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enter image description here

If the gravitational vector field of the earth is something as in the picture above, then the net field would sum up to zero by symmetry, but why don't we experience weightlessness?

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closed as unclear what you're asking by Yashas, Jon Custer, Chris, Kyle Kanos, ZeroTheHero May 3 at 22:08

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    $\begingroup$ You literally said a field exists and you ask why we don't feel weightlessness. We have mass and there's a field => there's a force acting on us. $\endgroup$ – Yashas May 2 at 7:11
  • $\begingroup$ Can you explain "then the net field would sum up to zero by symmetry"? $\endgroup$ – Yashas May 2 at 7:12
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    $\begingroup$ Hint: you are not sitting exactly in the middle of the earth. $\endgroup$ – Michael Angelo May 2 at 7:28
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    $\begingroup$ "the net field would sum up to zero by symmetry" True, but only in one point. In the very centre of the planet, the "arrows" point equally from all directions. They cancel each other out - but only there, in the centre, not anywhere else. Not at the surface, for example. At any other point in your image, the "arrows" do not cancel out. $\endgroup$ – Steeven May 2 at 7:56
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    $\begingroup$ It seems like it should be fairly obvious that this applies only to the entire Earth as a whole. I don't know about you, but I'm only a small person on the Earth, not the Earth itself. $\endgroup$ – JMac May 2 at 12:48
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As per your logic, the gravitational field will sum upto zero only at the center of the Earth (which is the earth's inner core). We are living on the surface of the Earth which is why we are experiencing the force acting on us

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Actually you need a calculus - to integrate all gravity forces over infinitesimal masses in a body - to understand this.

Calculus visually

a) Object near surface

enter image description here

Net gravity force is directed towards the center of mass

b) Object closer to center

enter image description here

Net gravity force is still directed towards the center of mass. However it's magnitude is smaller than in (a) case because now you can see that there exists a net force which drags object outwards from the center too.

c) Object at the center

enter image description here

Net gravity force is zero - because individual forces cancels each other out completely.

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Since Earth has finite radius, so on its surface there will be net gravitational field pulling you towards the centre of Earth

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