Gravitational pull on probe between the Sun and the Earth

AI Thread Summary
To determine the distance from Earth where a space probe experiences balanced gravitational forces from both the Earth and the Sun, one must equate the gravitational pull exerted by each body. The distance from the Earth to the Sun is represented as 'd', while 'r' denotes the distance from the Earth to the probe. The gravitational force can be expressed using Newton's law of universal gravitation, where the force from the Earth is proportional to 1/r² and the force from the Sun is proportional to 1/(d-r)². Setting these two forces equal allows for the calculation of 'r', providing the necessary distance for balance. Understanding the relationship between gravitational force and distance is crucial for solving this problem.
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How far from Earth must a space probe be along a line toward the Sun so that the Sun's gravitational pull on the probe balances the Earth's pull?

I'm actually just confused as to how to set this up. I know that I need to consider d being the distance from the Earth to the sun and r being the distance from the Earth to the probe. And use (d-r). Any help as to how I should set this up would be greatly appreciated. Part of what I'm confused with is that when referring to pull I'm thinking that is a force right. I'm completely lost as to how to start this one.
 
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Equate the gravitational attractive power on the probe by the Earth and the sun.
 

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