Which of newton's laws best applies to satellite in space
Newton's law of Inertia (First Law)
Newton's law of Universal Gravitation for example the moon, the earth applies a gravitational pull on the moon but the moon doesn't fall on earth because the moon travels an appropriate speed to keep its distance from the earth.
Newton's First Law (inertia) is what causes the satellite to maintain its tangential speed, so it doesn't crash down into the earth. (It wants to keep going in the direction of the tangent to its elliptical orbit.) Newton's Law of gravitation dictates that it can't go in that tangential direction that it wants to go, because the force of gravity pulls it down toward the earth. It is essentially continuously falling toward the earth. For a circular orbit, its straight path is curved downward by the force of gravity in such a way that its path parallels the surface of the earth. For an elliptical orbit, the path is curved such that the center of gravity of the satellite-earth system is one of the foci of the satellite's elliptical path. Newton's second law also applies especially if you are looking at describing an elliptical orbit. The second law would dictate that the angular momentum of the satellite is a constant. So as the satellite approaches the earth and the force of gravity increases, the satellite would speed up. As it moves around it and away, the force of gravity would decrease and it would slow down. But for your simple textbook kind of question, I would suspect that it is looking for answer number 1. Newton's Law of Inertia (First Law).
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