This period of chronology and those following are confirmed by 7 independent factors: (1) The 450 years of Acts 13:20 (2) The Exodus Astronomical Synchronism (3) The theocratic years (4) The Jubilee periods (5) The  individual judgeships and oppressions that make up the entire period  (6) The years of Israel's sin in Ezek. 4:5-6, and (7) 70 violated land Sabbaths leading to the Babylonian exile.
        Our Astronomical synchronism for the Exodus is found by determining the date and weekday of the feast of Pentecost for the year of the Exodus.  First we determine the weekday.  Remember that Moses told Pharoah that they must go three days journey into the wilderness to keep a feast to Yahweh?  (Exodus 8:27, 10:9).  He was not bluffing.  For Yahweh had already told Moses that he would bring the people back to worship him at "this mountain," i.e. Mt. Sinai.  Now the wilderness of Sinai was much more than three days journey from Egypt.  So the "three days" means that it takes "three days" to get from the border of the Sinai wilderness to Sinai.  So they entered the widlerness of Sinai on the first day of the third month (Exodus 19:1).  So they were encamped at Sinai on the fourth day of the month, on which Yahweh instructs them to cleanse themsleves and be ready for the third day.  Counting inclusively (as is the Hebrew method), this would be Sivan 4, Sivan 5, and Sivan 6 (the third day).  So Exodus 19 has three days of travel, plus two days of preparation (washing clothes, Exodus 19:10), and then they were to be ready the third day when the Law was given.  Thus there is no way to skip over the Sabbath day without working or traveling on it, unless the sixth day of the month is either a Friday or a Sabbath.
            Now, the Sabbath was the day made holy by God, which means it was set apart as holy time for his use.  On it he instructed the people to call a holy assembly, to meet with God in prayer, worship, and reading His Law (Lev. 23:1-3).  Therefore, does it not follow that the third day spoken of (the 6th of Sivan) was a Sabbath day in the year of the Exodus?  So we have that the Sabbath fell 50 days after the feast of Passover that year, which is confirmed by Astronomy.  Now suppose that some say it fell on Friday that year?  Would this undermine the value of the confirmation?  Not at all!  For first they must construct a Biblical Chronology consistent with the Scriptural data that makes Pentecost come out to a Friday or another Sabbath.  The nearest years for this are 1638 b.c.e. (+5 years) ( 1631 b.c.e. is ruled out because a Sabbath falls in the first three days of Sivan, and 1628 b.c.e.) (-4 years).

Astronomical Data from aa.exe:

       The Year is  2509 A.M. (Anno Mundi: Year 1 = 4140 B.C.E.).

  Passover                      4/11/-1632       FRI         Julday: 1125436
  Last High Sabbath        4/17/-1632      THR        Julday: 1125442
  Pentecost               5/31/-1632   SAB      Julday: 1125486
  Trumpets                      9/21/-1632      SUN        Julday: 1125599
  Day of Atonement        9/30/-1632      TUE         Julday: 1125608
  Tabernacles                10/ 5/-1632      SUN        Julday: 1125613
  Last High Sabbath      10/12/-1632     SUN        Julday: 1125620

        Feast Days begin on preceeding day at sunset.  For example if the feast is listed as 4/1, then the feast high sabbath begins on 3/31 at sunset and ends on 4/1 at sunset.

        The Julday for the given feast day is listed.  This is to enable the user to measure the number of days between any two feasts.  For example it often happens that the number of days between two feasts about 3 1/2 years apart comes to one of the prophetic time periods mentioned in the book of Daniel, viz. the 1335, 1290, or 1150 (2300 evening-morning sacrifices), or the book of Revelation, viz. 1260.

1. AVIV (Nisan)          THR  3/27/-1632         29 days Jul: 1125421.16
2. ZIV (Iyyar)              FRI  4/25/-1632           30 days Jul: 1125450.17
3. Sivan                      SUN  5/25/-1632         29 days Jul: 1125480.18
4. Shoshana              MON  6/23/-1632         30 days Jul: 1125509.19
5. Av                          WED  7/23/-1632         30 days Jul: 1125539.20
6. Elul                        FRI  8/22/-1632            29 days Jul: 1125569.19
7. ETHANIM (Tishri)        SAB  9/20/-1632            30 days Jul: 1125598.17
8. BUL (Marchesvan)      MON 10/20/-1632         30 days Jul: 1125628.14
9. Kislev                   WED 11/19/-1632         29 days Jul: 1125658.12
10. Tebeth               THR 12/18/-1632          30 days Jul: 1125687.11
11. Shebat               SAB  1/17/-1631           29 days Jul: 1125717.12
12. Adar                   SUN  2/15/-1631           29 days Jul: 1125746.14
13. Adar II                MON  3/16/-1631         30 days Jul: 1125775.15

