Solar Eclipse Prime Page

Hybrid Solar Eclipse of -0541 Jul 31 (0542 Jul 31 BCE)

Fred Espenak

Introduction

The Hybrid Solar Eclipse of -0541 Jul 31 (0542 Jul 31 BCE) is visible from the geographic regions shown on the map to the right. Click on the map to enlarge it. For an explanation of the features appearing in the map, see Key to Solar Eclipse Maps.

The instant of greatest eclipse takes place on -0541 Jul 31 at 11:55:50 TD (07:00:40 UT1). This is 6.3 days after the Moon reaches perigee. During the eclipse, the Sun is in the constellation Leo. The synodic month in which the eclipse takes place has a Brown Lunation Number of -30468.

The eclipse belongs to Saros 56 and is number 36 of 74 eclipses in the series. All eclipses in this series occur at the Moon’s descending node. The Moon moves northward with respect to the node with each succeeding eclipse in the series and gamma increases.

The solar eclipse of -0541 Jul 31 is one of the rare hybrid solar eclipses. In this particular case the eclipse path starts out as annular. Further down the track it changes to total and then back to annular before the path ends. It is a very short hybrid eclipse with a duration at greatest eclipse of 00m09s. The eclipse magnitude is 1.0015, while Gamma has a value of 0.0609.

The hybrid solar eclipse of -0541 Jul 31 is preceded two weeks earlier by a penumbral lunar eclipse on -0541 Jul 17, and it is followed two weeks later by a penumbral lunar eclipse on -0541 Aug 16.

These eclipses all take place during a single eclipse season.

The eclipse predictions are given in both Terrestrial Dynamical Time (TD) and Universal Time (UT1). The parameter ΔT is used to convert between these two times (i.e., UT1 = TD - ΔT). ΔT has a value of 17710.4 seconds for this eclipse. The uncertainty in ΔT is 445.7 seconds corresponding to a standard error in longitude of the eclipse path of ± 1.86°.

The following links provide maps and data for the eclipse.

Orthographic Map: Hybrid Solar Eclipse of -0541 Jul 31 - global map of eclipse visibility
Google Map: Hybrid Solar Eclipse of -0541 Jul 31 - interactive map of the eclipse path
Path Table: Hybrid Solar Eclipse of -0541 Jul 31 - coordinates of the central line and path limits
Circumstances Table: Hybrid Solar Eclipse of -0541 Jul 31 - eclipse times for hundreds of cities
Saros 56 Table - data for all eclipses in the Saros series

The tables below contain detailed predictions and additional information on the Hybrid Solar Eclipse of -0541 Jul 31 .

Eclipse Data: Hybrid Solar Eclipse of -0541 Jul 31

Eclipse Characteristics
Parameter	Value
Eclipse Magnitude	1.00153
Eclipse Obscuration	1.00307
Gamma	0.06094

Conjunction Times
Event	Calendar Date and Time	Julian Date
Greatest Eclipse	-0541 Jul 31 at 11:55:50.0 TD (07:00:39.6 UT1)	1523668.792125
Ecliptic Conjunction	-0541 Jul 31 at 11:55:09.7 TD (06:59:59.3 UT1)	1523668.791659
Equatorial Conjunction	-0541 Jul 31 at 11:53:36.7 TD (06:58:26.3 UT1)	1523668.790583

Geocentric Coordinates of Sun and Moon
-0541 Jul 31 at 11:55:50.0 TD (07:00:39.6 UT1)
Coordinate	Sun	Moon
Right Ascension	08h10m25.1s	08h10m29.7s
Declination	+20°20'55.1"	+20°24'13.9"
Semi-Diameter	15'51.6"	15'38.0"
Eq. Hor. Parallax	08.7"	0°57'22.4"

Geocentric Libration of Moon
Angle	Value
l	5.5°
b	0.0°
c	11.1°

Prediction Paramaters
Paramater	Value
Ephemerides	JPL DE406
ΔT	17710.4 s
k (penumbra)	0.2725076
k (umbra)	0.2722810
Saros Series	56 (36/74)

