@hackage › astro

Amateur astronomical computations

Usage

Install stack

It will take care of everything.

Build the project

stack build

Run unit tests

stack test

Documentation

Useful types

Decimal hours and Decimal degrees

Types to represent hours (used in celestial coordinate systems and as time zone) and degrees (used in coordinate systems).

import Data.Astro.Types



-- 10h 15m 19.7s

dh :: DecimalHours

dh = fromHMS 10 15 19.7

-- DH 10.255472222222222



(h, m, s) = toHMS dh

-- (10,15,19.699999999999562)





-- 51°28′40″

dd :: DecimalDegrees

dd = fromDMS 51 28 40

-- DD 51.477777777777774



(d, m, s) = toDMS dd

-- (51,28,39.999999999987494)

Geographic Coordinates

import Data.Astro.Types



-- the Royal Observatory, Greenwich

ro :: GeographicCoordinates

ro = GeoC (fromDMS 51 28 40) (-(fromDMS 0 0 5))

-- GeoC {geoLatitude = DD 51.4778, geoLongitude = DD (-0.0014)}

Time

The main time datetime type used in the library is JulianDate defined in Data.Astro.Time.JulianDate. JulianDate is just a number of days since noon of 1 January 4713 BC:

import Data.Astro.Time.JulianDate



-- 2017-06-25 9:29:00 (GMT)

jd :: JulianDate

jd = fromYMDHMS 2017 6 25 9 29 0

-- JD 2457929.895138889

LocalCiviTime and LocalCivilDate are Julian dates with time zones:

import Data.Astro.Time.JulianDate

import Data.Astro.Types



-- 2017-06-25 10:29:00 +0100 (BST)

lct :: LocalCivilTime

lct = lctFromYMDHMS (DH 1) 2017 6 25 10 29 0

-- 2017-06-25 10:29:00.0000 +1.0



lctJD :: JulianDate

lctJD = lctUniversalTime lct

-- JD 2457929.895138889



lctTZ :: DecimalHours

lctTZ = lctTimeZone lct

-- DH 1.0



lcd :: LocalCivilDate

lcd = lcdFromYMD (DH 1) 2017 6 25



lcdJD :: JulianDate

lcdJD = lcdDate lcd

-- JD 2457929.5



lcdTZ :: DecimalHours

lcdTZ = lcdTimeZone lcd

-- DH 1.0

Celestial coordinate systems

The celestical coordinate systems are defined in Data.Astro.Coordinate.

If you would like to locate Sirius in the sky you need to know the altitude or 'how far up' angle in the sky and azimuth - 'how far round' angle from the north direction to the east. this describes the Horizontal coordinate system:

alt Horizontal coordinate system

import Data.Astro.Coordinate

import Data.Astro.Types



hc :: HorizonCoordinates

hc = HC (DD 30.5) (DD 180)

-- HC {hAltitude = DD 30.0, hAzimuth = DD 180.0}

Unfortunately the Horizontal coordinate system values depend on the position of the observer. And it's not handy when you need to share coordinates of some celestial object with your friend in Japan.

The second coordinate system is the Equatorial coordinate system. This coordinate system uses the location of the centre of the Earth as the zero point so it does not depend on the observer's location.

We have two flavours of equatorial coordinates:

the first one uses the vernal equinox as a starting direction for the 'how far round' coordinate (right ascension, α),
the second one uses the meridian instead of the vernal equinox (hour angle).

We can consider the second one as a transition coordinate system between the horizontal one and the 'true' equatorial one.

import Data.Astro.Coordinate

import Data.Astro.Types



ec1 :: EquatorialCoordinates1

ec1 = EC1 (DD 71.7) (DH 8)

-- EC1 {e1Declination = DD 71.7, e1RightAscension = DH 8.0}



ec2 :: EquatorialCoordinates2

ec2 = EC1 (DD 77.7) (DH 11)

-- EC2 {e2Declination = DD 77.7, e2HoursAngle = DH 11.0}

Transformations

Say, now is 2017-06-25 10:29 BST and we are somewhere near the Royal Observatory, Greenwich.

