Observations and modeling of the Martian atmosphere indicate that the water vapor present in its atmosphere today is mostly converted into atomic hydrogen by solar ultraviolet photons which can penetrate deep into the atmosphere of Mars. The H atom thus created combined immediately to form H2, which then slowly diffuses up. Once this H2 reaches the ionosphere it reacts with other ions and molecules to form H. These hydrogen atoms thus created, being the lightest element, then proceed to occupy the highest layer of the Martian atmosphere, the exosphere. Some of the hydrogen atoms escape into space because Mars’ gravity is not strong enough to hold on to those energetic atoms. Such an escape mechanism is called Jeans escape and is the primary mode of escape for H from Mars. Therefore, if we can determine the present day escape rate of water from Mars by constraining the escape rate of H, it can be extrapolated back in time to determine the total amount of water lost by Mars over its 4.2 billion year history.