Question about satellite orbit

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To determine the distance from Earth where a space probe experiences balanced gravitational forces from both Earth and the Sun, one must apply the principles of gravitational force and vector addition. The gravitational force can be expressed using Newton's law of universal gravitation, which states that the force is proportional to the product of the masses and inversely proportional to the square of the distance between them. For a spaceship traveling to the Moon, the point where the net gravitational force is zero lies along the line connecting the centers of the Earth and the Moon, requiring calculations based on their respective masses and distances. Understanding these concepts is essential for solving such gravitational problems. The discussion emphasizes the importance of foundational knowledge in physics for addressing these questions.
InstaGaeta
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I'm a beginner in physics and have a couple easy question;

How far from Earth must a space porbe be along a line toward the sun so that the sun's gravitational pull balances the earth's?

A spaceship is going from the Earth to the moon in a trajectory along the line joining the centers of the two bodies. At what distance from the Earth will the net gravtitational force on the spaceship be zero?

Thanks for you time.
 
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