Joshua's Long Day - An Astronomical Solution

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Joshua's Long Day - An Astronomical Solution
(Revised, with appendix showing method)

"Then spake Joshua to the LORD in the day when the LORD delivered up the Amorites before the children of Israel, and he said in the sight of Israel, Sun, stand thou still upon Gibeon; and thou, Moon, in the valley of Ajalon. And the sun stood still, and the moon stayed, until the people had avenged themselves upon their enemies. Is not this written in the book of Jasher? So the sun stood still in the midst of heaven, and hasted not to go down about a whole day." (Joshua 10:12-13).

Popular interpretations regard the standing still of the sun and moon as evidence for a hiatus in the mechanics of the solar system, caused either by the miraculous slowing down and stopping of the earth's rotation, or by the arresting of the movements in space of the sun and moon for an undefined part of a day. Note also that it would require a tilt or wobble of the ecliptic¹ to maintain both bodies overhead at the latitude of Gibeon and Ajalon which is approximately 31ºN. This is 8º north of the tropic of Cancer. This latter is the most northerly the sun can reach at mid-summer in the northern hemisphere.

Another Interpretation

The above theories assume that the effect of the stand-still would be as that observed from a static observer on the earth's surface. Joshua however was not static and we are given quite a lot of information about his movements that day. We are given a summary of the day's events in vv.9-11, "Joshua therefore came unto them suddenly, and went up from Gilgal all night. And the LORD discomfited them before Israel, and slew them with a great slaughter at Gibeon, and chased them along the way that goeth up to Bethhoron, and smote them to Azekah, and unto Makkedah" And it came to pass, as they fled from before Israel, and were in the going down to Bethhoron, that the LORD cast down great stones from heaven upon them unto Azekah, and they died: they were more which died with hailstones than they whom the children of Israel slew with the sword."

Given that Joshua, after marching all night, spent the best part of the day fighting his enemies, it is instructive to consider how the regular movement of the sun and moon could interact with his movements so that, wherever he or the observer was, the sun would appear to be in line with Gibeon and the moon over the Valley of Ajalon.

In 1909 the astronomer Maunder² deduced that, for the heavenly bodies to be able to take those positions, the time of year must have been near the north solstice and the waning moon around the time of the last quarter. He estimated a date on or about 22 July (in the Julian calendar) without stating the year and he did not pursue the astronomical analysis further in his explanations, except to note that their only method for knowing the time of day would have been from the position of the sun.

Joshua, after his night march, defeated the enemy who were besieging Gibeon, the implication being that they surprised the five kings and their armies, still in their pyjamas so to speak, with a raid around dawn, which was about 4:50 AM that day. The enemy fled down the way to Beth-Horon where they were rained upon by what sound like meteorites³ or bolides (v.10). That is, they were panicked into fleeing in the only available direction, which was away from their own cities all of which were in the South where they really wanted to go and seek refuge. The following Map⁴ plots a route for which, to an observer on the track, the sun appeared to be over Gibeon and the moon appeared to be over the Valley of Aijalon on the fifth day after the Northward Solstice in 1406 BC; a day chosen in conjunction with Biblical chronological data that can be traced back from 1948 AD to the year 573 BC that can be shown to have been the year of the 17th jubilee. The astronomical data date the start of Joshua's campaign against the five kings on Sunday 11 July 1406 BC[J], immediately after a Saturday Sabbath.

Clockwise Route with moon "Over" Aijalon Valley and sun "Over" Gibeon.

The map shows the clockwise route for which sun and moon remained in line with Gibeon and the Valley of Aijalon for over four hours. Both sun and moon rose in the north-east and set in the north-west but the moon was between 2 and 3 hours ahead of the sun. The sun rose higher than the moon, being only about 8 degrees from being directly overhead at mid-day. However it was the direction of sun and moon that was critical and, to avoid too much clutter, the direction lines for these are shown at only a few points in the diagram. The intermediate points marked on the route are at intervals of 5 minutes. At the actual datum point for the Valley of Aijalon the moon was due south and the sun only a fraction of a degree south of due east that constrains this datum to be almost at the same latitude as Gibeon. This location is not part of the track because obviously the moon could not appear to be overhead at that point. It could not be observed as 'over' the Valley of Aijalon until an observer had moved north of that point.

Note that the tracks shown on the underlying map are mainly ridge-ways, which was the safest way to travel in earlier times, also the astronomical data shows that the pursuit was up the way of Beth-Horon, rather than down as is usually depicted when describing this campaign. The overlaid route of Joshua and/or part of his army is on the centre line of the angles that the sun and moon make when in line over Gibeon and the Valley of Aijalon respectively at each instant on the track. However neither the sun and moon, nor the places mentioned are point objects (the sun subtends an angle of about half a degree at the eye). This means the track could have been wider and more irregular without violating the data. Joshua’s prayer was for the moon to stand still over the Valley of Aijalon. This location is not defined in the narrative⁵.

