelocity_ms);//at low speeds, this is 1, at close to C, this approaches infinity
//This insinuates that as you get closer to C, you can't accelerate very fast or you'll get crushed
return(massBody.Mass * lorentzFactor * accelerationMetersPerSecondSquared);
}
/// <summary>
/// This calculates the downward force due to Gravity / Time Gradient
/// This does not currently contain the lorentzFactor to account for any velocity or acceleration
/// </summary>
/// <param name="massBody1"></param>
/// <param name="massBody2"></param>
/// <param name="additionalDistanceBeyondRadii"></param>
/// <returns></returns>
public static double WeightForceDueToMass(this MassBody massBody1, MassBody massBody2, double additionalDistanceBeyondRadii = 0)
{
var distanceBetweenCenters = massBody1.Radius + massBody2.Radius + additionalDistanceBeyondRadii;
var mass = massBody1.Mass * massBody2.Mass;
var distanceBetweenCentersSquared = (distanceBetweenCenters * distanceBetweenCenters);
return((Constants.GRAVITATIONAL_CONSTANT_nm2kg2 * mass) / distanceBetweenCentersSquared);
}
//*********************************************************
public static double TotalEnergyOfMovingMass(this MassBody massBody, double velocity_ms)
{
var massComponent = (massBody.Mass * massBody.Mass) * Constants.SPEED_OF_LIGHT_SQUARED_ms;
var momentum = MomentumForceDueToVelocity(massBody, velocity_ms);
var momentumComponent = (momentum * momentum) * Constants.SPEED_OF_LIGHT_SQUARED_ms;
return(Math.Sqrt(massComponent + momentumComponent));
}
/// <summary>
/// Top level method for deterimining Time Gradient an object is "in".
/// Calculates the time gradient due to proximity to a Mass, as well as to the object's own acceleration
/// (check this. Could be double calculating based on Acceleration, and then Velocity on the next line)
/// </summary>
/// <param name="massBody1"></param>
/// <param name="massBody2"></param>
/// <param name="additionalDistanceBeyondRadii"></param>
/// <returns></returns>
public static MassBody CalculateTimeDilation(this MassBody massBody1, MassBody massBody2 = null, double additionalDistanceBeyondRadii = 0)
{
var massDilation = 1 - (massBody2 != null ? massBody1.GetTimeDilationFactorDueToMass(massBody2, additionalDistanceBeyondRadii) : 1);
var velocityDilation = 1 - GetTimeDilationFactorDueToVelocity(massBody1.Velocity);
var returnMassBody = massBody1.Copy();
returnMassBody.TimeDilation = 1 - massDilation - velocityDilation;
return(returnMassBody);
}
/// <summary>
///
/// T' = T * Sqrt( 1 - (2gR/C_squared))
/// </summary>
/// <param name="massBody1">
/// .Radius - in Meters
/// .Mass - in Kilograms
/// .Acceleration - in Meters / Second squared
/// </param>
/// <param name="massBody2">
/// .Radius - in Meters
/// .Mass - in Kilograms
/// </param>
/// <param name="additionalDistanceBeyondRadii">in Meters</param>
/// <returns></returns>
public static double GetTimeDilationFactorDueToMass(this MassBody massBody1, MassBody massBody2, double additionalDistanceBeyondRadii = 0)
{
var unDilatedTime = 1; //I know this is unnecessary, but it makes it easier to relate the formula back to relativity formulas
var velocityMetersPerSecondSquared = massBody1.CalculateWeightForce(massBody2, additionalDistanceBeyondRadii).WeightForce; //This needs to be the velocity at that point in space, or on the surface.
//This is actually the Lorentz Factor/Gamma, with the "2 * radius" multiplied in. Why? Why (2 * radius)?
//See LorentzFormula.cs line 17-43 ish
//var radius = massBody1.Radius + massBody2.Radius + additionalDistanceBeyondRadii;
//var dilatedTime = unDilatedTime * Math.Sqrt(1 - ((2 * radius * velocityMetersPerSecondSquared) / Constants.SPEED_OF_LIGHT_SQUARED_ms));
//Mws: this was wrong above. Should be
var dilatedTime = unDilatedTime * Math.Sqrt(1 - ((2 * velocityMetersPerSecondSquared) / Constants.SPEED_OF_LIGHT_SQUARED_ms));
return(dilatedTime);
}
//If a mass is experiencing Acceleration / Weight Force / Centrifugal Force, etc, it is not centered within the Time Gradient affecting it
//This is simplified. The acceleration should really be a 3D vector in relationship to the vector between the 2 centers of mass
public static MassBody CalculateWeightForce(this MassBody massBody1, MassBody massBody2 = null, double additionalDistanceBeyondRadii = 0)
{
//Should we overwrite any weightforce already in here?
var returnMassBody = massBody1.Copy();
if (massBody2 != null)
{
returnMassBody.WeightForce += WeightForceDueToMass(massBody1, massBody2, additionalDistanceBeyondRadii);
}
if (massBody1.Acceleration > 0)
{
returnMassBody.WeightForce += WeightForceDueToAcceleration(massBody1, massBody1.Acceleration, 0);
}
return(returnMassBody);
}
/// <summary>
/// This calculates the momentum that you have from a constant speed. you won't feel "weight" unless you are in another time gradient
/// </summary>
/// <param name="massBody"></param>
/// <param name="velocity_ms"></param>
/// <returns></returns>
public static double MomentumForceDueToVelocity(this MassBody massBody, double velocity_ms)
{
var lorentzFactor = LorentzFormula.IncreaseDueToVelocity_LorentzFactor_Gamma(velocity_ms);//at low speeds, this is 1, at close to C, this approaches infinity
return(massBody.Mass * lorentzFactor * velocity_ms);
}