Explanation of Solar Eclipse Data Tables

Penumbral Shadow Contacts and Extremes: Hybrid Solar Eclipse of -0541 Jul 31

Contacts of Penumbral Shadow with Earth
Contact Event	Contact	Time TD	Time UT1	Latitude	Longitude
First External Contact	P1	09:04:28.3	04:09:17.9	19°12.7'N	020°52.2'E
First Internal Contact	P2	11:06:35.0	06:11:24.6	24°24.2'N	011°54.8'W
Last Internal Contact	P3	12:45:07.0	07:49:56.6	09°50.7'S	149°27.3'E
Last External Contact	P4	14:47:19.2	09:52:08.8	15°04.8'S	116°51.9'E

Extreme Northern and Southern Path Limits of Penumbra
Contact Event	Contact	Time TD	Time UT1	Latitude	Longitude
North Extreme Path Limit 1	N1	10:35:26.9	05:40:16.5	50°52.5'N	021°35.0'W
South Extreme Path Limit 1	S1	10:09:06.7	05:13:56.3	10°00.4'S	015°54.1'E
North Extreme Path Limit 2	N2	13:16:28.9	08:21:18.5	18°02.5'N	152°14.2'E
South Extreme Path Limit 2	S2	13:42:18.8	08:47:08.4	43°34.9'S	118°11.6'E

Explanation of Penumbral Shadow Contacts and Extremes Tables

Umbral Shadow Contacts and Extremes: Hybrid Solar Eclipse of -0541 Jul 31

Contacts of Umbral Shadow with Earth
Contact Event	Contact	Time TD	Time UT1	Latitude	Longitude
First External Contact	U1	10:04:58.8	05:09:48.4	20°22.4'N	005°15.3'E
First Internal Contact	U2	10:05:51.0	05:10:40.6	20°23.9'N	005°01.6'E
Last Internal Contact	U3	13:45:48.2	08:50:37.8	13°53.1'S	132°42.9'E
Last External Contact	U4	13:46:46.4	08:51:36.0	13°54.8'S	132°27.7'E

Extreme Northern and Southern Path Limits of Umbra
Contact Event	Contact	Time TD	Time UT1	Latitude	Longitude
North Extreme Path Limit 1	N1	10:05:30.8	05:10:20.4	20°35.6'N	005°01.7'E
South Extreme Path Limit 1	S1	10:05:19.0	05:10:08.6	20°10.7'N	005°15.3'E
North Extreme Path Limit 2	N2	13:46:10.8	08:51:00.5	13°40.0'S	132°42.4'E
South Extreme Path Limit 2	S2	13:46:23.8	08:51:13.4	14°07.9'S	132°28.2'E

Explanation of Umbral Shadow Contacts and Extremes Tables

Central Line Extremes and Duration: Hybrid Solar Eclipse of -0541 Jul 31

Extreme Limits of the Central Line
Contact Event	Contact	Time TD	Time UT1	Latitude	Longitude
Extreme Central Line Limit 1	C1	10:05:24.9	05:10:14.5	20°23.2'N	005°08.5'E
Extreme Central Line Limit 2	C2	13:46:17.3	08:51:06.9	13°54.0'S	132°35.3'E

Explanation of Central Line Extremes Table

Greatest Eclipse and Greatest Duration
Event	Time TD	Time UT1	Latitude	Longitude	Sun Altitude	Sun Azimuth	Path Width	Central Duration
Greatest Eclipse	11:55:50.0	07:00:39.6	23°48.4'N	002°39.7'E	86.4°	198.0°	5.3 km	00m09.27s
Greatest Duration	10:05:24.9	05:10:14.5	20°23.2'N	005°08.5'E	0.0°	68.2°	51.3 km	00m50.83s

Explanation of Greatest Eclipse and Greatest Duration

Polynomial Besselian Elements: Hybrid Solar Eclipse of -0541 Jul 31

Polynomial Besselian Elements
-0541 Jul 31 at 12:00:00.0 TD (=t0)
n	x	y	d	l1	l2	μ
0	0.05483	0.04610	20.3479	0.55037	0.00419	359.5724
1	0.51495	-0.16960	-0.0084	0.00012	0.00012	15.0003
2	-0.00006	-0.00013	-0.0000	-0.00001	-0.00001	0.0000
3	-0.00001	0.00000	-	-	-	-

