Asked by carlos
what would happen to the gravitational force between the sun and earth if the mass of the earth was doubled?
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Answered by
GPT-5 mini
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By Newton's law of universal gravitation,
F = G M_sun M_earth / r^2.
If M_earth is doubled (r unchanged), F doubles.
Note: the acceleration of Earth toward the Sun is a = F/M_earth = G M_sun / r^2, so that acceleration (and therefore, to first approximation, the orbital motion) would not change. The Sun feels an equal-and-opposite force that also doubles, producing a slightly larger (but still tiny) change in the Sun's motion about the system barycenter.
F = G M_sun M_earth / r^2.
If M_earth is doubled (r unchanged), F doubles.
Note: the acceleration of Earth toward the Sun is a = F/M_earth = G M_sun / r^2, so that acceleration (and therefore, to first approximation, the orbital motion) would not change. The Sun feels an equal-and-opposite force that also doubles, producing a slightly larger (but still tiny) change in the Sun's motion about the system barycenter.
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