Orbiting the Earth | 绕地球轨道运动

📚 Orbiting the Earth | 绕地球轨道运动

An Earth satellite stays in orbit because the gravitational pull of the Earth continuously changes the direction of the satellite’s velocity. For a circular orbit, this gravitational force acts as the centripetal force, so the satellite is in a state of free fall around the Earth rather than falling straight down.

地球卫星之所以能保持在轨道上，是因为地球的引力不断改变卫星速度的方向。对于圆轨道，这个引力充当向心力，因此卫星处于绕地球自由下落的状态，而不是竖直掉落。

1. Gravity as the centripetal force | 引力作为向心力

For a satellite of mass m moving in a circular orbit of radius r around the Earth (mass M), Newton’s law of gravitation gives the attractive force between the Earth and the satellite.

对于质量为 m 的卫星绕地球（质量为 M）在半径为 r 的圆轨道上运动，牛顿万有引力定律给出地球与卫星之间的吸引力。

F = GMm / r²

For a circular path at constant speed v, the resultant force toward the centre of the circle must equal the centripetal force mv²/r. Since gravity is the only force providing this centripetal requirement, we can equate the two expressions.

对于以恒定速率 v 沿圆轨道运动的天体，指向圆心的合力必须等于向心力 mv²/r。由于引力是提供这一向心需求的唯一力，我们可以令两个表达式相等。

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