Let convert the current location of the Sun in horizon coordinates (altitude: 49°18′21.77″, azimuth: 118°55′19.53″) to equatorial coordinates and back to horizon ones:

import Data.Astro.Time.JulianDate

import Data.Astro.Coordinate

import Data.Astro.Types



ro :: GeographicCoordinates

ro = GeoC (fromDMS 51 28 40) (-(fromDMS 0 0 5))



dt :: LocalCivilTime

dt = lctFromYMDHMS (DH 1) 2017 6 25 10 29 0



sunHC :: HorizonCoordinates

sunHC = HC (fromDMS 49 18 21.77) (fromDMS 118 55 19.53)

-- HC {hAltitude = DD 49.30604722222222, hAzimuth = DD 118.92209166666666}



sunEC2 :: EquatorialCoordinates2

sunEC2 = horizonToEquatorial (geoLatitude ro) sunHC

-- EC2 {e2Declination = DD 23.378295912623855, e2HoursAngle = DH 21.437117068873537}



sunEC1 :: EquatorialCoordinates1

sunEC1 = EC1 (e2Declination sunEC2) (haToRA (e2HoursAngle sunEC2) (geoLongitude ro) (lctUniversalTime dt))

-- EC1 {e1Declination = DD 23.378295912623855, e1RightAscension = DH 6.29383725890224}





sunEC2' :: EquatorialCoordinates2

sunEC2' = EC2 (e1Declination sunEC1) (raToHA (e1RightAscension sunEC1) (geoLongitude ro) (lctUniversalTime dt))

-- EC2 {e2Declination = DD 23.378295912623855, e2HoursAngle = DH 21.437117068873537}



sunHC' :: HorizonCoordinates

sunHC' = equatorialToHorizon (geoLatitude ro) sunEC2'

-- HC {hAltitude = DD 49.30604722222222, hAzimuth = DD 118.92209166666666}

You can use function-shortcuts to simplify transformation EquatorialCoordinates1 <-> HorizonCoordinates: ec1ToHC and hcToEC1:

import Data.Astro.Time.JulianDate

import Data.Astro.Coordinate

import Data.Astro.Types



ro :: GeographicCoordinates

ro = GeoC (fromDMS 51 28 40) (-(fromDMS 0 0 5))



dt :: LocalCivilTime

dt = lctFromYMDHMS (DH 1) 2017 6 25 10 29 0



sunHC :: HorizonCoordinates

sunHC = HC (fromDMS 49 18 21.77) (fromDMS 118 55 19.53)

-- HC {hAltitude = DD 49.30604722222222, hAzimuth = DD 118.92209166666666}



sunEC1 :: EquatorialCoordinates1

sunEC1 = hcToEC1 ro (lctUniversalTime dt) sunHC

-- EC1 {e1Declination = DD 23.378295912623855, e1RightAscension = DH 6.29383725890224}



sunHC' :: HorizonCoordinates

sunHC' = ec1ToHC ro (lctUniversalTime dt) sunEC1

-- HC {hAltitude = DD 49.30604722222222, hAzimuth = DD 118.92209166666666}

Stars

The ancient astronomers noted that there were 2 types of stars: some of them were fixed, travelling the same way across the sky every sidereal day and another were wanderers (planetai in ancient Greek).

Of course, stars are not fixed, they are travelling with high speeds but distances to them are so high that their movement is very difficult to note. So we can assume that they are fixed for our purposes.

Given the "fixed" equatorial coordinates of the star we only need to transform them to the horizon coordinates to find out where the star in the sky.

In the example below we will use Data.Astro.Star module which defines equatorial coordinates of some stars:

import Data.Astro.Time.JulianDate

import Data.Astro.Coordinate

import Data.Astro.Types

import Data.Astro.Star





ro :: GeographicCoordinates

ro = GeoC (fromDMS 51 28 40) (-(fromDMS 0 0 5))



dt :: LocalCivilTime

dt = lctFromYMDHMS (DH 1) 2017 6 25 10 29 0



-- Calculate location of Betelgeuse



betelgeuseEC1 :: EquatorialCoordinates1

betelgeuseEC1 = starCoordinates Betelgeuse

-- EC1 {e1Declination = DD 7.407064, e1RightAscension = DH 5.919529}



betelgeuseHC :: HorizonCoordinates

betelgeuseHC = ec1ToHC ro (lctUniversalTime dt) betelgeuseEC1

-- HC {hAltitude = DD 38.30483892505852, hAzimuth = DD 136.75755644642248}

Rise and Set

Data.Astro.CelestialObject.RiseSet module defines RiseSet type to represent time and azimuth of rise and set.

Let calculate rise and set time of Rigel:

import Data.Astro.Time.JulianDate

import Data.Astro.Coordinate

import Data.Astro.Types

import Data.Astro.Effects

import Data.Astro.CelestialObject.RiseSet

import Data.Astro.Star





ro :: GeographicCoordinates

ro = GeoC (fromDMS 51 28 40) (-(fromDMS 0 0 5))



today :: LocalCivilDate

today = lcdFromYMD (DH 1) 2017 6 25



-- Calculate location of Betelgeuse



rigelEC1 :: EquatorialCoordinates1

rigelEC1 = starCoordinates Rigel



verticalShift :: DecimalDegrees

verticalShift = refract (DD 0) 12 1012

-- DD 0.5660098245614035



rigelRiseSet :: RiseSetLCT

rigelRiseSet = riseAndSetLCT ro today verticalShift rigelEC1

-- RiseSet (2017-06-25 06:38:18.4713 +1.0,DD 102.51249855335433) (2017-06-25 17:20:33.4902 +1.0,DD 257.48750144664564)

As we can see Rigel rose today at 06:38:18 and will set at 17:20:33, azimuths of rise and set 102.51° and 257.49° correspondingly.

