/// <summary>
/// Fogg's information for this routine came from Dole "Habitable Planets
/// for Man", Blaisdell Publishing Company, NY, 1964. From this, he came
/// up with his eq.12, which is the equation for the base_angular_velocity
/// below. Going a bit further, he found an equation for the change in
/// angular velocity per time (dw/dt) from P. Goldreich and S. Soter's paper
/// "Q in the Solar System" in Icarus, vol 5, pp.375-389 (1966). Comparing
/// to the change in angular velocity for the Earth, we can come up with an
/// approximation for our new planet (his eq.13) and take that into account.
/// </summary>
public static Double DayLength(ref SolarSystem system, Double mass, Double radius, Double orbital_period, Double eccentricity, Boolean giant)
{
system.spin_resonance = false;
Double k2 = giant ? 0.24 : 0.33;
Double planetary_mass_in_grams = mass * Constants.SOLAR_MASS_IN_GRAMS;
Double equatorial_radius_in_cm = radius * Constants.CM_PER_KM;
Double base_angular_velocity = Math.Sqrt(2.0 * Constants.J * (planetary_mass_in_grams) / (k2 * Math.Pow(equatorial_radius_in_cm, 2.0)));
/* This next term describes how much a planet's rotation is slowed by */
/* it's moons. Find out what dw/dt is after figuring out Goldreich and */
/* Soter's Q'. */
Double change_in_angular_velocity = 0.0;
Double temp = base_angular_velocity + (change_in_angular_velocity * system.age);
/* 'temp' is now the angular velocity. Now we change from rad/sec to */
/* hours/rotation. */
temp = 1.0 / ((temp / SolarSystem.radians_per_rotation) * Constants.SECONDS_PER_HOUR);
if (!(temp >= orbital_period))
{
return(temp);
}
Double spin_resonance_period = ((1.0 - eccentricity) / (1.0 + eccentricity)) * orbital_period;
system.Callback("...maybe: " + spin_resonance_period + "\n");
if (eccentricity > 0.01)
{
system.Callback("...resonance...\n");
temp = spin_resonance_period;
system.spin_resonance = true;
}
else
{
temp = orbital_period;
}
return(temp);
}
public static Planet DistributePlanetaryMasses(ref SolarSystem system, Double stellar_mass_ratio, Double stellar_luminosity_ratio, Double inner_dust, Double outer_dust)
{
SetInitialConditions(system, inner_dust, outer_dust);
Double planetesimal_inner_bound = InnermostPlanet(stellar_mass_ratio);
Double planetesimal_outer_bound = OutermostPlanet(stellar_mass_ratio);
while (system.dust_left)
{
Double a = system.random.Range(planetesimal_inner_bound, planetesimal_outer_bound);
Double e = system.random.Eccentricity();
Double mass = Constants.PROTOPLANET_MASS;
if (system.verbose)
{
system.Callback("Checking " + a + " AU.\n");
}
if (!DustAvailable(system, InnerEffectLimit(system, a, e, mass), OuterEffectLimit(system, a, e, mass)))
{
if (system.verbose)
{
system.Callback(".. failed.\n");
}
continue;
}
system.Callback(".. Injecting protoplanet.\n");
system.dust_density = Constants.DUST_DENSITY_COEFF * Math.Sqrt(stellar_mass_ratio) * Math.Exp(-Constants.ALPHA * Math.Pow(a, 1.0 / Constants.N));
Double crit_mass = CriticalLimit(a, e, stellar_luminosity_ratio);
AccreteDust(ref system, ref mass, a, e, crit_mass, planetesimal_inner_bound, planetesimal_outer_bound);
if ((mass != 0.0) && (mass != Constants.PROTOPLANET_MASS))
{
CoalescePlanetesimals(ref system, a, e, mass, crit_mass, stellar_luminosity_ratio, planetesimal_inner_bound, planetesimal_outer_bound);
}
else
{
system.Callback(".. failed due to large neighbor.\n");
}
}
return(system.planet_head);
}
/// <summary>
/// This implements Fogg's eq.17. The 'inventory' returned is unitless.
