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One classical thermal escape mechanism is Jeans escape, [1] named after British astronomer Sir James Jeans, who first described this process of atmospheric loss. [2] In a quantity of gas, the average velocity of any one molecule is measured by the gas's temperature, but the velocities of individual molecules change as they collide with one another, gaining and losing kinetic energy.
An alternative expression for the escape velocity v e particularly useful at the surface on the body is: = where r is the distance between the center of the body and the point at which escape velocity is being calculated and g is the gravitational acceleration at that distance (i.e., the surface gravity). [11]
But the maximal velocity on the new orbit could be approximated to 33.5 km/s by assuming that it reached practical "infinity" at 3.5 km/s and that such Earth-bound "infinity" also moves with Earth's orbital velocity of about 30 km/s. The InSight mission to Mars launched with a C 3 of 8.19 km 2 /s 2. [5]
However, the equatorial escape velocity, nearly 36 km/s, is much higher than that of Earth. [38] Saturn is the only planet of the Solar System that is less dense than water—about 30% less. [39] Although Saturn's core is considerably denser than water, the average specific density of the planet is 0.69 g/cm 3, because of the atmosphere.
The formula for an escape velocity is derived as follows. The specific energy (energy per unit mass) of any space vehicle is composed of two components, the specific potential energy and the specific kinetic energy. The specific potential energy associated with a planet of mass M is given by =
Graphs of escape velocity against surface temperature of some Solar System objects showing which gases are retained. The objects are drawn to scale, and their data points are at the black dots in the middle. The atmospheres of the planets Venus and Mars are principally composed of carbon dioxide and nitrogen, argon and oxygen. [4]
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This envelope reaches temperatures of 10,000 K. The planet is estimated to be losing (1–5) × 10 8 kg of hydrogen per second. This type of atmosphere loss may be common to all planets orbiting Sun-like stars closer than around 0.1 AU. [54] In addition to hydrogen, carbon, and oxygen, HD 209458 b is thought to have water vapor in its atmosphere.