From bbc147598130358af4e1cbd8bf000c3c634ff574 Mon Sep 17 00:00:00 2001
From: Wim De Meester <deepskywim@gmail.com>
Date: Fri, 31 Jul 2020 12:43:45 +0200
Subject: [PATCH 1/3] Calculate if three bodies are in a straight line.

---
 changelog.md                                  |  6 +++
 readme.md                                     |  6 +++
 .../Coordinates/EquatorialCoordinates.php     | 42 +++++++++++++++++++
 tests/Unit/EquatorialCoordinatesTest.php      | 23 +++++++++-
 4 files changed, 76 insertions(+), 1 deletion(-)

diff --git a/changelog.md b/changelog.md
index e50f885..ff325b3 100644
--- a/changelog.md
+++ b/changelog.md
@@ -2,6 +2,12 @@
 
 All notable changes to `laravel-astronomy-library` will be documented in this file.
 
+## Version 4.5
+
+### Added
+
+- Added methods to check if three bodies are in a straight line and to calculate the deviation from a straight line.
+
 ## Version 4.4
 
 ### Added
diff --git a/readme.md b/readme.md
index d049f29..c89c5be 100644
--- a/readme.md
+++ b/readme.md
@@ -195,6 +195,12 @@ $galactic = $coords->convertToGalactic();
 $parallacticAngle = $coords->getParallacticAngle($geo_coords, $siderial_time);
 $hour_angle = $coords->getHourAngle($siderial_time);
 $angular_separation = $coords->angularSeparation($coords2)->getCoordinate();
+
+// Check if three bodies are in a straight line
+$castor = new EquatorialCoordinates(7.571222, 31.89756);
+$pollux = new EquatorialCoordinates(7.750002778, 28.03681);
+$mars = new EquatorialCoordinates(8.022644129, 21.472188347);
+$isInStraightLine = $mars->isInStraightLine($castor, $pollux);
 ```
 
 ### Coordinate methods on ecliptical coordinates
diff --git a/src/deepskylog/AstronomyLibrary/Coordinates/EquatorialCoordinates.php b/src/deepskylog/AstronomyLibrary/Coordinates/EquatorialCoordinates.php
index 8eb7fca..513f11b 100644
--- a/src/deepskylog/AstronomyLibrary/Coordinates/EquatorialCoordinates.php
+++ b/src/deepskylog/AstronomyLibrary/Coordinates/EquatorialCoordinates.php
@@ -327,4 +327,46 @@ public function angularSeparation(
 
         return new Coordinate($d);
     }
+
+    /**
+     * Returns true if the three bodies are in a straight line.
+     *
+     * @param EquatorialCoordinates $coords2   The coordinates of the second object
+     * @param EquatorialCoordinates $coords3   The coordinates of the thirds object
+     * @param float                 $threshold The threshold for the method
+     *                                         (default value is 10e-06)
+     *
+     * @return bool True if the three bodies are in a straight line
+     */
+    public function isInStraightLine(
+        self $coords2,
+        self $coords3,
+        float $threshold = 1e-6
+    ): bool {
+        $result = tan(deg2rad($this->getDeclination()->getCoordinate())) *
+                sin(
+                    deg2rad(
+                        $coords2->getRA()->getCoordinate() * 15.0
+                        - $coords3->getRA()->getCoordinate() * 15.0
+                    )
+                ) + tan(deg2rad($coords2->getDeclination()->getCoordinate())) *
+                sin(
+                    deg2rad(
+                        $coords3->getRA()->getCoordinate() * 15.0
+                        - $this->getRA()->getCoordinate() * 15.0
+                    )
+                ) + tan(deg2rad($coords3->getDeclination()->getCoordinate())) *
+                sin(
+                    deg2rad(
+                        $this->getRA()->getCoordinate() * 15.0
+                        - $coords2->getRA()->getCoordinate() * 15.0
+                    )
+                );
+
+        if (abs($result) < $threshold) {
+            return true;
+        }
+
+        return false;
+    }
 }
diff --git a/tests/Unit/EquatorialCoordinatesTest.php b/tests/Unit/EquatorialCoordinatesTest.php
index 13b5b99..ab70e11 100644
--- a/tests/Unit/EquatorialCoordinatesTest.php
+++ b/tests/Unit/EquatorialCoordinatesTest.php
@@ -36,7 +36,7 @@ class EquatorialCoordinatesTest extends BaseTestCase
      *
      * @var string
      */
-    protected $appPath = __DIR__.'/../../vendor/laravel/laravel/bootstrap/app.php';
+    protected $appPath = __DIR__ . '/../../vendor/laravel/laravel/bootstrap/app.php';
 
     /**
      * Setup the test environment.
