def add_current_pos(axis, current_ha, current_dec):
"""Adds current position to existing axis in existing plot.
"""
current_alt, current_az, _, __ = equ_to_altaz(current_ha, current_dec)
pos_plot = axis.plot(current_az,
current_alt,
color='black',
marker='o',
markersize=10,
markeredgewidth=1,
markerfacecolor='None')
return pos_plot
def add_star_and_traj(axis, star_ha, star_dec):
"""Adds star and trajectory to existing axis in exsiting plot.
"""
#Calculate star_az and star_alt
star_alt, star_az, _, __ = equ_to_altaz(star_ha, star_dec)
#Define star trajectory (dec stays constant, hour angle increases)
traj_ha = np.arange(-11.999, 11.999, 0.05)
traj_dec = np.ones(len(traj_ha)) * star_dec
#Calculate star trajectory in alt and az
traj_alt = np.zeros(len(traj_ha))
traj_az = np.zeros(len(traj_ha))
traj_alt, traj_az = equ_to_altaz(traj_ha, traj_dec)
#Create array, where to put the hour angle ticks
#Define lower tick limit (round down from star_ha but stop at -11)
low_tick_lim = np.floor(star_ha)
if low_tick_lim < -11:
low_tick_lim = -11
traj_ticks_ha = np.arange(low_tick_lim, 12)
traj_ticks_dec = np.ones(len(traj_ticks_ha)) * star_dec
#Calculate the corresponding azimuth ticks
__, traj_ticks_az = equ_to_altaz(traj_ticks_ha, traj_ticks_dec)
#Tranform to integers for style
traj_ticks_ha = traj_ticks_ha.astype(int)
star_plot = axis.plot(star_az, star_alt, 'b*')
traj_plot = axis.plot(traj_az, traj_alt, 'b.', markersize=0.75)
#return_list.append(star_plot)
#return_list.append(traj_plot)
#Create upper x-axis ticks and labels
#Add second axis to get x_labels at upper x-axis
ax2 = axis.twiny()
ax2.set_xlim(axis.get_xlim())
ax2.set_xticks(traj_ticks_az)
ax2.set_xticklabels(traj_ticks_ha)
ax2.set_xlabel("Hour angle [h]")
return star_plot, traj_plot, ax2
def calculate_target_alt_az_ha(self):
""" Calculates target alt, az, hour angle and leftover observing time.
Seperate function to be able to refresh it in gui via after.
Because alt, az and ha change with time.
"""
if not self.target_ra or not self.target_dec:
return 0
try:
#Compute the hour angle in range [-12,12]
#Right now only as target_ha_float. Formated ha not needed currently.
self.target_ha_float=(self.LST_float-self.target_ra_float)
if self.target_ha_float>12.:
self.target_ha_float=self.target_ha_float-24.
#Calculate alt and az
#Calculate target altitude and azimuth
(self.target_alt_float,
self.target_az_float,
self.target_alt,
self.target_az)=equ_to_altaz(self.target_ha_float,self.target_dec_float)
#Calculate the leftover observing time as float
obs_time_float=approx_obs_time(self.target_ha_float,self.target_dec_float)
#Format to 00h00min
hours=int(obs_time_float)
rest=abs(obs_time_float-hours)*60
minutes=int(round(rest))
self.target_obs_time="{:02}h{:02}min".format(hours,minutes)
except ValueError:
print('Found Error')
return 0
def fit_pointing_term(ha_obs, ha_obs_error,
dec_obs, dec_obs_error,
ha_calc, dec_calc,
Date, terms, LST=None,
plot=True, ObservationDate='all'):
"""Calculates Pointing term corrections.
Prints Results.
Plots Results if chosen.
Input:
ha_ons, ha_obs_error
(array of observed hour angles and erros)
dec_obs, dec_obs_error
(array of observed declinations and erros)
ha_calc, dec_calc
(arrays of calculated hour angle and declination)
Date
(array of observed dates)
terms
(list of terms to be fitted or 'all')
LST=None
(array of Local Sidereal Times
plot=True
(Boolean if Results should be plotted)
ObservationDate
(String of one Date that should be picked out of Date array or 'all')
"""
#terms array is an arary of strings containing the chosen pointing terms
#IH and ID are always fitted
#Define which terms are fitted if input is 'all'
if terms == 'all':
terms = ['CH','NP','MA','ME','TF','FO','DCES','DCEC','DLIN']
#We want to be able to specify a certain
#Date of Observation and need to mask
#the arrays for this purpose
if ObservationDate != 'all':
ha_calc=ha_calc[Date==ObservationDate]
ha_obs=ha_obs[Date==ObservationDate]
dec_calc=dec_calc[Date==ObservationDate]
dec_obs=dec_obs[Date==ObservationDate]
#Calculating and applying IH and ID
(ha_diff, ha_diff_error,
ha_corr, ha_corr_error,
ha_diff_corr,
ha_diff_corr_error)=apply_IH(ha_obs,ha_obs_error,ha_calc,
Date,
ObservationDate=ObservationDate)
(dec_diff, dec_diff_error,
dec_corr, dec_corr_error,
dec_diff_corr,
dec_diff_corr_error)=apply_ID(dec_obs,dec_obs_error,dec_calc,
Date,
ObservationDate=ObservationDate)
#To avoid to correct twice (want intital values for ha_corr in second correction) (need it in MA, ME and all)
dec_corr_first=dec_corr
ha_corr_first=ha_corr
dec_corr_first_error=dec_corr_error
ha_corr_first_error=ha_corr_error
#Define empty lists in which corrections are stored
ha_correction_list=[]
dec_correction_list=[]
ha_correction_error_list=[]
dec_correction_error_list=[]
#Fitting following Numerical Recipes by W. H. Press page 781 f.
