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Implemented Python version of transit search functions.
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Don Cross
@@ -591,6 +591,31 @@ to represent the date and time in this Time object.
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---
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<a name="TransitInfo"></a>
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### class TransitInfo
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**Information about a transit of Mercury or Venus, as seen from the Earth.**
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Returned by [`SearchTransit`](#SearchTransit) or [`NextTransit`](#NextTransit) to report
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information about a transit of Mercury or Venus.
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A transit is when Mercury or Venus passes between the Sun and Earth so that
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the other planet is seen in silhouette against the Sun.
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The calculations are performed from the point of view of a geocentric observer.
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peak : Time
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When the planet is most aligned with the Sun, as seen from the Earth.
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finish : Time
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The date and time at the end of the transit.
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This is the moment the planet is last seen against the Sun in its background.
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separation : float
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The minimum angular separation, in arcminutes, between the centers of the Sun and the planet.
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This angle pertains to the time stored in `peak`.
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| Type | Attribute | Description |
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| --- | --- | --- |
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| [`Time`](#Time) | `start` | The date and time at the beginning of the transit. This is the moment the planet first becomes visible against the Sun in its background. |
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---
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<a name="Vector"></a>
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### class Vector
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@@ -1422,6 +1447,24 @@ See [`SearchPlanetApsis`](#SearchPlanetApsis) for more details.
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---
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<a name="NextTransit"></a>
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### NextTransit(body, prevTransitTime)
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**Searches for another transit of Mercury or Venus.**
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After calling [`SearchTransit`](#SearchTransit) to find a transit of Mercury or Venus,
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this function finds the next transit after that.
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Keep calling this function as many times as you want to keep finding more transits.
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| Type | Parameter | Description |
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| --- | --- | --- |
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| [`Body`](#Body) | `body` | The planet whose transit is to be found. Must be `Body.Mercury` or `Body.Venus`. |
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| [`Time`](#Time) | `prevTransitTime` | A date and time near the previous transit. |
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### Returns: [`TransitInfo`](#TransitInfo)
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---
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<a name="RefractionAngle"></a>
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### RefractionAngle(refraction, altitude)
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@@ -2119,6 +2162,26 @@ limitDays : float
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---
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<a name="SearchTransit"></a>
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### SearchTransit(body, startTime)
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**Searches for the first transit of Mercury or Venus after a given date.**
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Finds the first transit of Mercury or Venus after a specified date.
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A transit is when an inferior planet passes between the Sun and the Earth
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so that the silhouette of the planet is visible against the Sun in the background.
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To continue the search, pass the `finish` time in the returned structure to
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[`NextTransit`](#NextTransit).
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| Type | Parameter | Description |
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| --- | --- | --- |
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| [`Body`](#Body) | `body` | The planet whose transit is to be found. Must be `Body.Mercury` or `Body.Venus`. |
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| [`Time`](#Time) | `startTime` | The date and time for starting the search for a transit. |
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### Returns: [`TransitInfo`](#TransitInfo)
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---
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<a name="Seasons"></a>
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### Seasons(year)
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@@ -6653,6 +6653,20 @@ def _LocalMoonShadow(time, observer):
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return _CalcShadow(_MOON_MEAN_RADIUS_KM, time, o, m)
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def _PlanetShadow(body, planet_radius_km, time):
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# Calculate light-travel-corrected vector from Earth to planet.
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g = GeoVector(body, time, False)
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# Calculate light-travel-corrected vector from Earth to Sun.
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e = GeoVector(Body.Sun, time, False)
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# Deduce light-travel-corrected vector from Sun to planet.
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p = Vector(g.x - e.x, g.y - e.y, g.z - e.z, time)
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# Calcluate Earth's position from the planet's point of view.
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e.x = -g.x
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e.y = -g.y
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e.z = -g.z
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return _CalcShadow(planet_radius_km, time, e, p)
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def _ShadowDistanceSlope(shadowfunc, time):
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dt = 1.0 / 86400.0
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t1 = time.AddDays(-dt)
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@@ -6662,6 +6676,14 @@ def _ShadowDistanceSlope(shadowfunc, time):
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return (shadow2.r - shadow1.r) / dt
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def _PlanetShadowSlope(context, time):
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(body, planet_radius_km) = context
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dt = 1.0 / 86400.0
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shadow1 = _PlanetShadow(body, planet_radius_km, time.AddDays(-dt))
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shadow2 = _PlanetShadow(body, planet_radius_km, time.AddDays(+dt))
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return (shadow2.r - shadow1.r) / dt
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def _PeakEarthShadow(search_center_time):
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window = 0.03 # initial search window, in days, before/after given time
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t1 = search_center_time.AddDays(-window)
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@@ -6686,6 +6708,14 @@ def _PeakLocalMoonShadow(search_center_time, observer):
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tx = Search(_ShadowDistanceSlope, lambda time: _LocalMoonShadow(time, observer), t1, t2, 1.0)
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return _LocalMoonShadow(tx, observer)
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def _PeakPlanetShadow(body, planet_radius_km, search_center_time):
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# Search for when the body's shadow is closest to the center of the Earth.
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window = 1.0 # days before/after inferior conjunction to search for minimum shadow distance.
