Answer: a) David crossed the Kidron Brook and climbed the Mount of Olives.
We learn of David’s escape in 2 Samuel 15. His route is mentioned in verses 23 and 30.
Keep in mind that, at this point, the City of David occupies much of the same area as the stronghold the Jebusites had built. We often see Jerusalem after all of the expansion phases, so it appears much larger than David’s time. Today, bulldozers and earth movers have leveled or at least reduced a lot of the extreme difference in elevation and a modern municipality as engulfed the area, as this view from the top of the Mount of Olives shows.
Photo by Jake Figi via Wikimedia Commons
This photo (below) from 1851 shows how extreme the terrain was in the past
Photo by Francis Frith via Wikimedia Commons
Below: Screenshot from bottom video showing the valleys. While the terrain features are exaggerated, the video serves to show the valleys and high ground providing the military advantages of Jerusalem. With the exception of the Kidron Valley such details are often lost in modern pictures. The Hinnon Valley traditionally includes the area labeled "Gehenna" in this video.
The high ground
King David's Jerusalem outlined in yellow
Below: David's most likely path of escape, starting at the Fountain Gate and making his way through the Kidron Valley and over the Mount of Olives.
The Eerdmans Bible dictionary, 1987, (Myers, 392) says: "FOUNTAIN GATE (Heb. sa˓ar hā˓ayin). A The gate in the southeastern part of Jerusalem, located near the steps that lead down from the city of David to the Spring Gihon (Neh. 2:14, 15; 12:37). First constructed as part of the Jebusite city which preceded Jerusalem."
Below: A Map of Jerusalem from a Bible dictionary from 1912. I added the labels and arrows indicating the valleys and the yellow outline of the City of David
Internet Archive Book Images, No restrictions, via Wikimedia Commons
Below: First video: Kidron Valley - Where King David Walked. The short video ends with a view of what by tradition is called "Jehoshaphat's Tomb." The tree along the same ridgeline, about center screen, is blocking the top of the so called "Pillar of Absalom," or "Absalom's Tomb," But this is not the King's Valley.
2 Samuel 18:16-18 says:
Then Joab blew the trumpet, and the troops came back from pursuing Israel, for Joab restrained them. And they took Absalom and threw him into a great pit in the forest and raised over him a very great heap of stones. And all Israel fled every one to his own home. 18 Now Absalom in his lifetime had taken and set up for himself the pillar that is in the King’s Valley, for he said, “I have no son to keep my name in remembrance.” He called the pillar after his own name, and it is called Absalom’s monument to this day.
"Pillar of Absalom"
Photo by Ariel Horowitz via Wikimedia Commons
Bottom video: The topography of Jerusalem. A quick overview of the area surrounding Jerusalem.
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