if 'CH' in terms:
(ha_corr, ha_corr_error,
CH, CH_error, CH_correction) = apply_CH(ha_corr_first,
ha_corr_first_error,
dec_corr_first,
dec_corr_first_error,
ha_diff_corr,
ha_diff_corr_error)
#Save for later use in different variable names
#Need that for 'all'
dec_corr = dec_corr_first
dec_corr_error= dec_corr_first_error
ha_corr_error_CH=ha_corr_error
#Append CH_correction into correction list
ha_correction_list.append(CH_correction)
#And Error
ha_correction_error_list.append(ha_corr_error_CH)
if 'NP' in terms:
(ha_corr, ha_corr_error,
NP, NP_error, NP_correction) = apply_NP(ha_corr_first,
ha_corr_first_error,
dec_corr_first,
dec_corr_first_error,
ha_diff_corr,
ha_diff_corr_error)
#Need that for 'all'
dec_corr = dec_corr_first
dec_corr_error= dec_corr_first_error
ha_corr_error_NP=ha_corr_error
#Append NP_correction into correction list
ha_correction_list.append(NP_correction)
#And Error
ha_correction_error_list.append(ha_corr_error_NP)
if 'MA' in terms:
(ha_corr, ha_corr_error,
dec_corr, dec_corr_error,
MA, MA_error,
MA_correction_ha,
MA_correction_dec) = apply_MA(ha_corr_first, ha_corr_first_error,
dec_corr_first, dec_corr_first_error,
ha_diff_corr, ha_diff_corr_error,
dec_diff_corr, dec_diff_corr_error)
ha_corr_error_MA=ha_corr_error
dec_corr_error_MA=dec_corr_error
#Append MA_correction into correction list
ha_correction_list.append(MA_correction_ha)
dec_correction_list.append(MA_correction_dec)
#And Errors
ha_correction_error_list.append(ha_corr_error_MA)
dec_correction_error_list.append(dec_corr_error_MA)
if 'ME' in terms:
(ha_corr, ha_corr_error,
dec_corr, dec_corr_error,
ME, ME_error,
ME_correction_ha,
ME_correction_dec) = apply_ME(ha_corr_first, ha_corr_first_error,
dec_corr_first, dec_corr_first_error,
ha_diff_corr, ha_diff_corr_error,
dec_diff_corr, dec_diff_corr_error)
ha_corr_error_ME=ha_corr_error
dec_corr_error_ME=dec_corr_error
#Append ME_correction into correction list
ha_correction_list.append(ME_correction_ha)
dec_correction_list.append(ME_correction_dec)
#And Errors
ha_correction_error_list.append(ha_corr_error_ME)
dec_correction_error_list.append(dec_corr_error_ME)
if 'FO' in terms:
(dec_corr, dec_corr_error,
FO, FO_error,
FO_correction) = apply_FO(ha_corr_first,
ha_corr_first_error,
dec_corr_first,
dec_corr_first_error,
dec_diff_corr,
dec_diff_corr_error)
#Need that for 'all'
ha_corr = ha_corr_first
ha_corr_error= ha_corr_first_error
dec_corr_error_FO=dec_corr_error
#Append FO_correction into correction list
dec_correction_list.append(FO_correction)
#And Errors
dec_correction_error_list.append(dec_corr_error_FO)
if 'DCES' in terms:
(dec_corr, dec_corr_error,
DCES, DCES_error,
DCES_correction) = apply_DCES(dec_corr_first,
dec_corr_first_error,
dec_diff_corr,
dec_diff_corr_error)
#Need that for 'all'
ha_corr= ha_corr_first
ha_corr_error= ha_corr_first_error
dec_corr_error_DCES= dec_corr_error
#Append DCES_correction into correction list
dec_correction_list.append(DCES_correction)
#And Errors
dec_correction_error_list.append(dec_corr_error_DCES)
if 'DCEC' in terms:
(dec_corr, dec_corr_error,
DCEC, DCEC_error,
DCEC_correction) = apply_DCEC(dec_corr_first,
dec_corr_first_error,
dec_diff_corr,
dec_diff_corr_error)
#Need that for 'all'
ha_corr= ha_corr_first
ha_corr_error= ha_corr_first_error
dec_corr_error_DCEC= dec_corr_error
#Append DCEC_correction into correction list
dec_correction_list.append(DCEC_correction)
#And Errors
dec_correction_error_list.append(dec_corr_error_DCEC)
if 'DLIN' in terms :
(dec_corr, dec_corr_error,
DLIN, DLIN_error,
DLIN_correction) = apply_DLIN(dec_corr_first,
dec_corr_first_error,
dec_diff_corr,
dec_diff_corr_error)
#Need that for 'all'
ha_corr= ha_corr_first
ha_corr_error= ha_corr_first_error
dec_corr_error_DLIN= dec_corr_error
#Append DLIN_correction into correction list
dec_correction_list.append(DLIN_correction)
#And Errors
dec_correction_error_list.append(dec_corr_error_DLIN)
if 'TF' in terms:
(ha_corr, ha_corr_error,
dec_corr, dec_corr_error,
TF, TF_error,
TF_correction_ha,
TF_correction_dec) = apply_TF(ha_corr_first, ha_corr_first_error,
dec_corr_first, dec_corr_first_error,
ha_diff_corr, ha_diff_corr_error,
dec_diff_corr, dec_diff_corr_error)
ha_corr_error_TF=ha_corr_error
dec_corr_error_TF=dec_corr_error
#Append TF_correction into correction list
ha_correction_list.append(TF_correction_ha)
dec_correction_list.append(TF_correction_dec)
#And Errors
ha_correction_error_list.append(ha_corr_error_TF)
dec_correction_error_list.append(dec_corr_error_TF)
#All fitting is done
#Add corrections together
#
ha_corr = ha_corr_first + sum(ha_correction_list)
squared_ha_errors=[error**2 for error in ha_correction_error_list]
ha_corr_error = np.sqrt(ha_corr_first_error**2+sum(squared_ha_errors))
dec_corr = dec_corr_first + sum(dec_correction_list)
squared_dec_errors=[error**2 for error in dec_correction_error_list]
dec_corr_error=np.sqrt(dec_corr_first_error**2+sum(squared_dec_errors))
#Second array of differences with second corrections
ha_diff_corr_sec = ha_obs - ha_corr
ha_diff_corr_sec_error=np.sqrt(ha_obs_error**2+ha_corr_error**2)
dec_diff_corr_sec = dec_obs - dec_corr