     * Months begin at sunset on the day listed (not the day before)
 

        The conquest, however, began the fall preceeding the end of the 40th year with Heshbon, viz. [1592.25], viz. 39« years from the Exodus.  Proof: Israel went out of Egypt in the  spring on the 15th day of Aviv, the first month (Numbers 33:3), and Aaron died in the 40th year, the 5th month, and the 1st day, which was 39 whole years, 4 whole months, and 1 day from the  Exodus (Numbers 33:38); the 4 months and 1 day are the first half of the 40th year.  In Numbers  20:29 we are told that the death of Aaron was mourned for 30 days, which brings us to the 6th  month and the 1st day since the 5th month was 29 days long, and we count inclusively from the  death of Aaron.  After Aaron dies the conquest begins with the king of Arad (Num. 21:1-3) and  Sihon, king of the Amorites (Num. 21:23-35), in which the city of Heshbon falls.  In Numbers 29:7  we have instructions concerning Tabernacles and the Day of Atonement refered to as On the  tenth day of this seventh Month, and if that is not clear enough then an absolute limitation in Deut. 1:3-4: in the eleventh month.  Therefore we conclude that the Conquest began in the 6th month of
the 39th year, or 39.5 years after the Exodus.

        The conquest duration is deduced from two notations in the Scripture.  Caleb said he was 85 at the conquest's termination (Josh. 14:10), and 40 (Josh. 14:7) at the spying out of the land in  the second year.  Therefore, 85-40 = 45 (Josh. 14:10).  On the other hand, they wandered for 38  years after the spying out of the land (Deut. 2:14).  Therefore, the conquest was 45-38 = 7 years long.  Deut. 2:24 dates the beginning of the conquest of Heshbon.
        First note that from the beginning of the conquest to the Oppression of Amon is 300 years (Judges 11:26).  Second, Jephthah's speech, in which he noted this, was made at the end of Amon's 18 year oppression (Judges 10:8), because right after the speech he subdues them (Judges 11:33).  Then, note that the 300 years does not include the 18 years of Amon's occupation.  For Jepthah notes that "Israel dwelt in Aroer and her towns ... 300 years," which is the very territory he recovered, which means the Amonites were occupying that area for 18 years.  The 300 years thus extend from the conquest of Heshbon and Aroer to the Amonite oppression, which began when Jair died.  Furthermore, "that year" (Judges 10:8) refers to the year of Jair's death (Judges 10:5).
        Now we can chart out this period, filling in the unknowns:

        Conquest                      7
        Joshua & Elders           y         Joshua 24:31
        Cushan                         8         Judges 3:8
        Othniel                          40       Judges 3:11
        Eglon                            18        Judges 3:14
        Ehud                             80       Judges 3:30
        Shamgar                       z         Judges 3:31
        Jabin                             20       Judges 4:3
        Deborah                        40       Judges 5:31
        Midian                             7       Judges 6:1
        Gideon                          40       Judges 8:28
        Abimelech                      3       Judges 9:22
        Tola                               23       Judges 10:2
        Jair                                22       Judges 10:3

                            Total   308 + y + z

        So we see that the sum is greater than the required amount, viz. 308 + y + z  > 300.  The  solution to this conundrum is that some of the judges in this period had to be concurrent or  overlapping, or have judged during an oppression.    It is evident that Shamgar was during the  Judgeship of Ehud, or that Ehud's last year was partial, and Shamgar finished it.  For it is stated  that when Ehud died, they were sold to Jabin (Judges 4:1-2).  Therefore, in the overall  chronology: z = 0.  This leaves us with 308 + y  > 300.
         The only other place where the Judges are not distinctly separated by oppressions in this period is in the Tola-Jair connection, hence this is the only connection allowing any overlap.  Note that the pattern is "a judge arose," and then "judges," and then "dies."  It is said, "after him [Tola]  arose Jair," (Judges 10:3) so Jair arose after Tola, but it does not say how long.  As long as Tola  preceeds Jair by some amount.   We will let w represent Tola-Jair.
         The mathematical notation now becomes:
 