We used refract function of Data.Astro.Effects module with reasonable default parameters to calculate vertical shift.

Planets

The planets is completely different story. We cannot assume that the planets have "fixed" location in equatorial coordinates like stars.

What we can do is to describe details of the planets' orbit and calculate their positions at any given moment.

Planets and planet details are defined in Data.Astro.Planet module. j2010PlanetDetails returns details for the given planet. This module also defines planetPosition, planetDistance1 and planetAngularDiameter to calculate position of the given planet, distance to the planet and angular size of the planet correspondingly.

1 at the end of the planetDistance1 means that this function uses not very precise method to do calculations. Sometimes there are 2-methods available in the library, but not always.

Let us do some planets-related calculations.

Do some initialisation:

import Data.Astro.Time.JulianDate

import Data.Astro.Coordinate

import Data.Astro.Types

import Data.Astro.Effects

import Data.Astro.CelestialObject.RiseSet

import Data.Astro.Planet



ro :: GeographicCoordinates

ro = GeoC (fromDMS 51 28 40) (-(fromDMS 0 0 5))



dt :: LocalCivilTime

dt = lctFromYMDHMS (DH 1) 2017 6 25 10 29 0



today :: LocalCivilDate

today = lcdFromYMD (DH 1) 2017 6 25



jupiterDetails :: PlanetDetails

jupiterDetails = j2010PlanetDetails Jupiter



earthDetails :: PlanetDetails

earthDetails = j2010PlanetDetails Earth



jupiterPosition :: JulianDate -> EquatorialCoordinates1

jupiterPosition = planetPosition planetTrueAnomaly1 jupiterDetails earthDetails

Calculate Jupiter's coordinates:

jupiterEC1 :: EquatorialCoordinates1

jupiterEC1 = jupiterPosition (lctUniversalTime dt)

-- EC1 {e1Declination = DD (-4.104626810672402), e1RightAscension = DH 12.863365504382228}



jupiterHC :: HorizonCoordinates

jupiterHC = ec1ToHC ro (lctUniversalTime dt) jupiterEC1

-- HC {hAltitude = DD (-30.67914598469227), hAzimuth = DD 52.29376845044007}

As be can see Jupiter is below the horizon now (the altitude is negative), that's unfortunate.

Now let us calculate distance to Jupiter:

jupiterDistance :: AstronomicalUnits

jupiterDistance = planetDistance1 jupiterDetails earthDetails (lctUniversalTime dt)

-- AU 5.193435872521039

1 Astronomical Unit is an average distance from the Earth to the Sun.

and calculate an angular size now:

jupiterAngularSize :: DecimalDegrees

jupiterAngularSize = planetAngularDiameter jupiterDetails jupiterDistance

-- DD 1.052289877865987e-2



toDMS jupiterAngularSize

-- (0,0,37.88243560317554)

Rise and Set

Calculate rise and set times of planets are not easy task, because planets change their equatorial coordinates during the day.

riseAndSet2 function of Data.Astro.CelestialObject.RiseSet module applies iterative approach: calculates rise and set date for midday coordinates and then recalculates rise time for rise coordinates and set for set coordinates obtained from the previous step:

verticalShift :: DecimalDegrees

verticalShift = refract (DD 0) 12 1012

-- DD 0.5660098245614035



jupiterRiseSet :: RiseSetMB

jupiterRiseSet = riseAndSet2 0.000001 jupiterPosition ro verticalShift today

-- RiseSet

--    (Just (2017-06-25 13:53:27.3109 +1.0,DD 95.88943953535569))

--    (Just (2017-06-25 01:21:23.5835 +1.0,DD 264.1289033612776))

We can see now why at 10 am Jupiter is below horizon because it will rise only at 1:53 pm.