dec_diff_corr_sec_error=np.sqrt(dec_obs_error**2+dec_corr_error**2)
# all fitting done, now start plotting
if plot==True:
plt.figure(1)
plt.subplot(121)
plt.plot(ha_obs,ha_calc,'bo',label='ha_calc')
plt.plot(ha_obs,ha_corr,'rx',label='ha_corr')
plt.plot(np.arange(-12,12),np.arange(-12,12),'k')
plt.xlabel('observed hour angle [h]')
plt.ylabel('modeled hour angle [h]',labelpad=1)
plt.ylim(-12,12)
plt.xlim(-12,12)
plt.legend(loc='best',numpoints=1)
plt.subplot(122)
plt.plot(dec_obs,dec_calc,'bo',label='dec_calc')
plt.plot(dec_obs,dec_corr,'rx',label='dec_corr')
plt.plot(np.arange(-10,90),np.arange(-10,90),'k')
plt.xlabel('observed declination [deg]')
plt.ylabel('modeled declination [deg]',labelpad=1)
plt.legend(loc='best',numpoints=1)
plt.show()
#We also want to plot ha_diff and dec_diff
#vs ha and dec (for the moment ha_obs and dec_obs)
#At first we create data
#to plot the Field of View of the Guidung Camera
ha_space=np.linspace(ha_obs.min(),ha_obs.max())
dec_space=np.linspace(dec_obs.min(),dec_obs.max())
#If we only observe a specific date then we don't need to do much
if ObservationDate != 'all':
### HA_Diff vs. HA_Obs ###
#Plotting the original differences
plt.figure()
plt.subplot(221)
plt.errorbar(ha_obs,ha_diff*60,yerr=ha_diff_error*60,
linestyle='none',marker='o',label=ObservationDate)
plt.xlabel('observed hour angle [h]')
plt.ylabel('ra_diff = ra_obs - ra_calc [min]')
#We also include a FOV area which is computed by 4'x 4' FOV of the guidung camera (4'=0.0044h=0.067°)
plt.plot(ha_space,0.0022*np.ones(len(ha_space))*60,
color='black',label='FOV')
plt.plot(ha_space,-0.0022*np.ones(len(ha_space))*60,color='black')
#plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.title('Initial Data')
#Plotting the IH corrected differences
plt.subplot(222)
plt.errorbar(ha_obs,ha_diff_corr*60,yerr=ha_diff_corr_error*60,
linestyle='none',marker='o',label=ObservationDate)
plt.xlabel('observed hour angle [h]')
plt.ylabel('ra_diff_cor = ra_obs - ra_corr [min]')
#We also include a FOV area which is computed by 4'x 4' FOV of the guidung camera (4'=0.0044h=0.067°)
plt.plot(ha_space,0.0022*np.ones(len(ha_space))*60,
color='black',label='FOV')
plt.plot(ha_space,-0.0022*np.ones(len(ha_space))*60,color='black')
#plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.title('First Correction')
#Plotting the second correction if the folowing terms are chosen
if ('CH' in terms or
'NP' in terms or
'MA' in terms or
'ME' in terms or
'TF' in terms) :
plt.subplot(224)
plt.errorbar(ha_obs,ha_diff_corr_sec*60,
yerr=ha_diff_corr_sec_error*60,
linestyle='none',marker='o',label=ObservationDate)
plt.xlabel('observed hour angle [h]')
plt.ylabel('ra_diff_cor_sec = ra_obs - ra_corr [min]')
plt.title('Second Correction')
plt.plot(ha_space,0.0022*np.ones(len(ha_space))*60,
color='black',label='FOV')
plt.plot(ha_space,-0.0022*np.ones(len(ha_space))*60,color='black')
#plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.show()
### HA_Diff vs. DEC_Obs ###
plt.figure()
plt.subplot(221)
plt.errorbar(dec_obs, ha_diff*60,yerr=ha_diff_error*60,
linestyle='none',marker='o', label=ObservationDate)
plt.xlabel('observed declination [°]')
plt.ylabel('ra_diff = ra_obs - ra_calc [min]')
plt.plot(dec_space,0.0022*np.ones(len(dec_space))*60,
color='black',label='FOV')
plt.plot(dec_space,-0.0022*np.ones(len(dec_space))*60,color='black')
#plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.title('Initial Data')
plt.subplot(222)
plt.errorbar(dec_obs, ha_diff_corr*60,yerr=ha_diff_corr_error*60,
linestyle='none',marker='o',label=ObservationDate)
plt.xlabel('observed declination [°]')
plt.ylabel('ra_diff_cor = ra_obs - ra_corr [min]')
plt.plot(dec_space,0.0022*np.ones(len(dec_space))*60,
color='black',label='FOV')
plt.plot(dec_space,-0.0022*np.ones(len(dec_space))*60,color='black')
#plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.title('First Correction')
#Second Correction: Plot only in these cases
if ('CH' in terms or
'NP' in terms or
'MA' in terms or
'ME' in terms or
'TF' in terms):
plt.subplot(224)
plt.errorbar(dec_obs,ha_diff_corr_sec*60,yerr=ha_diff_corr_error*60,
linestyle='none',marker='o',label=ObservationDate)
plt.xlabel('observed declination[°]')
plt.ylabel('ra_diff_cor_sec = ra_obs - ra_corr [min]')
plt.title('Second Correction')
plt.plot(dec_space,0.0022*np.ones(len(dec_space))*60,
color='black',label='FOV')
plt.plot(dec_space,-0.0022*np.ones(len(dec_space))*60,
color='black')
#plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.show()
### DEC_Diff vs. HA_Obs ###
plt.figure()
plt.subplot(221)
plt.errorbar(ha_obs,dec_diff*60,yerr=dec_diff_error*60,
linestyle='none',marker='o',
label=ObservationDate)
plt.xlabel('observed hour angle [h]')
plt.ylabel("dec_diff = dec_obs-dec_calc [']")
plt.plot(ha_space,0.033*np.ones(len(ha_space))*60,
color='black',label='FOV')
plt.plot(ha_space,-0.033*np.ones(len(ha_space))*60,
color='black')
#plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.title('Initial Data')
plt.subplot(222)
plt.errorbar(ha_obs,dec_diff_corr*60,yerr=dec_diff_corr_error*60,
linestyle='none',marker='o',
label=ObservationDate)
