def project_to_surface(orb, times):
"""Takes list of positions and times and projects to body's surface."""
bd = orb.prim
positions = orb.get_positions(times=times)[0]
bodyThetas = 2*np.pi/bd.rotPeriod * np.array(times) + bd.rotIni
sphericalPositions = cartesian_to_spherical(positions)
surfaceCoords = sphericalPositions[:,1:]
for ii in range(len(times)):
longitude = surfaceCoords[ii,0] - Orbit.map_angle(bodyThetas[ii])
count = 0
while abs(longitude) > np.pi:
longitude = longitude - np.sign(longitude) * 2*np.pi
count = count+1
if count > 10:
print('Why?')
break
surfaceCoords[ii,0] = longitude
return surfaceCoords
def add_orbit(figure, orb, startTime, endTime=None, numPts=201,
dateFormat=None, apses=False, nodes=False, fullPeriod=True,
color=(255,255,255), name='', style='solid', fade=True,):
if fade:
fadedColor = fade_color(color,3)
else:
fadedColor = color
period = orb.get_period()
if fullPeriod and (endTime is None):
endTime = startTime + period
# start and end mean anomalies
mStart = orb.get_mean_anomaly(startTime)
if (period < (endTime-startTime) or fullPeriod) and (orb.ecc < 1):
mEnd = mStart + 2*math.pi
else:
mEnd = mStart + 2*math.pi/period * (endTime-startTime)
# get points clustered around apoapsis and periapsis
if orb.ecc < 1:
a = mStart - (mStart%math.pi)
b = a + math.pi
else:
if mStart < 0:
a = mStart
b = 0
else:
a = 0
b = mEnd
# orbit crosses two apo/peri-apses
if ((mEnd >= b + math.pi) and (orb.ecc < 1)):
c = b + math.pi
d = c + math.pi
n = math.ceil(math.pi/(mEnd-mStart)*numPts)
kStart = n*math.acos((a+b-2*mStart)/(b-a))/math.pi
kEnd = n*math.acos((c+d-2*mEnd)/(d-c))/math.pi
ks1 = [[kStart]]
ks1.append([*range(math.ceil(kStart), n)])
ks1 = [k for sublist in ks1 for k in sublist]
meanAnoms1 = \
[0.5*(a+b) + 0.5*(b-a) *math.cos((n-k)/n*math.pi) for k in ks1];
ks2 = [*range(0,n)]
meanAnoms2 = \
[0.5*(b+c) + 0.5*(c-b) *math.cos((n-k)/n*math.pi) for k in ks2];
ks3 = [*range(0,math.ceil(kEnd))]
ks3.append(kEnd)
meanAnoms3 = \
[0.5*(c+d) + 0.5*(d-c) *math.cos((n-k)/n*math.pi) for k in ks3];
meanAnoms = np.append(meanAnoms1, meanAnoms2)
meanAnoms = np.append(meanAnoms, meanAnoms3)
times = startTime + period/(2*math.pi) * (meanAnoms - mStart)
# orbit crosses one apo/peri-apsis
elif mEnd > b:
if orb.ecc < 1:
c = b + math.pi
n1 = math.ceil(math.pi/(mEnd-mStart)*numPts)
n2 = n1
else:
c = mEnd
n1 = math.ceil(abs(mStart/(mEnd-mStart))*numPts)
n2 = math.ceil(abs(mEnd/(mEnd-mStart))*numPts)
kStart = n1*math.acos((a+b-2*mStart)/(b-a))/math.pi
kEnd = n2*math.acos((b+c-2*mEnd)/(c-b))/math.pi
ks1 = [[kStart]]
ks1.append([*range(math.ceil(kStart), n1)])
ks1 = [k for sublist in ks1 for k in sublist]
meanAnoms1 = \