@@ -216,4 +216,25 @@ public function testAngularSeparation()
             0.0001
         );
     }
+
+    /**
+     * Test bodies in straight line/**.
+     *
+     * @return None
+     */
+    public function testBodiesInStraightLine()
+    {
+        // Castor
+        $castor = new EquatorialCoordinates(7.571222, 31.89756);
+        // Pollux
+        $pollux = new EquatorialCoordinates(7.750002778, 28.03681);
+
+        // Mars on Sep 30, 1994
+        $mars = new EquatorialCoordinates(7.97293055, 21.58983);
+        $this->assertFalse($mars->isInStraightLine($castor, $pollux));
+
+        // Mars on Oct 1, 1994, 5h TD
+        $mars = new EquatorialCoordinates(8.022644129, 21.472188347);
+        $this->assertTrue($mars->isInStraightLine($castor, $pollux));
+    }
 }

From 29cc4d3d82344428b7e7ec1e9e28cd8ee65055bb Mon Sep 17 00:00:00 2001
From: Wim De Meester <deepskywim@gmail.com>
Date: Fri, 31 Jul 2020 14:52:16 +0200
Subject: [PATCH 2/3] Added method to calculate the deviation from a straight
 line

---
 .../Coordinates/EclipticalCoordinates.php     |  3 ++
 .../Coordinates/EquatorialCoordinates.php     | 54 ++++++++++++++++++-
 .../Coordinates/GalacticCoordinates.php       |  1 +
 .../Coordinates/HorizontalCoordinates.php     |  7 ++-
 .../AstronomyLibrary/Targets/Moon.php         |  2 +-
 .../AstronomyLibrary/Targets/Target.php       | 28 ++++++----
 src/deepskylog/AstronomyLibrary/Time.php      | 14 ++---
 tests/Unit/EquatorialCoordinatesTest.php      | 37 ++++++++++++-
 8 files changed, 124 insertions(+), 22 deletions(-)

diff --git a/src/deepskylog/AstronomyLibrary/Coordinates/EclipticalCoordinates.php b/src/deepskylog/AstronomyLibrary/Coordinates/EclipticalCoordinates.php
index a3094a4..b15a189 100644
--- a/src/deepskylog/AstronomyLibrary/Coordinates/EclipticalCoordinates.php
+++ b/src/deepskylog/AstronomyLibrary/Coordinates/EclipticalCoordinates.php
@@ -108,6 +108,7 @@ public function printLatitude(): string
 
     /**
      * Converts the ecliptical coordinates to equatorial coordinates.
+     * Chapter 13 of Astronomical Algorithms.
      *
      * @param float $nutObliquity The nutation in obliquity
      *
@@ -141,6 +142,7 @@ public function convertToEquatorial(float $nutObliquity): EquatorialCoordinates
     /**
      * Converts the ecliptical coordinates to equatorial coordinates in
      * the J2000 equinox.
+     * Chapter 13 of Astronomical Algorithms.
      *
      * @return EquatorialCoordinates The equatorial coordinates
      */
@@ -152,6 +154,7 @@ public function convertToEquatorialJ2000(): EquatorialCoordinates
     /**
      * Converts the ecliptical coordinates to equatorial coordinates in
      * the B1950 equinox.
+     * Chapter 13 of Astronomical Algorithms.
