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G accelerationby scientifico
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#1
Jan813, 10:15 AM

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Hello, comparing the formula of gravitational attraction with F = m*a you get that the smaller mass disappear.
I don't think this is physically correct, do you ? thank you 


#2
Jan813, 10:18 AM

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#4
Jan813, 10:24 AM

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G acceleration
To briefly summarize ZapperZ's FAQ entry (since it mostly just derives what you seem to have already realized): what you have noticed is the fact that, ignoring air resistance, all objects fall at the same rate if dropped from the same height. Galileo noticed this a long time ago. It's not only physically correct—it's the defining feature of gravity.



#5
Jan813, 10:36 AM

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For m comparable to M, this doesn't work. Zz. 


#6
Jan813, 10:55 AM

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The instantaneous acceleration of an body in a gravitational field is independent of its mass, regardless what the mass ratios are. That's what the OP derived, but doubts. Whether the gravitational field changes over time, because the other object moves too, is a different issue. 


#7
Jan813, 11:01 AM

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For what the OP is asking, the reason is shown in the derivation in the FAQ. Zz. 


#8
Jan813, 11:14 AM

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More to the point: the OP said, "I've done this calculation, and it leads to conclusion X which I can't believe is true." Your response was to link to a question that is, "Why is X true?" that shows it's true (at least under the right circumstances) by repeating the same sort of calculation the OP did. That is not very helpful. The OP wouldn't ask, "Why is the conclusion true?" because he doesn't think it's true! All you've done is start from the belief that it's true and repeated what he already knew. Whatever further caveats and restrictions you want to add don't change that fundamental fact. The correct response to OP's question is just: yes, actually, it is essentially true. If they then want to delve into why it's true—why gravitational and inertial mass seem to be equivalent—then that can be delved into as a follow up, as can the caveats that show it's actually just a limiting behaviour. 


#9
Jan813, 11:54 AM

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#10
Jan813, 02:30 PM

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Why don't you try to work this out yourself. You are on a planet of mass M. Planet A has mass M as well while planet B has mass M/2. Do you really think that from your point of view on your planet, both planets will "fall" at the IDENTICAL rate? Try it. And don't forget that your planet is also falling towards the center of mass of the 2planet system. Zz. 


#11
Jan813, 03:10 PM

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If I have two bodies on the earth m1 and m2 both with m << M, is their gravitational acceleration EXACTLY the same or the heavier body has a very slightly higher acceleration ?



#12
Jan813, 04:22 PM

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m << M doesn't matter for the instantaneous acceleration, which is the same for m1 and m2 at the same distance from M, no matter how great M is. But the total time until collision will be shorter for the heavier m, if M is not much greater than the m's. 


#13
Jan813, 05:38 PM

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To an external viewer, both small objects accelerate at the same rate. The only difference is that the acceleration of the large mass is just slightly greater with the heavier small mass. If your frame of reference is the large mass, then the acceleration of the small objects and the large object have to be added together. A viewer on the large mass will see the heavier small object accelerate at a slightly greater rate than the smaller small object. 


#14
Jan813, 10:35 PM

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The only way it is not true is if you use a (Newtonian) non inertial frame to measure the rate of falling. I think that must be what you are doing, but I don't know why. 


#15
Jan913, 07:09 AM

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I have learned that a hammer and a feather (in vacuum) will not have the same acceleration. Appearently it has because these objects are so small compared to the earth, that the earth mass will dominate almost totally. The hammer will hit the ground a split second before the feather. Maybe this was off topic, but might help I hope.
Vidar 


#16
Jan913, 07:30 AM

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#17
Jan913, 10:51 AM

P: 181

so heavier body hit the earth before the lighter one because its stronger gravitational field gets the earth a bit closer to it ?
said that I dont understand physically why acceleration is independent from m 


#18
Jan913, 11:18 AM

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But I am guessing you are looking for a good analogy, or intuitive explanation, which will help to drive it home? hmm... by analogy, it is similar to coulomb's law, replacing charge with mass, so then it just so happens that mass gets cancelled out of the equation. By intuition... the gravitational force gets stronger with stronger mass, but then the inertia increases as well, so gravity has more to pull on, so the two effects cancel out, so that increasing the mass doesn't increase the acceleration (or decrease it). I can't think of any other ways to explain it. 


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