/// </summary>
public static Double VolInventory(SolarSystem system, Double mass, Double escape_vel, Double rms_vel, Double stellar_mass, Int32 zone, Boolean greenhouse_effect)
{
Double proportion_const;
Double velocity_ratio = escape_vel / rms_vel;
if (!(velocity_ratio >= Constants.GAS_RETENTION_THRESHOLD))
{
return(0.0);
}
switch (zone)
{
case 1:
proportion_const = 100000.0;
break;
case 2:
proportion_const = 75000.0;
break;
case 3:
proportion_const = 250.0;
break;
default:
proportion_const = 10.0;
system.Callback("Error: orbital zone not initialized correctly!\n");
break;
}
Double mass_in_earth_units = mass * Constants.EARTH_MASSES_PER_SOLAR_MASS;
Double temp1 = (proportion_const * mass_in_earth_units) / stellar_mass;
Double temp2 = system.random.About(temp1, 0.2);
if (greenhouse_effect)
{
return(temp2);
}
return(temp2 / 100.0);
}
public static void CoalescePlanetesimals(ref SolarSystem system, Double a, Double e, Double mass, Double crit_mass, Double stellar_luminosity_ratio, Double body_inner_bound, Double body_outer_bound)
{
Boolean coalesced = false;
Planet node1 = system.planet_head;
Planet node2 = null;
Planet node3 = null;
while (node1 != null)
{
node2 = node1;
Double temp = node1.a - a;
Double dist1;
Double dist2;
if (temp > 0.0)
{
dist1 = a * (1.0 + e) * (1.0 + system.reduced_mass) - a;
/* x aphelion */
system.reduced_mass = Math.Pow(node1.mass / (1.0 + node1.mass), 1.0 / 4.0);
dist2 = node1.a
- node1.a * (1.0 - node1.e) * (1.0 - system.reduced_mass);
}
else
{
dist1 = a - a * (1.0 - e) * (1.0 - system.reduced_mass);
/* x perihelion */
system.reduced_mass = Math.Pow(node1.mass / (1.0 + node1.mass), 1.0 / 4.0);
dist2 = node1.a * (1.0 + node1.e) * (1.0 + system.reduced_mass)
- node1.a;
}
if ((Math.Abs(temp) <= Math.Abs(dist1)) || (Math.Abs(temp) <= Math.Abs(dist2)))
{
system.Callback("Collision between two planetesimals!\n");
Double a3 = (node1.mass + mass) / (node1.mass / node1.a + mass / a);
temp = node1.mass * Math.Sqrt(node1.a) * Math.Sqrt(1.0 - Math.Pow(node1.e, 2.0));
temp = temp + mass * Math.Sqrt(a) * Math.Sqrt(Math.Sqrt(1.0 - Math.Pow(e, 2.0)));
temp = temp / ((node1.mass + mass) * Math.Sqrt(a3));
temp = 1.0 - Math.Pow(temp, 2.0);
if ((temp < 0.0) || (temp >= 1.0))
{
temp = 0.0;
}
e = Math.Sqrt(temp);
temp = node1.mass + mass;
AccreteDust(ref system, ref temp, a3, e, stellar_luminosity_ratio, body_inner_bound, body_outer_bound);
node1.a = a3;
node1.e = e;
node1.mass = temp;
node1 = null;
coalesced = true;
}
else
{
node1 = node1.next_planet;
}
}
if (coalesced)
{
return;
}
node3 = new Planet
{
a = a,
e = e,
gas_giant = mass >= crit_mass,
mass = mass
};
system.bodies.Add(node3);
if (system.planet_head == null)
{
system.planet_head = node3;
node3.next_planet = null;
}
else
{
node1 = system.planet_head;
if (a < node1.a)
{
node3.next_planet = node1;
system.planet_head = node3;
}
else if (system.planet_head.next_planet == null)
{
system.planet_head.next_planet = node3;
node3.next_planet = null;
}
else
{
while ((node1 != null) && (node1.a < a))
{
node2 = node1;
node1 = node1.next_planet;
}
node3.next_planet = node1;
node2.next_planet = node3;
}
}
}