      *
      * @return EquatorialCoordinates The equatorial coordinates
      */
diff --git a/src/deepskylog/AstronomyLibrary/Coordinates/EquatorialCoordinates.php b/src/deepskylog/AstronomyLibrary/Coordinates/EquatorialCoordinates.php
index 513f11b..b1e3197 100644
--- a/src/deepskylog/AstronomyLibrary/Coordinates/EquatorialCoordinates.php
+++ b/src/deepskylog/AstronomyLibrary/Coordinates/EquatorialCoordinates.php
@@ -111,6 +111,7 @@ public function printRA(): string
     /**
      * Converts the equatorial coordinates to ecliptical coordinates in
      * the current equinox.
+     * Chapter 13 of Astronomical Algorithms.
      *
      * @param float $nutObliquity The nutation in obliquity
      *
@@ -144,6 +145,7 @@ public function convertToEcliptical(float $nutObliquity): EclipticalCoordinates
     /**
      * Converts the equatorial coordinates to ecliptical coordinates in
      * the J2000 equinox.
+     * Chapter 13 of Astronomical Algorithms.
      *
      * @return EclipticalCoordinates The ecliptical coordinates
      */
@@ -155,6 +157,7 @@ public function convertToEclipticalJ2000(): EclipticalCoordinates
     /**
      * Converts the equatorial coordinates to ecliptical coordinates in
      * the B1950 equinox.
+     * Chapter 13 of Astronomical Algorithms.
      *
      * @return EclipticalCoordinates The ecliptical coordinates
      */
@@ -165,6 +168,7 @@ public function convertToEclipticalB1950(): EclipticalCoordinates
 
     /**
      * Converts the equatorial coordinates to local horizontal coordinates.
+     * Chapter 13 of Astronomical Algorithms.
      *
      * @param GeographicalCoordinates $geo_coords    the geographical
      *                                               coordinates
@@ -204,6 +208,7 @@ public function convertToHorizontal(
 
     /**
      * Converts the equatorial coordinates to galactic coordinates.
+     * Chapter 13 of Astronomical Algorithms.
      *
      * @return GalacticCoordinates The galactic coordinates
      */
@@ -236,7 +241,7 @@ public function convertToGalactic(): GalacticCoordinates
      * Returns the parallactic angle of the object. The parallactic angle is
      * negative before and positive after the passage throught the southern
      * meridian. This is the effect of the moon that is lying down at moonrise.
-     * Astronomical Algorithms - chapter 13.
+     * Chapter 14 of Astronomical Algorithms.
      *
      * @param GeographicalCoordinates $geo_coords    the geographical
      *                                               coordinates
@@ -282,6 +287,7 @@ public function getHourAngle(Carbon $siderial_time): float
     /**
      * Returns the angular separation between these coordinates and other
      * equatorial coordinates.
+     * Chapter 17 of Astronomical Algorithms.
      *
      * @param EquatorialCoordinates $coords2 the coordinates of the second object
      *
@@ -330,6 +336,7 @@ public function angularSeparation(
 
     /**
      * Returns true if the three bodies are in a straight line.
+     * Chapter 19 of Astronomical Algorithms.
      *
      * @param EquatorialCoordinates $coords2   The coordinates of the second object
      * @param EquatorialCoordinates $coords3   The coordinates of the thirds object
@@ -369,4 +376,49 @@ public function isInStraightLine(
 
         return false;
     }
+
+    /**
+     * Returns the deviation from a straight line.
+     * Chapter 19 of Astronomical Algorithms.
