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Let's say there are two objects.. one the size of a bowling ball weighing 10 pounds.. and the other object is the earth's moon.. they are both the same distance from the earth.. now.. wouldn't the earth pull the bowling ball to it faster than the moon because the moon has a much larger gravitational pull of its own to combat the earths gravity?

Does this not go against what we are taught in school and demonstrated in Galileo's Leaning Tower of Pisa experiment..?

Qmechanic
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user55665484375
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    Opposite is true, as the moon pulls the earth as well. See https://physics.stackexchange.com/q/3534/180843 – Sten Jan 02 '24 at 21:15
  • I am not sure what do you mean by "pull of its own" – Pato Galmarini Jan 02 '24 at 21:22
  • No, as per $ma=GMm/r^2$, falling object acceleration $a$ is independent of object mass, it depends just on interceptor mass $M$. Analogically, Earth falling acceleration towards object is independent on Earth mass, just on object mass. – Agnius Vasiliauskas Jan 02 '24 at 21:33
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    No, @Agnius. Please see the linked dupe target. – PM 2Ring Jan 02 '24 at 23:09
  • I see. So my suggestion is true just in case $m \ll M$, which is what typical school courses have in mind when describing Newton gravity law. – Agnius Vasiliauskas Jan 03 '24 at 07:01
  • To validate this point substitute Earth mass and radius into formula to get $a$, namely $G × 5.97219 \cdot 10^{24} kg × (6~371~000 m)^{−2} = 9.8 m/s^2$ which is $g$. So it can be said that at least tennis ball or bowling ball or tank near Earth surface- all fall at the same rate $g$. – Agnius Vasiliauskas Jan 03 '24 at 07:19

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Two things. Under general relativity, all objects fall at the same speed, just like was proven on the Leaning Tower of Pisa. So don't think about the weight of the object falling. I like to compare it to a low pressure system of time, where it is the difference in the rate of time dilation above and below the object that dictates the rate of fall. The weight of the object has no impact on it.

Second, the moon is actually falling towards the earth, in exactly the same way that the space station is falling towards the earth. But because the moon is moving so fast, and it is a long distance up so gravity from the Earth is lower, that it always falls past the horizon, no matter where the horizon is. The space station is closer, in a region of higher gravity, so in order for it to be in a stationary falling orbit, it must be moving faster than the moon.

foolishmuse
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