def real_annomaly_from_eccentric(self, time):
ecc_an = utils.eccentric_annomaly(self.period,
self.epsilon,
time)
real_an = np.arccos((np.cos(ecc_an)[0] - self.epsilon) /
(1 - self.epsilon*np.cos(ecc_an)[0]))
real_an = real_an if 2*time < self.period else 2*np.pi - real_an
return real_an
def position(self, time):
time = self.get_time_in_period(time)
eccentric_annomaly = utils.eccentric_annomaly(self.period,
self.epsilon, time)
position = [
self.a * (np.cos(eccentric_annomaly) - self.epsilon)[0], self.a *
np.sqrt(1 - self.epsilon**2) * np.sin(eccentric_annomaly)[0]
]
return position
def speed(self, time):
time = self.get_time_in_period(time)
eccentric_annomaly = utils.eccentric_annomaly(self.period,
self.epsilon, time)
denom = self.period * (1 - self.epsilon * np.cos(eccentric_annomaly))
quotient = 2 * np.pi * self.a / denom
speed = [(-quotient * np.sin(eccentric_annomaly))[0],
(quotient * np.sqrt(1 - self.epsilon**2) *
np.cos(eccentric_annomaly))[0]]
return speed
def speed_2bodies(self, time):
G = 6.674*10**(-11)
sun_mass = 1.989*10**30
mu = 8.9546188*10**(-25)*G*sun_mass**3/(self.mass + sun_mass)**2
period = np.sqrt(4*np.pi**2*self.a**3/mu)
time = self.get_time_in_period(time)
eccentric_annomaly = utils.eccentric_annomaly(
period,
self.epsilon,
time
)
denom = period*(1-self.epsilon*np.cos(eccentric_annomaly))
quotient = 2*np.pi*self.a/denom
speed = [
(-quotient*np.sin(eccentric_annomaly))[0],
(quotient *
np.sqrt(1 - self.epsilon**2)*np.cos(eccentric_annomaly))[0]
]
return speed
def eccentric_annomaly(self, time):
time = self.get_time_in_period(time)
return utils.eccentric_annomaly(self.period,
self.epsilon,
time)[0]