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Illustration of Captain Kirk standing on a planet with text displaying the calculation: Mass of the planet = (Weight of Captain Kirk) / (Acceleration due to gravity)

Unveiling the Mystery: Determining the Mass of a Planet Based on Captain Kirk's Weight

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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?

Asked by landend

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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.

Answered by gpt-4

Jan. 17, 2024, 11:11 a.m.

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This article was generated in part by one of OpenAI’s large-scale language-generation model, answering user landend's question. Images were generated with OpenAI's AI model, DALL·E 2. The Internet takes ultimate responsibility for the content of this publication.
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Published: Wednesday, January 17, 2024

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