Tan ƒ1	0.0046369
Tan ƒ2	0.0046138

At time t1 (decimal hours), each besselian element is evaluated by:

x = x0 + x1*t + x2*t² + x3*t³ (or x = Σ [xn*tⁿ]; n = 0 to 3)

where: t = t1 - t0 (decimal hours) and t0 = 12.000

Explanation of Polynomial Besselian Elements

Links for the Hybrid Solar Eclipse of -0541 Jul 31 (0542 Jul 31 BCE)

Orthographic Map: Hybrid Solar Eclipse of -0541 Jul 31 - global map of eclipse visibility
Google Map: Hybrid Solar Eclipse of -0541 Jul 31 - interactive map of the eclipse path
Path Table: Hybrid Solar Eclipse of -0541 Jul 31 - coordinates of the central line and path limits
Circumstances Table: Hybrid Solar Eclipse of -0541 Jul 31 - eclipse times for hundreds of cities
Saros 56 Table - data for all eclipses in the Saros series
Hybrid Solar Eclipse of -0541 Jul 31 - Google search for links to this eclipse

Links to Additional Solar Eclipse Information

Home - home page of EclipseWise with predictions for both solar and lunar eclipses

Solar Eclipses - primary page for solar eclipse predictions
Solar Eclipse Links - detailed directory of links

Six Millennium Catalog of Solar Eclipses - covers the years -2999 to +3000 (3000 BCE to 3000 CE)
Saros Catalog of Solar Eclipses - covers Saros series -30 through 190
World Atlas of Solar Eclipse Maps - index page
Solar Eclipse Search Engine - search for solar eclipses from -1999 to +3000
Javascript Solar Eclipse Explorer - calculate all solar eclipses visible from a city

Thousand Year Canon of Solar Eclipses 1501 to 2500 - link to the publication

MrEclipse.com - eclipse resources and tips on photography
Solar Eclipses for Beginners - a primer on solar eclipse basics
MrEclipse Photo Index - an index of solar eclipse photographs

Calendar

The Gregorian calendar (also called the Western calendar) is internationally the most widely used civil calendar. It is named for Pope Gregory XIII, who introduced it in 1582. On this website, the Gregorian calendar is used for all calendar dates from 1582 Oct 15 onwards. Before that date, the Julian calendar is used. For more information on this topic, see Calendar Dates.

The Julian calendar does not include the year 0. Thus the year 1 BCE is followed by the year 1 CE (See: BCE/CE Dating Conventions). This is awkward for arithmetic calculations. Years in this catalog are numbered astronomically and include the year 0. Historians should note there is a difference of one year between astronomical dates and BCE dates. Thus, the astronomical year 0 corresponds to 1 BCE, and astronomical year -1 corresponds to 2 BCE, etc..

Eclipse Predictions

Predictions for the Hybrid Solar Eclipse of -0541 Jul 31 were generated using the JPL DE406 solar and lunar ephemerides. The lunar coordinates were calculated with respect to the Moon's Center of Mass. The predictions are given in both Terrestrial Dynamical Time (TD) and Universal Time (UT1). The parameter ΔT is used to convert between these two times (i.e., UT1 = TD - ΔT). ΔT has a value of 17710.4 seconds for this eclipse. The uncertainty in ΔT is 445.7 seconds corresponding to a standard error in longitude of the eclipse path of ± 1.86°.

Acknowledgments

Some of the content on this website is based on the book Thousand Year Canon of Solar Eclipses 1501 to 2500. All eclipse calculations are by Fred Espenak, and he assumes full responsibility for their accuracy.

Permission is granted to reproduce eclipse data when accompanied by a link to this page and an acknowledgment:

"Eclipse Predictions by Fred Espenak, www.EclipseWise.com"

The use of diagrams and maps is permitted provided that they are NOT altered (except for re-sizing) and the embedded credit line is NOT removed or covered.