How Do Newton's Laws Explain Changes in Gravitational Forces and Orbital Ratios?

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Doubling the distance between two masses reduces the gravitational force to one-fourth of its original value, as described by Newton's law of universal gravitation. The equation for gravitational force is F = G(m1*m2)/r^2, where r is the distance between the masses. According to Newton’s version of Kepler’s third law, if the mass of the sun is doubled, the ratio (T^2/r^3) remains unchanged, as it depends only on the orbital radius. This indicates that the orbital period T is unaffected by changes in the sun's mass when considering the ratio. Understanding these principles is essential for grasping the dynamics of gravitational forces and orbital mechanics.
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Homework Statement



1. What happens to the gravitational force between two masses when the distance between the masses is doubled?

2. According to Newton’s version of Kepler’s third law, how does the ratio (T^2/r^3) change if the mass of the sun is doubled?
 
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For the first one, what's the equation of gravitational force? What happens if you double the distance and keep everything else the same? Tell us what you think.
 

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