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t1 = search_center_time.AddDays(-window)
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t2 = search_center_time.AddDays(+window)
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tx = Search(_PlanetShadowSlope, (body, planet_radius_km), t1, t2, 1.0)
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return _PlanetShadow(body, planet_radius_km, tx)
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class _ShadowDiffContext:
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def __init__(self, radius_limit, direction):
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self.radius_limit = radius_limit
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@@ -7266,3 +7296,135 @@ def NextLocalSolarEclipse(prevEclipseTime, observer):
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"""
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startTime = prevEclipseTime.AddDays(10.0)
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return SearchLocalSolarEclipse(startTime, observer)
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class TransitInfo:
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"""Information about a transit of Mercury or Venus, as seen from the Earth.
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Returned by #SearchTransit or #NextTransit to report
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information about a transit of Mercury or Venus.
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A transit is when Mercury or Venus passes between the Sun and Earth so that
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the other planet is seen in silhouette against the Sun.
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The calculations are performed from the point of view of a geocentric observer.
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Attributes
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----------
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start : Time
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The date and time at the beginning of the transit.
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This is the moment the planet first becomes visible against the Sun in its background.
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peak : Time
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When the planet is most aligned with the Sun, as seen from the Earth.
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finish : Time
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The date and time at the end of the transit.
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This is the moment the planet is last seen against the Sun in its background.
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separation : float
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The minimum angular separation, in arcminutes, between the centers of the Sun and the planet.
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This angle pertains to the time stored in `peak`.
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"""
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def __init__(self, start, peak, finish, separation):
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self.start = start
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self.peak = peak
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self.finish = finish
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self.separation = separation
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def _PlanetShadowBoundary(context, time):
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(body, planet_radius_km, direction) = context
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shadow = _PlanetShadow(body, planet_radius_km, time)
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return direction * (shadow.r - shadow.p)
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def _PlanetTransitBoundary(body, planet_radius_km, t1, t2, direction):
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# Search for the time the planet's penumbra begins/ends making contact with the center of the Earth.
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# context = new SearchContext_PlanetShadowBoundary(body, planet_radius_km, direction);
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tx = Search(_PlanetShadowBoundary, (body, planet_radius_km, direction), t1, t2, 1.0)
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if tx is None:
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raise Error('Planet transit boundary search failed')
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return tx
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def SearchTransit(body, startTime):
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"""Searches for the first transit of Mercury or Venus after a given date.
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Finds the first transit of Mercury or Venus after a specified date.
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A transit is when an inferior planet passes between the Sun and the Earth
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so that the silhouette of the planet is visible against the Sun in the background.
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To continue the search, pass the `finish` time in the returned structure to
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#NextTransit.
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Parameters
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----------
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body : Body
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The planet whose transit is to be found. Must be `Body.Mercury` or `Body.Venus`.
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startTime : Time
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The date and time for starting the search for a transit.
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Returns
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-------
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TransitInfo
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"""
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threshold_angle = 0.4 # maximum angular separation to attempt transit calculation
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dt_days = 1.0
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# Validate the planet and find its mean radius.
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if body == Body.Mercury:
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planet_radius_km = 2439.7
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elif body == Body.Venus:
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planet_radius_km = 6051.8
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else:
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raise InvalidBodyError()
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search_time = startTime
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while True:
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# Search for the next inferior conjunction of the given planet.
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# This is the next time the Earth and the other planet have the same
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# ecliptic longitude as seen from the Sun.
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conj = SearchRelativeLongitude(body, 0.0, search_time)
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# Calculate the angular separation between the body and the Sun at this time.
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conj_separation = AngleFromSun(body, conj)
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if conj_separation < threshold_angle:
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# The planet's angular separation from the Sun is small enough
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# to consider it a transit candidate.
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# Search for the moment when the line passing through the Sun
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# and planet are closest to the Earth's center.
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shadow = _PeakPlanetShadow(body, planet_radius_km, conj)
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if shadow.r < shadow.p: # does the planet's penumbra touch the Earth's center?
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# Find the beginning and end of the penumbral contact.
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time_before = shadow.time.AddDays(-dt_days)
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start = _PlanetTransitBoundary(body, planet_radius_km, time_before, shadow.time, -1.0)
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time_after = shadow.time.AddDays(+dt_days)
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finish = _PlanetTransitBoundary(body, planet_radius_km, shadow.time, time_after, +1.0)
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min_separation = 60.0 * AngleFromSun(body, shadow.time)
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return TransitInfo(start, shadow.time, finish, min_separation)
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# This inferior conjunction was not a transit. Try the next inferior conjunction.
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search_time = conj.AddDays(10.0)
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def NextTransit(body, prevTransitTime):
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"""Searches for another transit of Mercury or Venus.
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After calling #SearchTransit to find a transit of Mercury or Venus,
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this function finds the next transit after that.
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Keep calling this function as many times as you want to keep finding more transits.
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Parameters
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----------
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body : Body
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The planet whose transit is to be found. Must be `Body.Mercury` or `Body.Venus`.
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prevTransitTime : Time
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A date and time near the previous transit.
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Returns
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-------
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TransitInfo
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"""
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startTime = prevTransitTime.AddDays(100.0)
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return SearchTransit(body, startTime)
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