Motion in Straight Line

Determine the escape velocity of a body from the moon. Take the moon to be a uniform sphere of radius 1.74 x 10 6 m and mass 7.36 x 10 22 kg. Does your answer throw light on why the moon has no atmosphere? (G = 6.67 x 10 -11 Nm 2 /kg 2 ) - Wired Faculty

Question

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Determine the escape velocity of a body from the moon. Take the moon to be a uniform sphere of radius 1.74 x 10⁶ m and mass 7.36 x 10²² kg. Does your answer throw light on why the moon has no atmosphere? (G = 6.67 x 10^-11 Nm²/kg²)

Solution

Escape velocity from the surface of the moon is,

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where,
M is the mass of the moon, and
R is radius of the moon.
Here, we have

straight R equals 1.74 cross times 10 to the power of 6 straight m

straight M equals 7.36 cross times 10 to the power of 22 kg

straight G equals 6.67 cross times 10 to the power of negative 11 end exponent Nm squared divided by kg squared

∴ Escape velocity is,

straight v subscript straight e equals square root of fraction numerator 2 cross times 6.67 cross times 10 to the power of negative 11 end exponent cross times 7.36 cross times 10 squared over denominator 1.74 cross times 10 to the power of 6 end fraction end root straight m divided by straight s

equals 2.3754 space cross times space 10 cubed straight m divided by sec

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Since escape velocity for the moon is 2.38 km/sec which is small as compared to the average speed of gas molecules at the moon, therefore the moon cannot bind the atmosphere.

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