Sun

Some examples of doing the Sun's related calculations:

import Data.Astro.Time.JulianDate

import Data.Astro.Coordinate

import Data.Astro.Types

import Data.Astro.Sun



ro :: GeographicCoordinates

ro = GeoC (fromDMS 51 28 40) (-(fromDMS 0 0 5))



dt :: LocalCivilTime

dt = lctFromYMDHMS (DH 1) 2017 6 25 10 29 0



today :: LocalCivilDate

today = lcdFromYMD (DH 1) 2017 6 25



jd :: JulianDate

jd = lctUniversalTime dt



verticalShift :: DecimalDegrees

verticalShift = refract (DD 0) 12 1012



-- distance from the Earth to the Sun in kilometres

distance :: Double

distance = sunDistance jd

-- 1.5206375976421073e8



-- Angular Size

angularSize :: DecimalDegrees

angularSize = sunAngularSize jd

-- DD 0.5244849215333616



-- The Sun's coordinates

ec1 :: EquatorialCoordinates1

ec1 = sunPosition2 jd

-- EC1 {e1Declination = DD 23.37339098989099, e1RightAscension = DH 6.29262026252748}



hc :: HorizonCoordinates

hc = ec1ToHC ro jd ec1

-- HC {hAltitude = DD 49.312050979507404, hAzimuth = DD 118.94723825710143}





-- Rise and Set

riseSet :: RiseSetMB

riseSet = sunRiseAndSet ro 0.833333 today

-- RiseSet

--    (Just (2017-06-25 04:44:04.3304 +1.0,DD 49.043237261724215))

--    (Just (2017-06-25 21:21:14.4565 +1.0,DD 310.91655607595595))

Moon

The Moon's related calculations. Data.Astro.Moon module defines 2 new types of functions we haven't seen before: moonPhase and moonBrightLimbPositionAngle which calculate the phase (the area of the visible segment expressed as a fraction of the whole disk) and the position-angle which is the angle of the midpoint of the illuminated limb measured eastwards from the north point of the disk.

import Data.Astro.Time.JulianDate

import Data.Astro.Coordinate

import Data.Astro.Types

import Data.Astro.Effects

import Data.Astro.CelestialObject.RiseSet

import Data.Astro.Moon



ro :: GeographicCoordinates

ro = GeoC (fromDMS 51 28 40) (-(fromDMS 0 0 5))



dt :: LocalCivilTime

dt = lctFromYMDHMS (DH 1) 2017 6 25 10 29 0



today :: LocalCivilDate

today = lcdFromYMD (DH 1) 2017 6 25



jd :: JulianDate

jd = lctUniversalTime dt



-- distance from the Earth to the Moon in kilometres

mdu :: MoonDistanceUnits

mdu = moonDistance1 j2010MoonDetails jd

-- MDU 0.9550170577020396



distance :: Double

distance = mduToKm mdu

-- 367109.51199772174



-- Angular Size

angularSize :: DecimalDegrees

angularSize = moonAngularSize mdu

-- DD 0.5425033990980761



-- The Moon's coordinates

position :: JulianDate -> EquatorialCoordinates1

position = moonPosition1 j2010MoonDetails



ec1 :: EquatorialCoordinates1

ec1 = position jd

-- EC1 {e1Declination = DD 18.706180658927323, e1RightAscension = DH 7.56710547682055}



hc :: HorizonCoordinates

hc = ec1ToHC ro jd ec1

-- HC {hAltitude = DD 34.57694951316064, hAzimuth = DD 103.91119101451832}



-- Rise and Set

riseSet :: RiseSetMB

riseSet = riseAndSet2 0.000001 position ro verticalShift today

-- RiseSet

--    (Just (2017-06-25 06:22:51.4858 +1.0,DD 57.81458864497365))

--    (Just (2017-06-25 22:28:20.3023 +1.0,DD 300.4168238905249))



-- Phase

phase :: Double

phase = moonPhase j2010MoonDetails jd

-- 2.4716141948212922e-2





sunEC1 :: EquatorialCoordinates1

sunEC1 = sunPosition2 jd

-- EC1 {e1Declination = DD 23.37339098989099, e1RightAscension = DH 6.29262026252748}



limbAngle :: DecimalDegrees

limbAngle = moonBrightLimbPositionAngle ec1 sunEC1

-- DD 287.9869373767473

@hackage / astro

Metadata

Links

Installation

Readme

Amateur astronomical computations

Usage

Install stack

Build the project

Run unit tests

Documentation

Useful types

Decimal hours and Decimal degrees

Geographic Coordinates

Time

Celestial coordinate systems

Transformations

Stars

Rise and Set

Planets

Rise and Set

Sun

Moon

About

Metadata

Links

Installation

Readme

Amateur astronomical computations

Usage

Install stack

Build the project

Run unit tests

Documentation

Useful types

Decimal hours and Decimal degrees

Geographic Coordinates

Time

Celestial coordinate systems

Transformations

Stars

Rise and Set

Planets

Rise and Set

Sun

Moon