 263 + w + y = 300; 23 <= w <=37

         There is an additional piece of evidence that will help us.  Tola judged west of the Jordan,  and Jair judged east of the Jordan.  Hence, concurrency of administrations is likely.  Furthermore  this period is at least as long as Tola's 23 years.  Therefore, w >= 23.  On the other hand, it  seems unlikely that Transjordan went without a judge for very long.  It must also be noted that w  must not be greater than 37 if  y=0.  But y cannot equal zero.  For the period of Joshua and the elders must last till that generation is dead.  The oldest survivors to come out of Egypt were  Joshua and Caleb.  Caleb was 40 when the decree of death was passed upon all over the age of 20.  Hence,  the spared were 19 or less, the oldest being fully 21 years younger than him.  So when Caleb was 85, these were 85-21 = 64, but we must allow them to live to the average "threescore and ten" (70 years), so the period of Joshua and the elders must be at least 6 years,  viz. y >=6.  However, not only does the Scripture say that all that generation died, but all who could remember the signs in Egypt died (Joshua 24:31).  If a twelve year old could remember,  then 70 = 12 + 39.5 + 7 + 11.5, so y >=11.5.
         Therefore: y >= 11.5, and so 23 <= w <= 25.5
         This narrows our constraints down to 2.5 years!  Is there any confirmatory evidence?
Yes.
         This period requires us to maximize the sabbatical years which were not kept, that is the sabbatical years in the oppressions.  For any deficit will leave us short of the required 70 by the time we reach the exile.  The effect of stretching out Tola-Jair is to wipe out potential sabbatical  years for the oppressions.  Furthermore, we are already required to count all unobserved Jubilee land Sabbaths and include them in the total also.  The first sabbatical year is fixed within this period at the division of the land.  Analysis of stretching Tola-Jair 1 to 7 years gives the  following loss of sabbatical years: {1:0, 2:0, 3:0, 4:-3, 5:-4, 6:-4, 7:-1}.   Only shifting 1 to 3 years leaves the total unchanged.  Therefore, by this criteria, w <= 26.
         Therefore, the accuracy of any date, from the first oppression to the first year of Tola is +{1,2,3} years.  Since, it is preferable to maximize y, we select the ideal figure of w = 23   Therefore, Tola- Jair were concurrent, and Jair arose in the second year of Tola.
         Knowing the value of w, we solve for y:   263 + 23 + y = 300.    And y=14.

        Ammon             18         Judges 10:8
        Jepthah              6         Judges 12:7
        Ibzan                  7         Judges 12:9
        Elon                   10        Judges 12:11
        Abdon                 8         Judges 12:14
        Philistines          40        Judges 13:1
        Eli                       40       I Sam. 4:18
        Philistines          21        I Sam. 6:1; 7:2

                      Total   150

            The following results are obtained:

Conquest to Ammon          300 years
Ammon to Samuel              150 years

                      Grand Total   450 years

 kai kaqelwn eqnh epta en gh canaan kateklhronomhsen thn ghn autwn wV etesin
tetrakosioiV kai penthkonta kai meta tauta edwken kritaV ewV Salouhl profhtou
 
 "And destroying nations seven in land of Ca'na'an, He caused them to inherit their land
about 450 years, that is, after these things, He gave judges until Sh'muel the prophet" (Acts
13:20).

        So the 450 years of Acts 13:20 is confirmed without having to use it.  This is important, as both the actual text of Acts 13:20 and its translation and its interpretation are controverted.  I have given mine above.  Instead of taking the temporal phrase as leading from the division to the end of Samuel, I take it to start with the conquest and end at the beginning of Samuel.

        For the second Philistine servitude, figures are given for 7 months and 20 years.  This is rounded up to 21 years, thus treating the remaining 5 months as either Samuel's un-enumerated accession year, or the text simply does not mention the other 5 months (cf. I Sam. 6:1; 7:2).
        Recognition of the second Philistine oppression is necessary to complete the 390 years of sin (Ezek. 4:5-6), and the 70 violated land Sabbaths (II Chron. 36:21).  It is also necessary to keep an even 18 Jubilees between the entry into the land and Hezekiah's Jubilee (1591.25 and 709.25 respectively).   Also, leaving it out destroys an exact solution to Acts 13:20.
        Note that the Ark was at Kiriath Jearim much longer than 20 years.  Many misread I Sam. 7:1-2.  Verse two only indicates that it was 20 years till Israel again repented.