plt.xlabel('observed hour angle [h]')
plt.ylabel("dec_diff_corr = dec_obs-dec_corr [']")
plt.plot(ha_space,0.033*np.ones(len(ha_space))*60,
color='black',
label='FOV')
plt.plot(ha_space,-0.033*np.ones(len(ha_space))*60,
color='black')
#plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.title('First Correction')
#Second Correction: Plot only in these cases
if ('MA' in terms or
'ME' in terms or
'FO' in terms or
'DCES' in terms or
'DCEC' in terms or
'DLIN' in terms or
'TF' in terms):
plt.subplot(224)
plt.errorbar(ha_obs,dec_diff_corr_sec*60,
yerr=dec_diff_corr_sec_error*60,
linestyle='none',marker='o',
label=ObservationDate)
plt.xlabel('observed hour angle [h]')
plt.ylabel("dec_diff_corr_sec = dec_obs-dec_corr [']")
plt.title('Second Correction')
plt.plot(ha_space,0.033*np.ones(len(ha_space))*60,
color='black',label='FOV')
plt.plot(ha_space,-0.033*np.ones(len(ha_space))*60,
color='black')
#plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.show()
### DEC_Diff vs. DEC_Obs ###
plt.figure()
plt.subplot(221)
plt.errorbar(dec_obs,dec_diff*60,yerr=dec_diff_error*60,
linestyle='none',marker='o',
label=ObservationDate)
plt.xlabel('observed declination [°]')
plt.ylabel("dec_diff = dec_obs-dec_calc [']")
plt.plot(dec_space,0.033*np.ones(len(dec_space))*60,
color='black',label='FOV')
plt.plot(dec_space,-0.033*np.ones(len(dec_space))*60,color='black')
#plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.title('Initial Data')
plt.subplot(222)
plt.errorbar(dec_obs,dec_diff_corr*60,yerr=dec_diff_corr_error*60,
linestyle='none',marker='o',label=ObservationDate)
plt.xlabel('observed declination [°]')
plt.ylabel("dec_diff_corr = dec_obs-dec_corr [']")
plt.plot(dec_space,0.033*np.ones(len(dec_space))*60,
color='black',label='FOV')
plt.plot(dec_space,-0.033*np.ones(len(dec_space))*60,color='black')
#plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.title('First Correction')
#Second Correction: Plot only in these cases
if ('MA' in terms or
'ME' in terms or
'FO' in terms or
'DCES' in terms or
'DCEC' in terms or
'DLIN' in terms or
'TF' in terms):
plt.subplot(224)
plt.errorbar(dec_obs,dec_diff_corr_sec*60,yerr=dec_diff_corr_sec_error*60,
linestyle='none',marker='o',
label=ObservationDate)
plt.xlabel('observed declination [°]')
plt.ylabel("dec_diff_corr = dec_obs-dec_corr [']")
plt.title('Second correction')
plt.plot(dec_space,0.033*np.ones(len(dec_space))*60,
color='black',label='FOV')
plt.plot(dec_space,-0.033*np.ones(len(dec_space))*60,
color='black')
#plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.show()
#Plotting as Field of View
#Initital Data
plt.figure()
plt.subplot(221)
plt.errorbar(dec_diff*60,15.*ha_diff*60,linestyle='none',
marker='.',label=ObservationDate)
fig = plt.gcf()
ax = fig.gca()
circle1 = plt.Circle((0, 0), 0.0333*60, color='b',fill=False)
ax.add_artist(circle1)
plt.axis('scaled')
plt.xlabel("Declination Difference [']")
plt.ylabel("Hour Angle Difference [']")
plt.title('Initial Data')
#plt.legend(loc="upper left", bbox_to_anchor=(1,1))
#First correction
plt.subplot(222)
plt.errorbar(dec_diff_corr*60,15.*ha_diff_corr*60,
linestyle='none',marker='.',label=ObservationDate)
fig = plt.gcf()
ax = fig.gca()
circle1 = plt.Circle((0, 0), 0.0333*60, color='b',fill=False)
ax.add_artist(circle1)
plt.axis('scaled')
plt.xlabel("Declination Difference [']")
plt.ylabel("Hour Angle Difference [']")
plt.title('First Correction')
#plt.legend(loc="upper left", bbox_to_anchor=(1,1))
#Second Correction
plt.subplot(224)
plt.errorbar(dec_diff_corr_sec*60,15.*ha_diff_corr_sec*60,
linestyle='none',marker='.',label=ObservationDate)
fig = plt.gcf()
ax = fig.gca()
circle1 = plt.Circle((0, 0), 0.0333*60, color='b',fill=False)
ax.add_artist(circle1)
plt.axis('scaled')
plt.xlabel("Declination Difference [']")
plt.ylabel("Hour Angle Difference [']")
plt.title('Second Correction')
#plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.show()
#Differences vs Time
plt.figure()
plt.subplot(121)
plt.errorbar(LST,ha_diff*60,yerr=ha_diff_error*60,
linestyle='none',marker='o')
plt.ylabel('Hour Angle Difference [min] (not corr)')
plt.xlabel('LST [h]')
plt.subplot(122)
plt.errorbar(LST,dec_diff*60,yerr=dec_diff_error*60,
linestyle='none',marker='o')
plt.ylabel("Declination Difference ['] (not corr)")
plt.xlabel('LST [h]')
plt.show()
#Differences vs Time
plt.figure()
plt.subplot(121)
plt.errorbar(LST,ha_diff_corr_sec*60,yerr=ha_diff_corr_sec_error*60,
linestyle='none',marker='o')
plt.ylabel("Hour Angle Difference [min] (2nd corr)")
plt.xlabel('LST [h]')
plt.subplot(122)
plt.errorbar(LST,dec_diff_corr_sec*60,yerr=dec_diff_corr_sec_error*60,
linestyle='none',marker='o')
plt.ylabel("Declination Difference ['] (2nd corr)")
plt.xlabel('LST [h]')
plt.show()
#Scatter Plots: Area indicating error (first correction)
#Plot Positive differences in blue, negatives in red
dec_pos_bool = dec_diff_corr > 0
dec_neg_bool = dec_diff_corr < 0
ha_pos_bool = ha_diff_corr > 0
ha_neg_bool = ha_diff_corr < 0
dec_pos_sec_bool = dec_diff_corr_sec > 0
dec_neg_sec_bool = dec_diff_corr_sec < 0
ha_pos_sec_bool = ha_diff_corr_sec > 0
ha_neg_sec_bool = ha_diff_corr_sec < 0