+     *
+     * @param EquatorialCoordinates $coords2 The coordinates of the first object
+     * @param EquatorialCoordinates $coords3 The coordinates of the second object
+     *
+     * @return Coordinate the deviation from the straight line
+     */
+    public function deviationFromStraightLine(
+        self $coords2,
+        self $coords3
+    ): Coordinate {
+        $X1 = cos(deg2rad($coords2->getDeclination()->getCoordinate())) *
+                    cos(deg2rad($coords2->getRA()->getCoordinate() * 15.0));
+        $Y1 = cos(deg2rad($coords2->getDeclination()->getCoordinate())) *
+                    sin(deg2rad($coords2->getRA()->getCoordinate() * 15.0));
+        $Z1 = sin(deg2rad($coords2->getDeclination()->getCoordinate()));
+
+        $X2 = cos(deg2rad($coords3->getDeclination()->getCoordinate())) *
+                    cos(deg2rad($coords3->getRA()->getCoordinate() * 15.0));
+        $Y2 = cos(deg2rad($coords3->getDeclination()->getCoordinate())) *
+                    sin(deg2rad($coords3->getRA()->getCoordinate() * 15.0));
+        $Z2 = sin(deg2rad($coords3->getDeclination()->getCoordinate()));
+
+        $A = $Y1 * $Z2 - $Z1 * $Y2;
+        $B = $Z1 * $X2 - $X1 * $Z2;
+        $C = $X1 * $Y2 - $Y1 * $X2;
+
+        $m = tan(deg2rad($this->getRA()->getCoordinate() * 15.0));
+        $n = tan(deg2rad($this->getDeclination()->getCoordinate()))
+                    / cos(deg2rad($this->getRA()->getCoordinate() * 15.0));
+
+        $omega = rad2deg(
+            abs(
+                asin(
+                    ($A + $B * $m + $C * $n) /
+                    (sqrt($A * $A + $B * $B + $C * $C) * sqrt(1 + $m * $m + $n * $n))
+                )
+            )
+        );
+
+        return new Coordinate($omega, 0.0, 90.0);
+    }
 }
diff --git a/src/deepskylog/AstronomyLibrary/Coordinates/GalacticCoordinates.php b/src/deepskylog/AstronomyLibrary/Coordinates/GalacticCoordinates.php
index 0b12103..3709e91 100644
--- a/src/deepskylog/AstronomyLibrary/Coordinates/GalacticCoordinates.php
+++ b/src/deepskylog/AstronomyLibrary/Coordinates/GalacticCoordinates.php
@@ -108,6 +108,7 @@ public function printLatitude(): string
 
     /**
      * Converts the galactic coordinates to equatorial coordinates.
+     * Chapter 13 of Astronomical Algorithms.
      *
      * @return EquatorialCoordinates The equatorial coordinates
      */
diff --git a/src/deepskylog/AstronomyLibrary/Coordinates/HorizontalCoordinates.php b/src/deepskylog/AstronomyLibrary/Coordinates/HorizontalCoordinates.php
index f93f4f0..3abcf3d 100644
--- a/src/deepskylog/AstronomyLibrary/Coordinates/HorizontalCoordinates.php
+++ b/src/deepskylog/AstronomyLibrary/Coordinates/HorizontalCoordinates.php
@@ -110,6 +110,7 @@ public function printAltitude(): string
 
     /**
      * Converts the local horizontal coordinates to equatorial coordinates.
+     * Chapter 13 of Astronomical Algorithms.
      *
      * @param GeographicalCoordinates $geo_coords    the geographical
      *                                               coordinates
@@ -178,8 +179,9 @@ public function convertToEquatorial(
     /**
      * Calculates the refaction (in minutes of arc) if the apparent
      * height is given.
+     * Chapter 16 of Astronomical Algorithms.
      *
-     * @return float The refraction in minutes of arc.
+     * @return float the refraction in minutes of arc
      */
     public function calculateRefractionFromApparentAltitude(): float
     {
@@ -196,8 +198,9 @@ public function calculateRefractionFromApparentAltitude(): float
     /**
      * Calculates the refaction (in minutes of arc) if the true
      * height is given.
+     * Chapter 16 of Astronomical Algorithms.
      *
-     * @return float The refraction in minutes of arc.
