Escape speed on Titan and the value for limiting molecular mass of a gas, which can be retained under the effect of gravitational pull of Titan. Assume that the average atmospheric temperature on Titan is 95 K.
Answer to Problem 66Q
Solution:
Explanation of Solution
Given data:
The average atmospheric temperature is 95 K.
Formula used:
The formula of the escape velocity is as:
Here,
The requirement for the retention of gas is,
Here,
Explanation:
The diameter of Titan is 5150 km and the mass of Titan is
Since, radius is half of the diameter, the radius of Titan is,
Here, D is the diameter of Titan.
Substitute
Recall the formula of the escape velocity.
Substitute 2575.5 km for R,
Further solve as,
Recall the requirement for the retention of gas.
Substitute
Squaring both sides.
Conclusion:
Therefore, the gas with molecular mass greater than
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