plt.figure()
plt.subplot(122)
plt.scatter(ha_obs[dec_pos_bool], dec_obs[dec_pos_bool],
s=dec_diff_corr[dec_pos_bool]*1000,
color= 'blue')
plt.scatter(ha_obs[dec_neg_bool], dec_obs[dec_neg_bool],
s=abs(dec_diff_corr[dec_neg_bool]*1000),
color= 'red')
plt.ylabel('observed Declination [°]')
plt.xlabel('observed Hour Angle [h]')
plt.title('(1st) corrected Declination difference \n as markersize')
plt.subplot(121)
plt.scatter(ha_obs[ha_pos_bool], dec_obs[ha_pos_bool],
s=abs(ha_diff_corr[ha_pos_bool]*15*1000),
color='blue')
plt.scatter(ha_obs[ha_neg_bool], dec_obs[ha_neg_bool],
s=abs(ha_diff_corr[ha_neg_bool]*15*1000),
color='red')
plt.ylabel('observed Declination [°]')
plt.xlabel('observed Hour Angle [h]')
plt.title('(1st) corrected Hour Angle difference \n as markersize')
plt.show()
#Scatter Plots: Area indicating error (second correction)
plt.figure()
plt.subplot(122)
plt.scatter(ha_obs[dec_pos_sec_bool], dec_obs[dec_pos_sec_bool],
s=dec_diff_corr_sec[dec_pos_sec_bool]*1000,
color= 'blue')
plt.scatter(ha_obs[dec_neg_sec_bool], dec_obs[dec_neg_sec_bool],
s=abs(dec_diff_corr_sec[dec_neg_sec_bool]*1000),
color= 'red')
plt.ylabel('observed Declination [°]')
plt.xlabel('observed Hour Angle [h]')
plt.title('(2nd) corrected Declination difference \n as markersize')
plt.subplot(121)
plt.scatter(ha_obs[ha_pos_sec_bool], dec_obs[ha_pos_sec_bool],
s=abs(ha_diff_corr_sec[ha_pos_sec_bool]*15*1000),
color='blue')
plt.scatter(ha_obs[ha_neg_sec_bool], dec_obs[ha_neg_sec_bool],
s=abs(ha_diff_corr_sec[ha_neg_sec_bool]*15*1000),
color='red')
plt.xlabel('observed Declination [°]')
plt.ylabel('observed Hour Angle [h]')
plt.title('(2nd) corrected Hour Angle difference \n as markersize')
plt.show()
#3D Plots: error vs positions
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(dec_obs,ha_obs,dec_diff_corr_sec)
ax.set_xlabel('observed Declination [°]')
ax.set_ylabel('observed Hour Angle [h]')
ax.set_zlabel('dec_diff_corr_sec [°]')
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(dec_obs,ha_obs,ha_diff_corr_sec)
ax.set_xlabel('observed Declination [°]')
ax.set_ylabel('observed Hour Angle [h]')
ax.set_zlabel('ha_diff_corr_sec [h]')
plt.show()
#Also plot difference in alt az
#and overplot diffraction correction
#Calculate observed Alt and Az
alt_obs, az_obs = equ_to_altaz(ha_obs, dec_obs)
alt_calc, az_calc = equ_to_altaz(ha_calc, dec_calc)
#Calculate corrected Alt and Az
alt_corr_first, az_corr_first = equ_to_altaz(ha_corr_first,
dec_corr_first)
alt_corr, az_corr = equ_to_altaz(ha_corr, dec_corr)
#Calculate uncorrected alt difference
alt_diff = alt_obs - alt_calc
#Calculate corrected alt difference
alt_diff_corr_first = alt_obs - alt_corr_first
alt_diff_corr_sec = alt_obs - alt_corr
def calc_refraction(alt):
"""Calculate refraction in arcminutes
"""
#Choose temp and press
temp = 15
press = 97
#Calculate temperature/pressure factor
factor= press/101*283/(273+temp)
#Calculate refraction in arcminutes
R=(1/np.tan(np.radians(alt+7.31/(alt+4.4))))*factor
return R
#Create alt array
alt_space=np.linspace(10,90,1000)
#Plot
plt.figure()
plt.subplot(221)
plt.plot(alt_obs,alt_diff*60,
linestyle='none',marker='.',
label=ObservationDate)
plt.xlabel('observed altitude [°]')
plt.ylabel("alt_diff = alt_obs-alt_calc [']")
plt.title('Initial Data')
plt.plot(alt_space,calc_refraction(alt_space),
color='red', label='refraction')
plt.plot(alt_space,0.033*np.ones(len(alt_space))*60,
color='black',label='FOV')
plt.plot(alt_space,-0.033*np.ones(len(alt_space))*60,
color='black')
plt.subplot(222)
plt.plot(alt_obs,alt_diff_corr_first*60,
linestyle='none',marker='.',
label=ObservationDate)
plt.xlabel('observed altitude [°]')
plt.ylabel("alt_diff = alt_obs-alt_calc [']")
plt.title('First Correction')
plt.plot(alt_space,calc_refraction(alt_space),
color='red', label='refraction')
plt.plot(alt_space,0.033*np.ones(len(alt_space))*60,
color='black',label='FOV')
plt.plot(alt_space,-0.033*np.ones(len(alt_space))*60,
color='black')
plt.subplot(224)
plt.plot(alt_obs,alt_diff_corr_sec*60,
linestyle='none',marker='.',
label=ObservationDate)
plt.xlabel('observed altitude [°]')
plt.ylabel("alt_diff_corr = alt_obs-alt_corr [']")
plt.title('Second correction')
plt.plot(alt_space,calc_refraction(alt_space),
color='red', label='refraction')
plt.plot(alt_space,0.033*np.ones(len(alt_space))*60,
color='black',label='FOV')
plt.plot(alt_space,-0.033*np.ones(len(alt_space))*60,
color='black')
plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.show()
else:
#If we have all dates than we want to plot each date
#with a different color
#unique makes an array of dates
#where each date only appears once, so looping over this array
#and plotting all elements where the original date array
#is the unique date leads to different colors
### HA_DIFF VS- HA_OBS ###
plt.figure()
plt.subplot(221)
for element in np.unique(Date):
plt.errorbar(ha_obs[Date==element],ha_diff[Date==element],
yerr=ha_diff_error[Date==element],
linestyle='none',marker='.',label=element)
plt.xlabel('observed hour angle [h]')#
plt.ylabel('ra_diff = ra_obs - ra_calc [h]')
plt.title('Initial Data')