+     * @return float the refraction in minutes of arc
      */
     public function calculateRefractionFromTrueAltitude(): float
     {
diff --git a/src/deepskylog/AstronomyLibrary/Targets/Moon.php b/src/deepskylog/AstronomyLibrary/Targets/Moon.php
index 9344560..0f190ec 100644
--- a/src/deepskylog/AstronomyLibrary/Targets/Moon.php
+++ b/src/deepskylog/AstronomyLibrary/Targets/Moon.php
@@ -38,7 +38,7 @@ public function __construct()
     /**
      * Calculates the horizontal moon parallax.
      *
-     * To implement from chapter 29.
+     * To implement from chapter 30.
      *
      * @return float the horizontal moon parallax
      */
diff --git a/src/deepskylog/AstronomyLibrary/Targets/Target.php b/src/deepskylog/AstronomyLibrary/Targets/Target.php
index 00db2a9..63e26a3 100644
--- a/src/deepskylog/AstronomyLibrary/Targets/Target.php
+++ b/src/deepskylog/AstronomyLibrary/Targets/Target.php
@@ -209,12 +209,13 @@ public function getEquatorialCoordinatesTomorrow(): EquatorialCoordinates
 
     /**
      * Get the transit time of this object.
+     * Chapter 15 of Astronomical Algorithms.
      *
      * @return Carbon the transit time of the object
      **/
     public function getTransit(): Carbon
     {
-        if (! $this->_transit) {
+        if (!$this->_transit) {
             throw new RuntimeException(
                 'First execute the calculateEphemerides method'
             );
@@ -225,13 +226,14 @@ public function getTransit(): Carbon
 
     /**
      * Get the rising time of this object.
+     * Chapter 15 of Astronomical Algorithms.
      *
      * @return Carbon The rising time of the object or null if the object does not
      *                set
      **/
     public function getRising(): ?Carbon
     {
-        if (! $this->_transit) {
+        if (!$this->_transit) {
             throw new RuntimeException(
                 'First execute the calculateEphemerides method'
             );
@@ -242,13 +244,14 @@ public function getRising(): ?Carbon
 
     /**
      * Get the setting time of this object.
+     * Chapter 15 of Astronomical Algorithms.
      *
      * @return Carbon The setting time of the object or null if the object does
      *                not set
      **/
     public function getSetting(): ?Carbon
     {
-        if (! $this->_transit) {
+        if (!$this->_transit) {
             throw new RuntimeException(
                 'First execute the calculateEphemerides method'
             );
@@ -259,12 +262,13 @@ public function getSetting(): ?Carbon
 
     /**
      * Get the maximum height of the target during the year.
+     * Chapter 15 of Astronomical Algorithms.
      *
      * @return Coordinate the maximum height of the target during the year
      **/
     public function getMaxHeight(): ?Coordinate
     {
-        if (! $this->_transit) {
+        if (!$this->_transit) {
             throw new RuntimeException(
                 'First execute the calculateEphemerides method'
             );
@@ -278,12 +282,13 @@ public function getMaxHeight(): ?Coordinate
      * no astronomical darkness during the night, the maximum height
      * during the nautical brightness is taken.  If there is also no
      * nautical brightness, null is returned.
+     * Chapter 15 of Astronomical Algorithms.
      *
      * @return Coordinate the maximum height of the target during the year
      **/
     public function getMaxHeightAtNight(): ?Coordinate
     {
-        if (! $this->_transit) {
+        if (!$this->_transit) {
             throw new RuntimeException(
                 'First execute the calculateEphemerides method'
             );
@@ -294,12 +299,13 @@ public function getMaxHeightAtNight(): ?Coordinate
 
     /**
      * Get the best time to observe this target at the given date.
+     * Chapter 15 of Astronomical Algorithms.
      *
      * @return Carbon The best time to observe the target at the given date
      **/
     public function getBestTimeToObserve(): ?Carbon
     {
-        if (! $this->_transit) {
+        if (!$this->_transit) {
             throw new RuntimeException(
                 'First execute the calculateEphemerides method'
             );
@@ -310,6 +316,7 @@ public function getBestTimeToObserve(): ?Carbon
 
     /**
      * Calculate rising and the setting of the object.
+     * Chapter 15 of Astronomical Algorithms.