The Route Described

When Joshua had arrived at the observation point in the Valley of Aijalon at about 9:00 AM, he voiced his plea for the sun to stand still over Gibeon, implying that he’d already noticed that alignment. He can only have noticed the moon alignment after he had passed north of the Aijalon Valley location for him to utter his prayer. However we have no knowledge of how long it had been noticeable that the sun was in line with Gibeon from which he could have departed any time after sunrise and, marching in a westward or south westward direction, he would have his back to it. It was possible that he noticed that his shadow was pointing in the opposite direction from Gibeon and this would have helped his navigation. With this guide it is quite possible that he took a trackless short cut moving generally west, with the sun in alignment all the way or he may have taken the longer southern ridge-way to Aijalon. However there is no certain data that proves his actual route except that the data shows that he reached the vicinity of Aijalon about 4 hours after the dawn battle.

When Joshua was in a position where he could see down the routes to Azekah and Makkedah, he realised that the vanguard of the enemy were already escaping down the southern and western routes and he was too late to stop them. This brought forth his plea to the sun and moon. Although the plea was literally granted, albeit as a phenomenon from an observer's point of view, the day’s real miracle was that the Israelites were given enough energy and stamina to achieve all that they did that day after having marched all the previous night. It was not even necessary for Joshua to have realised in what way his prayer had been answered – he was far too involved in the pursuit to be bothered with continuing to the observe the heavenly bodies. In any case the sun was almost overhead and far too bright to look at and the small crescent moon would be practically invizible in the brightness of the day.

The summary quoted above tells us that, with the LORD's help, the Israelites chased the Amorites and smote them down to Azekah and to Makkedah⁶, therefore Joshua must have split his forces, while one contingent chased the rest of the enemy back up the way they had come, as quoted in v.10 above.

It is instructive to consider the 5 minute spacing of the data-points. At the start, his speed was about 1 mph. That suggests there may have been a battle going on as his troops forced the enemy back. This gradually speeded up and by the time he reached Upper Beth-Horon he was approaching 6 mph. The subsequent depicted route ranges far and wide beyond the ridgeway track. This may mean the scattering of the enemy but the route shown is a purely mathematical construct that was not necessarily followed for longer than necessary, indeed the chase may have been abandoned at the pinch point of Beth-Horon because, after the ‘great stone’ bombardment earlier, the route was likely to be cluttered with bodies and rocks, making any further pursuit in that direction difficult and less urgent. Joshua, or whoever was in charge of this contingent could then return to continue the chase west and south.

Events following Joshua's arrival at Azekah.

When Joshua reached that rendezvous he was no doubt informed that the five kings had taken refuge in a cave at Makkedah and he gave the order to barricade and guard the entrance while the rest of the Israelites were to continue the pursuit to prevent the remnants returning to their cites (vv.18-19). After destroying the remnants of those that had fled down to Azekah, he and his whole army then took Libnah. Libnah had not been involved with the five kings but it was necessary to secure their rear while laying siege to Lachish, which was taken the 2nd day (v32) that would be Monday 12 July. A list of the cities taken in southern campaign follows: Eglon (taken the same 2nd day), then Hebron and Debir.

Area of Joshua's Southern Campaign.

"So Joshua smote all the country of the hills, and of the south, and of the vale, and of the springs, and all their kings: he left none remaining, but utterly destroyed all that breathed, as the LORD God of Israel commanded
And And all these kings and their land did Joshua take at one time, because the LORD God of Israel fought for Israel.
Joshua smote them from Kadeshbarnea even unto Gaza, and all the country of Goshen, even unto Gibeon
And Joshua returned, and all Israel with him, unto the camp to Gilgal" (Jos 10:40-43)

Kadesh Barnea and the other places mentioned in verse 41 were much further south than the limit of this map and, although the king of Gezer came to help Lachish and was destroyed with all his people, the destruction of Gezer city is only mentioned in the ordered list of Jos. 12:9-24 immediately after the destruction of Eglon. The long list of the battles of the southern campaign appears to end with the hanging of the five kings who had been shut up in the cave at Makkedah, and I suggest that this was the occasion of the destruction of Eglon, Makkedah⁷ and its king (Jos.12:16), although 5 more kings are mentioned before those that can be definitely identified with the northern campaign. That gave a maximum of one week⁸ after Joshua had set out on his night march, for him and his armies to destroy at least 13 kings and their cities before the onset of the Sabbath⁹.

Conclusions.

A route has been calculated for Joshua for the period from early morning to early afternoon that meets the criteria for the sun to appear to stand over Gibeon and the moon over Ajalon. While not necessarily a representation of his actual route, it does prove that the observation interpretation is a valid one and that the morning had gone clockwise up the way of Beth-Horon as the record states (v10). The deleterious effect of the erroneous theories mentioned above is that it masks the information that the text reveals about Joshua's tactics that day in order to achieve the defeat of his enemies. Moreover such theories go against the Biblical record that the sun and moon were given for times and seasons, as well as for light by day and night. A hiatus in the movement of these heavenly bodies would render uncertainties in any continuous dating system and chronology.

Afterword.