        The principle unknown to be solved for is the length of Samuel's judgeship, since the rules of all the other judges are given in the Scripture. The 480 years of 1 Kings 6:1 omit the years of the oppressions.  Hence, they must be regarded as the years of theocratic rule, or years of independence.   Proof:  (1) It is an easy matter to show that there are more than 480 years in the stated interval.  Forty years (Deut. 2:7),  plus 450 years (Acts 13:20), plus Saul (40 years), David (40 years), equal 570 years, and this does not include the years of Samuel the prophet.  Since 570 >> 480, it follows that 480 cannot count all the years in the stated interval.
         The only other alternative to this interpretation of the 480 years is to assume a copiest error, in which case the proper procedure is to dismiss the 480 year figure.  The Period of Samuel's Judgeship, then can still be locked down by the Jubilee periods and the Exodus, Joseph, and Flood Astronomical Synchronisms.

        The 480 years of I Kings 6:1 has baffled  chronologers, excpet a few like Martin Antsey and David L. Cooper.  The text actually says "In the 480th year," the number being ordinal.  The years included in the 480 years are only those years of national theocracy (proof).  The nation of Israel was a theocracy when it was serving Yahweh.  When the nation was serving  the ba'als (idols and foreign gods,) these "theocratic" years were not counted.  There were seven servitudes (seven being the number of perfection, hence perfect judgement seven times over) lasting 135 years.  Hence the actual total of years  is 615 (480+135) from the Exodus to the end of the 480th theocratic year.   The 480th year actually runs from the middle of Solomon's 4th year (3.5)  to the middle of his 5th year (4.5).
 

        The 480 years are:
 
 

Wilderness	40	Deut. 2:7
Western Conquest	6.5	Explanation
Elders	14	Explanation
Othniel	40	Judges 3:11
Ehud	80	Judges 3:30
Deborah	40	Judges 5:31
Gideon	40	Judges 8;23
Tola-Jair	23	Judges 10:2
Jephthah	6	Judges 12:7
Ibzan	7	Judges 12:9
Elon	10	Judges 12:11
Abdon	8	Judges 12:14
Eli	40	I Sam. 4:18
Samuel	41	See below
Saul	40	Acts 13:21
David	40	II Sam. 2:11
Solomon	4.5 (middle of 5th year)	I Ki. 6:1
Total Years	480	.

 

 The Encyclopedia Britanica has this interesting comment, and I would like to know the source behind its claims that such counting methods were "usual."  If you can find the answer then email me at  "dangregg@execpc.com".

        The suggestion has also been made that, as is usual in Oriental chronologies, the years of foreign
domination were not counted, the beginning of each judge's rule being reckoned, not from the
victory which brought him into power, but from the death of his predecessor (11th Edition, Vol. 3,
pg. 867, 1910 [The underlines are mine]).

         Thus, the 480 years reflects the counting of years under native Israelite rule, omitting the years of foreign domination.  The only unknown dependent on this fact is the judgeship of Samuel.   Samuel was "old," (I Sam. 8:1, 5)  when the people asked for a king.  Supposing that  "old" means 80 years, we deduce the following.  Since, he died just before Saul (I Sam. 28:3; 31:6), he must have lived about 38 years during the reign of Saul, but he was also born in the Judgeship of Eli, and it appears that he was entered into his service when Eli was already loosing  his eyesight.  Hence Eli was probably quite old.  We also know that Samuel grew (I Sam. 3:19; 4:1), so that it appears that he was at least 20 when Eli died.  Allowing another 21 years for the second Philistine servitude, gives 41 years at the start of his judgeship.  If he was 80, when the people requested a king, and it took 2 years for Saul to be installed, then he was 82.  But 41+41 = 82.  So 41 years is about right for Samuel's judgeship based upon independent evidence.  He
would have died at about age 120.
            Before Samuel's judgeship is figured, 439 years are accounted for by independent means.  Thus to bring the total to 480, exactly 41 more years are required.