Q:

Has the lengthened day of Joshua 10 been modeled in a simulation to show how this could have occurred?

My question is, has anyone done or knows of anyone who have done an astronomical simulation of how this could have happen? Alternatively does anyone knows or have access to any simulation facilities for me to attempt such a simulation myself?

A:

The short answer is that, no, despite a persistent urban legend that NASA modeled this on one of their early computer systems, the reality is that such a simulation is impossible. According to Dr. Danny Faulkner writing for Answers in Genesis

From time to time, one hears that NASA computers have proved the account of the unusual day that accompanied the Battle of Gibeon found in Joshua 10:12–14. This marvelous little story about NASA computers began circulating in the late 1960s and early 1970s, during the heyday of the Apollo program. According to the story, in preparation for the Apollo moon landings, a computer at NASA calculated the positions of the earth, moon, and other solar system bodies with great precision far into the past and future.
This computer program produced a glitch in the fifteenth century BC, a glitch caused by solar system bodies not being in their correct positions, indicating that nearly a day was missing from time. An additional 40 minutes also was missing several centuries later, so that the total missing time was one full day.
Supposedly, NASA scientists and engineers puzzled over this problem until one of them opened the Bible to Joshua 10:12–14 and 2 Kings 20:8–11. The NASA personnel supposedly came to realize that their missing day could be explained by addition of nearly a day at the time of Joshua and an additional 40 minutes at the time of Hezekiah, thus proving that these biblical events actually occurred.
This story was carried in a few newspapers at the time, but it enjoyed widespread circulation among Christian audiences in the United States.

Dr. Faulkner then goes on the detail the origin of the false claim:

The person who appears to be responsible for this story is Harold Hill, president of the Curtis Engine Company in the late 1960s. Hill told the story a number of times before finally committing it to print in a 1974 book, How to Live Like a King’s Kid. Hill’s company had done contract work for NASA during the Apollo program, and Hill claimed that during this time he became aware of the computer confirmation of Joshua’s long day through his work at NASA. In some versions of the story, Hill worked for NASA, but Hill never did. Furthermore, the sort of work that Hill’s company did would not have placed him in a position to be privy to this sort of information. Hill claimed to have seen documentation of this supposed event as a NASA memo, but Hill could not produce the memo. Some people have speculated that if Hill actually did see such a memo, the memo may have been an April Fool’s Day prank.
The problem with this story is that a computer could not find such a discrepancy in the positions of solar system bodies. In order for a discrepancy to be found, we must know exactly where things were at some time in the past prior to Joshua’s long day, so that the calculated positions can be compared. A computer can calculate only where things ought to have been in the past; it cannot compute where things actually were in order to make a comparison.

So, in short, in order to be able to model such a scenario, we would need four points of measurement and two measurements:

The current time
The present position of orbital bodies
An exact time measurement before the events recorded in Joshua
The position of orbital bodies before Joshua

These measurements would allow us to calculate the exact amount of time that elapsed. We could then model where the planetary bodies should have been historically if orbits had stopped by simulating the orbits backwards in time to the timestamp before Joshua's events. But then we would need a point of comparison - Eg, does the calculated positions match the known positions before Joshua's event, or is it off by 24:40?
Unfortunately, we lack the data of two key things:

An exact timestamp of the events of Joshua (it is not enough to know the approximate year(s) or even months) and even if this were determined we would still need
The exact orbital positions of planetary bodies before Joshua.

So this is a simulation that will never be able to happen.

Note: This analysis is also supported by Dr. Tommy Mitchell and several other scientists

