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I'm trying to determine when seasons start and end on Mars. This point is at 0º, 90º, 180º, and 270º Ls (solar longitude).

PyEphem offers Heliocentric longitude and latitude. How can this be correlated to solar longitude displayed here:

http://www.planetary.org/explore/space-topics/mars/mars-calendar.html

I think that the two quantities are the same angle, but measured from different starting points. Using that assumption, you can use PyEphem to predict Martian seasons to within two or three days — but I really would have expected better, and am not sure why the agreement is not closer!

But this will at least get you started. Please let us know if you find out why these predictions are slightly different from those of the site you linked to! We should at some point compare them to the output of NASA Horizons, and of the Skyfield project that I am building as an improved PyEphem.

In any case, some code to compute Ls and use it to find Mars seasons:

# The angle that we call "the longitude of the Sun, as

# seen from Mars" should grow at the same rate as the

# "longitude of Mars as seen from the Sun" (since the

# two are the same line but viewed in opposite

# directions).

#

# The only problem is knowing what point to name "zero",

# so we have to learn what .hlon was when the first

# Martian year started:



from ephem import Mars, Date, degrees, newton

m = Mars()

m.compute('1955/4/11 23:00')

Ls0 = m.hlon



def Ls(date):

    m.compute(date)

    return degrees(m.hlon - Ls0).norm



# There!  Ls() should give Martian solar latitude.

# So the first round of seasons listed at the page

# http://www.planetary.org/explore/space-topics/mars/mars-calendar.html

# should give 90 degrees, 180 degrees, and 270 degrees:



for date in '1955/10/27', '1956/4/27', '1956/9/21':

    print Ls(date)



# The output is close to what we would expect:

#

# 90:11:58.3

# 179:57:32.2

# 270:13:22.6

#

# Great!  So what if we want to know, say, the date

# of the upcoming Spring Equinox or Summer Solstice?

# We need functions that are smooth, well-behaved,

# and cross zero at those two times, so that we can

# unleash Newton's Method upon them:



def spring_equinox(date):

    return Ls(date).znorm



def summer_solstice(date):

    return Ls(date) - degrees('90:00:00')



def find_spring_equinox(start_date):

    start_date = Date(start_date)

    y0 = Ls(start_date)

    y1 = Ls(start_date + 1)

    rate = y1 - y0

    angle_to_go = degrees(0.0 - y0).norm

    closer_date = start_date + angle_to_go / rate

    d = newton(spring_equinox, closer_date, closer_date + 1)

    return Date(d)



def find_summer_solstice(start_date):

    start_date = Date(start_date)

    y0 = Ls(start_date)

    y1 = Ls(start_date + 1)

    rate = y1 - y0

    angle_to_go = degrees(degrees('90:00:00') - y0).norm

    closer_date = start_date + angle_to_go / rate

    d = newton(summer_solstice, closer_date, closer_date + 1)

    return Date(d)



d = find_spring_equinox('2015/1/22')

print d, Ls(d)



d = find_summer_solstice('2015/1/22')

print d, Ls(d)



# Output:

# 2015/6/16 15:03:15 0:00:00.0

# 2015/12/31 21:12:07 90:00:00.0