The remarkable detail of the data hidden in Joshua's short prayer can only be either a faithfully preserved record of a contemporary eye-witness account, or it is evidence of an inspired record of astronomical data that would have been beyond the ancients to compute. I believe the second, if not both, conclusions apply and these computations have only been made possible since the advent of Kepler's orbital laws, Newton's Laws of motion, Poincaré's development of them into the laws of celestial mechanics for multiple bodies (extended for relativistic effects in the 20th century after Einstein). And it is only since the invention of programmable digital computers by Turing and the British war-time code breakers at Bletchley that it has been possible to make the necessary accurate calculations in a reasonable time.
I cannot conceive of any other reason for the recording of this event, that happened nearly 3,500 years ago, other than to bear witness in these latter days as to the divine origin of the Bible to this present largely Godless and deluded generation.

Appendix on the method used to compute the paths of sun and moon.

The following definitions apply to the diagrams below: Point A denotes the co-ordinates of The Valley of Aijalon, yet to be determined.
B represents the co-ordinates of settlement of Beth-Horon the Upper; G, the same for Gibeon.
S is an undefined point due south of the Aijalon Valley location on the same latitude as G.
C and D are due south of Beth-Horon on the same latitude as A and G respectively
φA is the complimentary azimuth angle of the sun when the moon is due south of the Aijalon Valley point. This is equal to 360° minus the sun azimuth angle (measured clockwise from the south).
φm is the azimuth angle of the moon as it is viewed from B.
φB is the geographically fixed angle CBG and is equal to 360° minus the sun azimuth angle at B.
Define the Length SG as g; AC as 'x'; AS as 'a' and BD as 'b'. Sun and soon azimuth angles were computed using Solex¹⁰

ΔDBG: φB = Tan-1(g/b), from known fixed co-ordinates B & G.

The sun azimuth angle at B will be 360 – φB at a particular time each day that will be at different times for each day of the year.

This same times will define the moon azimuth angle at B (φm) and will be different for each day as the moon cycles through each month as well as each year.

The length 'a' and hence point A may be solved for any particular day as follows:

ΔABC:
x = (b - a).Tan(φm)
ΔSAG:
a = (x + g).Tan(φA) giving:
a = (g + b.Tan(φm))/(Tan(φm) + Tan(φA))

Having Calculated a and hence the co-ordinates of A, The general case for any point on the path, P(x,y):

ΔQPA:

y + a = (c - x)/Tan(φs')

giving:

y = (c + a.Tan(φs')) / (Tan(φs') + Tan(φm))

ΔRPG:

x = y.Tan(φm)

A special case for the sun transit exists when φs = 0. For this interpretation, this must occur at Gibeon

This transit in 1406 BC should enable an accurate value for DeltaT ¹¹to be calculated to within a few seconds. (The literature estimates an uncertainty value of 1900 seconds for 1500 BC, however the recommended equation for years earlier than 500 BC appears to give values much closer to that computed for this date. My own estimate is that the Solex value of 33250 seconds for that date needs to be increased by 72 seconds.)

[1] The ecliptic is defined to be the plane of the (undisturbed) orbit of the earth around the sun.
[2] The Astronomy of the Bible; E. Walter Maunder, F.R.A.S. (available from archive.org)
[3] Although day-time meteorites have been experienced for a long time, daytime meteor showers have only been detectable since Radar was invented. The β-Taurid meteor showers occur in June and July that have been attributed to debris from the orbit of Encke's comet. This is a short period comet that returns at intervals of about 3½ years but it has been estimated to have been doing this for about 4700 years. It is probable that there was a greater concentration of orbital debris in its early life and that God harnessed this natural phenomenon to His purpose.
[4] Maps have been prepared from a program available from: www.biblemapper.com combined with plots overlaid using paint.net.
[5] The datum for the Valley of Aijalon is calculable from the astronomical data and varies with the chosen day (see Appendix).
[6] I have used the coordinates of Makkedah (modern el Moghar, about 14 miles West of Aijalon). This is different from that supplied by the map program, which places it about 8 miles west of Hebron.
[7] I interpret Jos.10:15 as a summary of that week's campaign when, as stated in v.43, Joshua and the Israelites did return to the camp at Gilgal. Note that there is no 'But' in the Hebrew text at the start of v.16 and, as there are only implied tenses in Hebrew, this verse could just refer to the fact that the 5 kings had fled to the cave and were to be imprisoned as the campaign continued.
[8] Interestingly, there was a total solar eclipse on Wednesday 14 July 1406 BC. The path of totality was over Cyprus and Syria to the north of Israel but the eclipse would have been almost total from Joshua's field of operations and no doubt added to the distress of the Canaanites.
[9] There was an ordinance in Israel that those executed were not to remain on a tree overnight and this would be especially true before the onset of the Sabbath (Deut.21:23, Jno.19:31).
[10] SOLEX121.EXE was used for astronomical calculations; available as a free download from: http://www.solexorb.it/
[11] Delta T is a measure of the slowing of the earth's rotation due mainly to the tidal action of the moon.

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