#We also include a FOV area which is computed by 4'x 4' FOV of the guidung camera (4'=0.0044h=0.067°)
plt.plot(ha_space,0.0022*np.ones(len(ha_space)),
color='black',label='FOV')
plt.plot(ha_space,-0.0022*np.ones(len(ha_space)),color='black')
plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.subplot(222)
for element in np.unique(Date):
plt.errorbar(ha_obs[Date==element],ha_diff_corr[Date==element],
yerr=ha_diff_corr_error[Date==element],
linestyle='none',marker='o',label=element)
plt.xlabel('observed hour angle [h]')
plt.ylabel('ra_diff_cor = ra_obs - ra_corr [h]')
plt.title('First correction')
plt.plot(ha_space,0.0022*np.ones(len(ha_space)),
color='black',label='FOV')
plt.plot(ha_space,-0.0022*np.ones(len(ha_space)),color='black')
plt.legend(loc="upper left", bbox_to_anchor=(1,1))
#Second Correction: Plot only in these cases
if ('CH' in terms or
'NP' in terms or
'MA' in terms or
'ME' in terms or
'TF' in terms):
plt.subplot(224)
for element in np.unique(Date):
plt.errorbar(ha_obs[Date==element],
ha_diff_corr_sec[Date==element],
yerr=ha_diff_corr_sec_error[Date==element],
linestyle='none',marker='o',label=element)
plt.xlabel('observed hour angle [h]')
plt.ylabel('ra_diff_cor_sec = ra_obs - ra_corr [h]')
plt.title('Second Correction'+' ('+term+')')
plt.plot(ha_space,0.0022*np.ones(len(ha_space)),
color='black',label='FOV')
plt.plot(ha_space,-0.0022*np.ones(len(ha_space)),color='black')
plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.show()
### HA_DIFF VS- DEC_OBS ###
plt.figure()
plt.subplot(221)
for element in np.unique(Date):
plt.errorbar(dec_obs[Date==element],ha_diff[Date==element],
yerr=ha_diff_error[Date==element],
linestyle='none',marker='o',label=element)
plt.xlabel('observed declination [°]')
plt.ylabel('ra_diff = ra_obs - ra_calc [h]')
plt.title('Initial Data')
plt.plot(dec_space,0.0022*np.ones(len(dec_space)),
color='black',label='FOV')
plt.plot(dec_space,-0.0022*np.ones(len(dec_space)),color='black')
plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.subplot(222)
for element in np.unique(Date):
plt.errorbar(dec_obs[Date==element],
ha_diff_corr[Date==element],
yerr=ha_diff_corr_error[Date==element],
linestyle='none',marker='o',label=element)
plt.xlabel('observed declination [°]')
plt.ylabel('ra_diff_cor = ra_obs - ra_corr [h]')
plt.title('First correction')
plt.plot(dec_space,0.0022*np.ones(len(dec_space)),
color='black',label='FOV')
plt.plot(dec_space,-0.0022*np.ones(len(dec_space)),color='black')
plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.show()
#Second Correction: Plot only in these cases
if ('CH' in terms or
'NP' in terms or
'MA' in terms or
'ME' in terms or
'TF' in terms) :
plt.subplot(224)
for element in np.unique(Date):
plt.errorbar(dec_obs[Date==element],
ha_diff_corr_sec[Date==element],
yerr=ha_diff_corr_error[Date==element],
linestyle='none',marker='o',label=element)
plt.xlabel('observed declination[°]')
plt.ylabel('ra_diff_cor_sec = ra_obs - ra_corr [h]')
plt.title('Second Correction'+' ('+term+')')
plt.plot(dec_space,0.0022*np.ones(len(dec_space)),
color='black',label='FOV')
plt.plot(dec_space,-0.0022*np.ones(len(dec_space)),
color='black')
plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.show()
###DEC_DIFF VS HA_OBS###
plt.figure()
plt.subplot(221)
for element in np.unique(Date):
plt.errorbar(ha_obs[Date==element],
dec_diff[Date==element],
yerr=dec_diff_error[Date==element],
linestyle='none',marker='o',label=element)
plt.xlabel('observed hour angle [h]')
plt.ylabel('dec_diff = dec_obs-dec_calc [°]')
plt.title('Initial Data')
plt.plot(ha_space,0.033*np.ones(len(ha_space)),
color='black',label='FOV')
plt.plot(ha_space,-0.033*np.ones(len(ha_space)),color='black')
plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.subplot(222)
for element in np.unique(Date):
plt.errorbar(ha_obs[Date==element],
dec_diff_corr[Date==element],
yerr=dec_diff_corr_error[Date==element],
linestyle='none',marker='o',label=element)
plt.xlabel('observed hour angle [h]')
plt.ylabel('dec_diff_corr = dec_obs-dec_corr [°]')
plt.title('First Correction')
plt.plot(ha_space,0.033*np.ones(len(ha_space)),
color='black',label='FOV')
plt.plot(ha_space,-0.033*np.ones(len(ha_space)),color='black')
plt.legend(loc="upper left", bbox_to_anchor=(1,1))
#Second Correction: Plot only in these cases
if ('MA' in terms or
'ME' in terms or
'FO' in terms or
'DCES' in terms or
'DCEC' in terms or
'DLIN' in terms or
'TF' in terms):
plt.subplot(224)
for element in np.unique(Date):
plt.errorbar(ha_obs[Date==element],
dec_diff_corr_sec[Date==element],
yerr=dec_diff_corr_sec_error[Date==element],
linestyle='none',marker='o',label=element)
plt.xlabel('observed hour angle [h]')
plt.ylabel('dec_diff_corr_sec = dec_obs-dec_corr [°]')
plt.title('Second Correction'+' ('+term+')')
plt.plot(ha_space,0.033*np.ones(len(ha_space)),
color='black',label='FOV')
plt.plot(ha_space,-0.033*np.ones(len(ha_space)),color='black')
plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.show()
###DEC_DIFF VS DEC_OBS
plt.figure()
plt.subplot(221)
for element in np.unique(Date):
plt.errorbar(dec_obs[Date==element],
dec_diff[Date==element],
yerr=dec_diff_error[Date==element],