      *
      * @param GeographicalCoordinates $geo_coords    The geographical
      *                                               coordinates of the observer
@@ -552,7 +559,7 @@ public function calculateEphemerides(
             }
         }
 
-        if (! $during_night) {
+        if (!$during_night) {
             $th = new Coordinate($transitHeight, -90.0, 90.0);
 
             // Calculate the height at the end of the night
@@ -654,6 +661,7 @@ public function calculateEphemerides(
 
     /**
      * Calculates the height of the object at a given moment.
+     * Chapter 15 of Astronomical Algorithms.
      *
      * @param float                   $theta0            Theta0 of the target
      * @param float                   $time              The time to calculate the
@@ -689,7 +697,7 @@ private function _calculateHeight(
         $theta = $this->_calculateTheta($theta0, $time);
         $n = $this->_calculateN($time, $deltaT);
 
-        if (! $targetDoesNotMove) {
+        if (!$targetDoesNotMove) {
             $alphaInterpol = $this->_interpolate(
                 $this->getEquatorialCoordinatesToday()->getRA()->getCoordinate(),
                 $n,
@@ -877,7 +885,7 @@ public function altitudeGraph(
         GeographicalCoordinates $geo_coords,
         Carbon $date
     ): string {
-        if (! $this->_altitudeChart) {
+        if (!$this->_altitudeChart) {
             $image = imagecreatetruecolor(1000, 400);
 
             // Show the night
@@ -1046,7 +1054,7 @@ public function altitudeGraph(
             $rawImageBytes = ob_get_clean();
 
             $this->_altitudeChart = "<img src='data:image/jpeg;base64,"
-                .base64_encode($rawImageBytes)."' />";
+                . base64_encode($rawImageBytes) . "' />";
         }
 
         return $this->_altitudeChart;
diff --git a/src/deepskylog/AstronomyLibrary/Time.php b/src/deepskylog/AstronomyLibrary/Time.php
index 83e8287..ac73f35 100644
--- a/src/deepskylog/AstronomyLibrary/Time.php
+++ b/src/deepskylog/AstronomyLibrary/Time.php
@@ -140,7 +140,7 @@ public static function fromJd(float $jd): Carbon
 
     /**
      * Returns the dynamical time as the time + delta t.
-     * Chapter 9 in Astronomical Algorithms.
+     * Chapter 10 in Astronomical Algorithms.
      *
      * @param Carbon $date The date
      *
@@ -153,7 +153,7 @@ public static function dynamicalTime(Carbon $date): Carbon
 
     /**
      * Calculates delta t for the given date.
-     * Chapter 9 in Astronomical Algorithms.
+     * Chapter 10 in Astronomical Algorithms.
      *
      * @param Carbon $date The date
      *
@@ -221,7 +221,7 @@ public static function deltaT(Carbon $date): float
 
     /**
      * Calculates the mean siderial time for the given date.
-     * Chapter 11 in Astronomical Algorithms.
+     * Chapter 12 in Astronomical Algorithms.
      *
      * @param Carbon                  $date   The date
      * @param GeographicalCoordinates $coords The geographical coordinates
@@ -265,7 +265,7 @@ public static function meanSiderialTime(
 
     /**
      * Calculates the apparent siderial time for the given date.
-     * Chapter 11 in Astronomical Algorithms.
+     * Chapter 12 in Astronomical Algorithms.
      *
      * @param Carbon                  $date     The date
      * @param GeographicalCoordinates $coords   The geographical coordinates
@@ -280,7 +280,7 @@ public static function apparentSiderialTime(
     ): Carbon {
         $date = $date->copy()->timezone('UTC');
         $siderialTime = self::meanSiderialTime($date, $coords);
-        if (! $nutation) {
+        if (!$nutation) {
             $jd = self::getJd($date);
 
             $nutation = self::nutation($jd);
@@ -296,7 +296,7 @@ public static function apparentSiderialTime(
     /**
      * Calculates the apparent siderial time for the given date, at midnight,
      * in Greenwich.