[0.5*(a+b) + 0.5*(b-a) *math.cos((n1-k)/n1*math.pi) for k in ks1];
ks2 = [*range(0,math.ceil(kEnd))]
ks2.append(kEnd)
meanAnoms2 = \
[0.5*(b+c) + 0.5*(c-b) *math.cos((n2-k)/n2*math.pi) for k in ks2];
meanAnoms = np.append(meanAnoms1, meanAnoms2)
times = startTime + period/(2*math.pi) * (meanAnoms - mStart)
# orbit crosses no apo/peri-apses
else:
if orb.ecc < 1:
n = math.ceil(2*math.pi/(mEnd-mStart)*numPts)
else:
n = numPts
kStart = n*math.acos((a+b-2*mStart)/(b-a))/math.pi
kEnd = n*math.acos((a+b-2*mEnd)/(b-a))/math.pi
ks = [[kStart]]
ks.append([*range(math.ceil(kStart), math.ceil(kEnd))])
ks.append([kEnd])
ks = [k for sublist in ks for k in sublist]
meanAnoms = np.array( \
[0.5*(a+b) + 0.5*(b-a) *math.cos((n-k)/n*math.pi) for k in ks]);
meanAnoms = meanAnoms.flatten()
times = startTime + period/(2*math.pi) * (meanAnoms - mStart)
pos, vel = orb.get_positions(times = times)
pos = np.transpose(pos)
vel = np.transpose(vel)
if orb.ecc<1:
for ii, m in enumerate(meanAnoms):
meanAnoms[ii] = Orbit.map_angle(m)
if not dateFormat is None:
day = dateFormat['day']
year = dateFormat['year']
cData = np.stack((norm(pos, axis = 0)/1000,
norm(vel, axis = 0),
np.floor(times/(3600*day*year))+1,
np.floor(times%(3600*day*year)/(day*3600)+1),
np.floor((times%(3600*day))/3600),
np.floor(((times%(3600*day))%3600)/60),
np.floor(((times%(3600*day))%3600)%60),
times,
meanAnoms),
axis=1);
hoverLabel = "r = %{customdata[0]:.3e} km" + "<br>" +\
"v = %{customdata[1]:.3e} m/s" + "<br>" + "<br>" +\
"Year %{customdata[2]:.0f}, " +\
"Day %{customdata[3]:.0f} " +\
"%{customdata[4]:0>2d}" + ":" +\
"%{customdata[5]:0>2d}" + ":" +\
"%{customdata[6]:0>2d}" + "<br>" +\
"UT: %{customdata[7]:.3f} s" + "<br>" +\
"Mean Anomaly: %{customdata[8]:.5f} rad" + "<br>" + "<br>" +\
"Semi-major Axis = " + "{:.0f}".format(orb.a) + " m" + "<br>" +\
"Eccentricity = " + "{:.4f}".format(orb.ecc) + "<br>" +\
"Inclination = " + "{:.4f}".format(orb.inc*180/math.pi) + "°" + "<br>" +\
"Argument of the Periapsis = " + "{:.4f}".format(orb.argp*180/math.pi) + "°" + "<br>" +\
"Longitude of Ascending Node = " + "{:.4f}".format(orb.lan*180/math.pi) + "°" + "<br>" +\
"Mean Anomaly at Epoch = " + "{:.4f}".format(orb.mo) + " rad" + "<br>" +\
"Epoch = " + "{:.2f}".format(orb.epoch) + " s"
else:
cData = norm(pos, axis = 0)/1000
hoverLabel = "r = %{customdata:.4e} km"
figure.add_trace(go.Scatter3d(
x = pos[0],
y = pos[1],
z = pos[2],
customdata = cData,
mode = "lines",
line = dict(
color = times,
colorscale = [[0, 'rgb'+str(fadedColor)],
[1, 'rgb'+str(color)]],
dash = style
),
hovertemplate = hoverLabel,
name = name,
showlegend = False,
))
if nodes:
add_nodes(figure, orb)
if apses:
add_apses(figure, orb)