linestyle='none',marker='o',label=element)
plt.xlabel('observed declination [°]')
plt.ylabel('dec_diff = dec_obs-dec_calc [°]')
plt.title('Initial Data')
plt.plot(dec_space,0.033*np.ones(len(dec_space)),
color='black',label='FOV')
plt.plot(dec_space,-0.033*np.ones(len(dec_space)),color='black')
plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.subplot(222)
for element in np.unique(Date):
plt.errorbar(dec_obs[Date==element],
dec_diff_corr[Date==element],
yerr=dec_diff_corr_error[Date==element],
linestyle='none',marker='o',label=element)
plt.xlabel('observed declination [°]')
plt.ylabel('dec_diff_corr = dec_obs-dec_corr [°]')
plt.title('First correction')
plt.plot(dec_space,0.033*np.ones(len(dec_space)),
color='black',label='FOV')
plt.plot(dec_space,-0.033*np.ones(len(dec_space)),color='black')
plt.legend(loc="upper left", bbox_to_anchor=(1,1))
#Second Correction: Plot only in these cases
if ('MA' in terms or
'ME' in terms or
'FO' in terms or
'DCES' in terms or
'DCEC' in terms or
'DLIN' in terms or
'TF' in terms):
plt.subplot(224)
for element in np.unique(Date):
plt.errorbar(dec_obs[Date==element],
dec_diff_corr_sec[Date==element],
yerr=dec_diff_error[Date==element],
linestyle='none',marker='o',label=element)
plt.xlabel('observed declination [°]')
plt.ylabel('dec_diff_corr = dec_obs-dec_corr [°]')
plt.title('Second correction'+' ('+term+')')
plt.plot(dec_space,0.033*np.ones(len(dec_space)),
color='black',label='FOV')
plt.plot(dec_space,-0.033*np.ones(len(dec_space)),
color='black')
plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.show()
#Plotting as Field of View
plt.figure()
plt.subplot(221)
for element in np.unique(Date):
plt.errorbar(dec_diff[Date==element],
15.*ha_diff[Date==element],
linestyle='none',marker='.',label=element)
fig = plt.gcf()
ax = fig.gca()
circle1 = plt.Circle((0, 0), 0.0333, color='b',fill=False)
ax.add_artist(circle1)
plt.axis('scaled')
plt.xlabel('Declination Difference [°]')
plt.ylabel('Hour Angle Difference [°]')
plt.title('Initial Data')
plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.subplot(222)
for element in np.unique(Date):
plt.errorbar(dec_diff_corr[Date==element],
15.*ha_diff_corr[Date==element],
linestyle='none',marker='.',label=element)
fig = plt.gcf()
ax = fig.gca()
circle1 = plt.Circle((0, 0), 0.0333, color='b',fill=False)
ax.add_artist(circle1)
plt.axis('scaled')
plt.xlabel('Declination Difference [°]')
plt.ylabel('Hour Angle Difference [°]')
plt.title('First Correction')
plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.subplot(224)
for element in np.unique(Date):
plt.errorbar(dec_diff_corr_sec[Date==element],
15.*ha_diff_corr_sec[Date==element],
linestyle='none',marker='.',label=element)
fig = plt.gcf()
ax = fig.gca()
circle1 = plt.Circle((0, 0), 0.0333, color='b',fill=False)
ax.add_artist(circle1)
plt.axis('scaled')
plt.xlabel('Declination Difference [°]')
plt.ylabel('Hour Angle Difference [°]')
plt.title('Second Correction')
plt.legend(loc="upper left", bbox_to_anchor=(1,1))
plt.show()
#return values
pfit = (ha_corr,dec_corr)
return pfit
from coord_operations import calc_alt_limit, calc_tree_limit, equ_to_altaz, altaz_to_equ, approx_obs_time star_ha = 3 star_dec = 30 #Create az and alt_limit and tree_limit array az = np.arange(-180, 180, 0.01) alt_limit = np.zeros(len(az)) tree_limit = np.zeros(len(az)) #Calculate limits alt_limit = calc_alt_limit(az) tree_limit = calc_tree_limit(az) #Calculate star_az and star_alt star_alt, star_az, _, __ = equ_to_altaz(star_ha, star_dec) #Define star trajectory (dec stays constant, hour angle increases) traj_ha = np.arange(-11.999, 11.999, 0.05) traj_dec = np.ones(len(traj_ha)) * star_dec #Calculate star trajectory in alt and az traj_alt = np.zeros(len(traj_ha)) traj_az = np.zeros(len(traj_ha)) traj_alt, traj_az = equ_to_altaz(traj_ha, traj_dec) #Create array, where to put the hour angle ticks traj_ticks_ha = np.arange(np.round(star_ha), 12) traj_ticks_dec = np.ones(len(traj_ticks_ha)) * star_dec #Calculate the corresponding azimuth ticks __, traj_ticks_az = equ_to_altaz(traj_ticks_ha, traj_ticks_dec) #Tranform to integers for style traj_ticks_ha = traj_ticks_ha.astype(int)
#Create arrays
ha_sign=np.array(ha_sign)
ha_hour=np.array(ha_hour)
ha_min=np.array(ha_min)
dec_sign=np.array(dec_sign)
dec_deg=np.array(dec_deg)
dec_min=np.array(dec_min)
mode=np.array(mode)
#Calculate ha and dec as floats
ha=(ha_hour+ha_min/60)*(1*(ha_sign=='+')-1*(ha_sign=='-'))
dec=(dec_deg+dec_min/60)*(1*(dec_sign=='+')-1*(dec_sign=='-'))
#Create initial altitude and azimuth arrays
alt=np.zeros(len(ha))
az=np.zeros(len(ha))
#Define path to write file
file_path=parrent_path / 'pointing_limits' / 'pointing_limits_alt_az.txt'
#Transform coordinates
for index in range(len(ha)):
(alt[index],az[index],dummy1,dummy2)=equ_to_altaz(ha[index],dec[index])
line="{} {} {}\n".format(alt[index],az[index],mode[index])
#With automatically closes the file in the end
with open(str(file_path), 'a') as writefile:
writefile.write(line)
def plot_traj_limits_altaz(star_ha, star_dec):
"""Plots limits and star trajectory in altitude and azimuth.