-     * Chapter 11 in Astronomical Algorithms.
+     * Chapter 12 in Astronomical Algorithms.
      *
      * @param Carbon $date The date
      *
@@ -316,7 +316,7 @@ public static function apparentSiderialTimeGreenwich(
 
     /**
      * Calculates the nutation for the given julian day.
-     * Chapter 21 of Astronomical Algorithms.
+     * Chapter 22 of Astronomical Algorithms.
      *
      * @param float $jd The Julian day
      *
diff --git a/tests/Unit/EquatorialCoordinatesTest.php b/tests/Unit/EquatorialCoordinatesTest.php
index ab70e11..9352ccd 100644
--- a/tests/Unit/EquatorialCoordinatesTest.php
+++ b/tests/Unit/EquatorialCoordinatesTest.php
@@ -218,7 +218,7 @@ public function testAngularSeparation()
     }
 
     /**
-     * Test bodies in straight line/**.
+     * Test bodies in straight line.
      *
      * @return None
      */
@@ -237,4 +237,39 @@ public function testBodiesInStraightLine()
         $mars = new EquatorialCoordinates(8.022644129, 21.472188347);
         $this->assertTrue($mars->isInStraightLine($castor, $pollux));
     }
+
+    /**
+     * Test deviation of three bodies from a straight line.
+     *
+     * @return None
+     */
+    public function testDeviationFromStraightLine()
+    {
+        // Delta Ori
+        $delta = new EquatorialCoordinates(5.5334444, -0.29913888);
+        // Epsilon Ori
+        $eps = new EquatorialCoordinates(5.60355833, -1.20194444);
+        // Ksi Ori
+        $ksi = new EquatorialCoordinates(5.679311111, -1.94258333);
+        $this->assertEqualsWithDelta(
+            $eps->deviationFromStraightLine($delta, $ksi)->getCoordinate(),
+            0.089876,
+            0.001
+        );
+
+        // Alpha Uma
+        $alpha = new EquatorialCoordinates(11.062129444, 61.750894444);
+
+        // Beta Uma
+        $beta = new EquatorialCoordinates(11.030689444, 56.3824027778);
+
+        // Polaris
+        $polaris = new EquatorialCoordinates(2.530195556, 89.26408889);
+
+        $this->assertEqualsWithDelta(
+            $polaris->deviationFromStraightLine($alpha, $beta)->getCoordinate(),
+            1.91853,
+            0.001
+        );
+    }
 }

From 5cb5a7e9109e64ca4cc59ef173f3bd8c478812cf Mon Sep 17 00:00:00 2001
From: Wim De Meester <wim.demeester@kuleuven.be>
Date: Fri, 31 Jul 2020 12:52:32 +0000
Subject: [PATCH 3/3] Apply fixes from StyleCI

---
 .../AstronomyLibrary/Targets/Target.php       | 20 +++++++++----------
 src/deepskylog/AstronomyLibrary/Time.php      |  2 +-
 tests/Unit/EquatorialCoordinatesTest.php      |  2 +-
 3 files changed, 12 insertions(+), 12 deletions(-)

diff --git a/src/deepskylog/AstronomyLibrary/Targets/Target.php b/src/deepskylog/AstronomyLibrary/Targets/Target.php
index 63e26a3..98410fb 100644
--- a/src/deepskylog/AstronomyLibrary/Targets/Target.php
+++ b/src/deepskylog/AstronomyLibrary/Targets/Target.php
@@ -215,7 +215,7 @@ public function getEquatorialCoordinatesTomorrow(): EquatorialCoordinates
      **/
     public function getTransit(): Carbon
     {
-        if (!$this->_transit) {
+        if (! $this->_transit) {
             throw new RuntimeException(
                 'First execute the calculateEphemerides method'
             );
@@ -233,7 +233,7 @@ public function getTransit(): Carbon
      **/
     public function getRising(): ?Carbon
     {
-        if (!$this->_transit) {
+        if (! $this->_transit) {
             throw new RuntimeException(
                 'First execute the calculateEphemerides method'
             );
@@ -251,7 +251,7 @@ public function getRising(): ?Carbon
      **/
     public function getSetting(): ?Carbon
