A Mountain Model Hypsometry: When Oceans Covered Titan

Abstract: By using a mountain model and distribution of Titan, a statistical distribution of the topographical elevations of the moon, its hypsometry, is attained. A comparison with data hypsometry and similarly modeled hypsometry for Earth show resemblance between the two, though such comparison for Titan makes for inconclusiveness in the validity of the approach. Both cases of hypsometry are then used to show coverage of the body's area as a function of volume. Values for hydrogen escape is then used to calculate a minimum time at which a given percentage of Titan would be covered with liquids. The predictions are that 900-1,200 million years ago, 50% of the surface of Titan was covered with an ocean. Some 60-80% of the surface of Titan was covered with liquid methane 2000 million years ago.