"""
#Create az and alt_limit and tree_limit array
az = np.arange(-180, 180, 0.01)
alt_limit = np.zeros(len(az))
tree_limit = np.zeros(len(az))
#Calculate limits
alt_limit = calc_alt_limit(az)
tree_limit = calc_tree_limit(az)
#Calculate star_az and star_alt
star_alt, star_az, _, __ = equ_to_altaz(star_ha, star_dec)
#Define star trajectory (dec stays constant, hour angle increases)
traj_ha = np.arange(-11.999, 11.999, 0.05)
traj_dec = np.ones(len(traj_ha)) * star_dec
#Calculate star trajectory in alt and az
traj_alt = np.zeros(len(traj_ha))
traj_az = np.zeros(len(traj_ha))
traj_alt, traj_az = equ_to_altaz(traj_ha, traj_dec)
#Create array, where to put the hour angle ticks
traj_ticks_ha = np.arange(np.round(star_ha), 12)
traj_ticks_dec = np.ones(len(traj_ticks_ha)) * star_dec
#Calculate the corresponding azimuth ticks
__, traj_ticks_az = equ_to_altaz(traj_ticks_ha, traj_ticks_dec)
#Tranform to integers for style
traj_ticks_ha = traj_ticks_ha.astype(int)
#Plot
fig = plt.figure()
ax1 = fig.add_subplot(111)
#Add second axis to get x_labels at upper x-axis
ax2 = ax1.twiny()
#Plot alt_limit,tree_limits and star position and trajectory
ax1.plot(az, alt_limit, color='red')
ax1.plot(az, tree_limit, color='#00cc00', linewidth=0.0)
ax1.plot(star_az, star_alt, 'b*')
ax1.plot(traj_az, traj_alt, 'b.', markersize=0.75)
#Fill the colors between the limits and 0 altitude
ax1.fill_between(az, alt_limit, np.zeros(len(az)), color='red', alpha=1)
ax1.fill_between(az,
tree_limit,
alt_limit,
color='#00cc00',
where=tree_limit > alt_limit,
alpha=1)
#Set the axis limits
ax1.set_xlim(-180, 180)
ax1.set_ylim(0, 90)
ax1.set_xlabel("Azimuth[°]")
#Later we could exclude circumpolar stars
#Create upper x-axis ticks and labels
ax2.set_xlim(ax1.get_xlim())
ax2.set_xticks(traj_ticks_az)
ax2.set_xticklabels(traj_ticks_ha)
ax2.set_xlabel("Hour angle [h]")
#plt.title('Waltz Pointing Limits')
plt.show()
def plot_traj_and_limits(star_ha, star_dec):
#Create az and alt_limit and tree_limit array
az = np.arange(-180, 180, 0.01)
alt_limit = np.zeros(len(az))
tree_limit = np.zeros(len(az))
alt_limit = calc_alt_limit(az)
tree_limit = calc_tree_limit(az)
#Plot alt_limits vs az and tree limits
plt.plot(az, alt_limit, color='red')
plt.plot(az, tree_limit, color='#00cc00', linewidth=0.0)
plt.fill_between(az, alt_limit, np.zeros(len(az)), color='red', alpha=1)
plt.fill_between(az,
tree_limit,
alt_limit,
color='#00cc00',
where=tree_limit > alt_limit,
alpha=1)
plt.axis([-180, 180, 0, 90])
plt.xlabel('Azimuth[°]')
plt.ylabel('Altitude[°]')
plt.title('Waltz Pointing Limits')
#Calculate star_az and star_alt
star_alt, star_az, _, __ = equ_to_altaz(star_ha, star_dec)
print(star_alt)
print(star_az)
#Define star trajectory (dec stays constant, hour angle increases)
traj_ha = np.arange(-11.999, 11.999, 0.05)
traj_dec = np.ones(len(traj_ha)) * star_dec
#Calculate star trajectory in alt and az
traj_alt = np.zeros(len(traj_ha))
traj_az = np.zeros(len(traj_ha))
traj_alt, traj_az = equ_to_altaz(traj_ha, traj_dec)
#plot star
plt.plot(star_az, star_alt, 'b*')
plt.plot(traj_az, traj_alt, 'b.', markersize=0.5)
plt.show()
#Define dec_limits and hour angle arrays
dec_limit = np.zeros(len(az))
ha = np.zeros(len(az))
#And tree limit array
dec_tree_limit = np.zeros(len(az))
ha_tree_limit = np.zeros(len(az))
#Transform altaz limits to ha,dec limits
ha, dec_limit = altaz_to_equ(alt_limit, az)
ha_tree_limit, dec_tree_limit = altaz_to_equ(tree_limit, az)
#Plot dec_limits vs ha
plt.plot(ha_tree_limit, dec_tree_limit, color='#00cc00', linewidth=0.0)
plt.plot(ha, dec_limit, color='red')
y_plot_limit = -30
plt.fill_between(ha_tree_limit,
dec_tree_limit,
np.ones(len(ha)) * y_plot_limit,
interpolate=True,
color='#00cc00',
where=dec_tree_limit > dec_limit,
alpha=1)
plt.fill_between(ha,
dec_limit,
np.ones(len(ha)) * y_plot_limit,
color='red',
alpha=1)
plt.axis([-12, 12, y_plot_limit, 90])
plt.xlabel('Hour Angle[h]')
plt.ylabel('Declination[°]')
plt.title('Waltz Pointing Limits')
#plot star
plt.plot(star_ha, star_dec, 'b*')
plt.plot(traj_ha, traj_dec, 'b.', markersize=0.5)
plt.show()