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Determining what is the deepest ocean is actually more difficult than it would seem. This is due to the fact that the ocean floor has trenches at various locations around the world that are much deeper than the average depth. If you are discussing the ocean with the greatest average depth, then that would be the Pacific Ocean. It has an average depth of approximately 4,280 meters according to Encarta, although calculations do vary somewhat.
The Pacific Ocean also has the deepest location of any ocean in the world. The Mariana Trench is the deepest known part of any ocean. It is in the western Pacific Ocean near the Mariana Islands. Countries near the trench include Japan, Papua New Guinea, and the Philippines. The trench is shaped like a crescent, about 2,400 kilometers long and an average of around 70 kilometers wide. Numerous measurements of the trench have been taken over the years by different probes. The Challenger expedition was the first probe to measure the waters. Between 1872 and 1876, they tested the waters and measured the deepest point as 9,636 meters. There is a large difference between this and measurements taken by the Japanese probe Kaiko, which in 1995 recorded the depth at 10,911 meters.
What is believed to be the deepest spot in the Mariana Trench is known as the Challenger Deep, named after the two Challenger expeditions that explored the trench. It is thought to be around 11,000 kilometers deep and shaped like a slot. (Even though it has only been surveyed to 10,911 meters, National Geographic puts it at over 11,000 meters deep.) The Mariana Trench was also surveyed earlier this year by the Nereus, a probe from the Woods Hole Oceanographic Institution. There are also a number of other deep points in the trench besides the Challenger Deep.
It is hard to imagine how deep the Mariana Trench actually is. One common comparison utilizes Mount Everest. If you placed Mt. Everest inside the Mariana Trench, there would be over 2,000 meters of water covering the mountain. The water pressure in the Mariana Trench is 15,750 psi, which is more than 1000 times greater than the standard atmospheric pressure at sea level. Despite the fact that the Mariana Trench is kilometers deep, scientists have found life down there. In one expedition, scientists found many single-celled organisms in dirt on the floor of the Challenger Deep. Quite a few scientists were amazed at how many of the organisms they found in the dirt because it disproved their previous suppositions.
Universe Today has articles on why the ocean is salty and the largest ocean in the world.
Astronomy Cast has an episode on Earth.