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Question: Captain Kirk (76.7 kg) beams down to a planet that is the same size as Uranus (radius of 2.61 x 107 m) and finds that he weighs 1,144 N.What is the mass of that planet?
Captain Kirk's weight on that planet (force of gravity) is given as 1,144 N. We can use the following formula to find the gravitational force: F = (G*m1*m2)/r^2 Where: F is the gravitational force (weight of Captain Kirk in this case), G is the gravitational constant (6.674 x 10^-11 m^3 kg^-1 s^-2), m1 is the mass of one object (mass of Captain Kirk in this case), m2 is the mass of the second object (mass of that planet, which we are trying to find), and r is the distance between the centers of the two masses (radius of the planet in this case). We rearrange the formula to solve for m2 (the mass of the planet): m2 = (F*r^2) / (G*m1) Substituting the given values: m2 = (1,144 N * (2.61 x 10^7 m)^2) / ((6.674 x 10^-11 m^3 kg^-1 s^-2) * 76.7 kg) From this calculation, we find that the mass of the planet is approximately 1.25 x 10^25 kg.
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