| The French
author Antoine de Saint-Exupery tells us that the Little Prince could
walk around his planet in about one hour. Assuming the Prince walked at
a normal rate, the radius of his planet must have been about 1 km. The
story implies the Prince's weight was normal, which means that the value
of "g" on his planet was the same as on Earth (about 10 m/s2).
What is the mass of this tiny planet?
The Prince's mass is 40 kg and he weighs 400 N. Remember that G = 6.67 x 10-11 N-m2/kg2. (Bonus... what is the planet's density?) |
From Newton's Universal Law of Gravitation,
mp = (Fwd2)/(Gm) so mp = (400 N)(1 km)(1 km) / [(6.67 x 10-11 N-m2/kg2)(40 kg)] = 1.5 x 1011 kg Density = mass / volume. Volume of a sphere is 4/3(pi)r3
= 4.19 km3 for this planet. Density is therefore
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