     {
-        if (!$this->_transit) {
+        if (! $this->_transit) {
             throw new RuntimeException(
                 'First execute the calculateEphemerides method'
             );
@@ -268,7 +268,7 @@ public function getSetting(): ?Carbon
      **/
     public function getMaxHeight(): ?Coordinate
     {
-        if (!$this->_transit) {
+        if (! $this->_transit) {
             throw new RuntimeException(
                 'First execute the calculateEphemerides method'
             );
@@ -288,7 +288,7 @@ public function getMaxHeight(): ?Coordinate
      **/
     public function getMaxHeightAtNight(): ?Coordinate
     {
-        if (!$this->_transit) {
+        if (! $this->_transit) {
             throw new RuntimeException(
                 'First execute the calculateEphemerides method'
             );
@@ -305,7 +305,7 @@ public function getMaxHeightAtNight(): ?Coordinate
      **/
     public function getBestTimeToObserve(): ?Carbon
     {
-        if (!$this->_transit) {
+        if (! $this->_transit) {
             throw new RuntimeException(
                 'First execute the calculateEphemerides method'
             );
@@ -559,7 +559,7 @@ public function calculateEphemerides(
             }
         }
 
-        if (!$during_night) {
+        if (! $during_night) {
             $th = new Coordinate($transitHeight, -90.0, 90.0);
 
             // Calculate the height at the end of the night
@@ -697,7 +697,7 @@ private function _calculateHeight(
         $theta = $this->_calculateTheta($theta0, $time);
         $n = $this->_calculateN($time, $deltaT);
 
-        if (!$targetDoesNotMove) {
+        if (! $targetDoesNotMove) {
             $alphaInterpol = $this->_interpolate(
                 $this->getEquatorialCoordinatesToday()->getRA()->getCoordinate(),
                 $n,
@@ -885,7 +885,7 @@ public function altitudeGraph(
         GeographicalCoordinates $geo_coords,
         Carbon $date
     ): string {
-        if (!$this->_altitudeChart) {
+        if (! $this->_altitudeChart) {
             $image = imagecreatetruecolor(1000, 400);
 
             // Show the night
@@ -1054,7 +1054,7 @@ public function altitudeGraph(
             $rawImageBytes = ob_get_clean();
 
             $this->_altitudeChart = "<img src='data:image/jpeg;base64,"
-                . base64_encode($rawImageBytes) . "' />";
+                .base64_encode($rawImageBytes)."' />";
         }
 
         return $this->_altitudeChart;
diff --git a/src/deepskylog/AstronomyLibrary/Time.php b/src/deepskylog/AstronomyLibrary/Time.php
index ac73f35..0b5d3f0 100644
--- a/src/deepskylog/AstronomyLibrary/Time.php
+++ b/src/deepskylog/AstronomyLibrary/Time.php
@@ -280,7 +280,7 @@ public static function apparentSiderialTime(
     ): Carbon {
         $date = $date->copy()->timezone('UTC');
         $siderialTime = self::meanSiderialTime($date, $coords);
-        if (!$nutation) {
+        if (! $nutation) {
             $jd = self::getJd($date);
 
             $nutation = self::nutation($jd);
diff --git a/tests/Unit/EquatorialCoordinatesTest.php b/tests/Unit/EquatorialCoordinatesTest.php
index 9352ccd..d27e880 100644
--- a/tests/Unit/EquatorialCoordinatesTest.php
+++ b/tests/Unit/EquatorialCoordinatesTest.php
@@ -36,7 +36,7 @@ class EquatorialCoordinatesTest extends BaseTestCase
      *
      * @var string
      */
-    protected $appPath = __DIR__ . '/../../vendor/laravel/laravel/bootstrap/app.php';
+    protected $appPath = __DIR__.'/../../vendor/laravel/laravel/bootstrap/app.php';
 
     /**
      * Setup the test environment.