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When a person is standing still, the action of the Earth on their body is a gravitational force. What is the reaction force? Is it the person's weight acting on the Earth?

Qmechanic
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user389246
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Newton's third law applied to gravity

Newton's 3rd law is always true in classical physics. For a person standing on the ground the Earth pulls on the person with gravity, so the person pulls on the the Earth with gravity. 3rd law force pairs are always of the same type (in this case gravity) and always act on different objects. For your example one acts on the person, and the other acts on the Earth.

$$ \vec{F}_\mathrm{Earth\rightarrow person} = - \vec{F}_\mathrm{person\rightarrow Earth} \quad (3^\mathrm{rd}\,\mathrm{law})$$

What about the normal force?

The normal force pushing up on the person prevents them from falling. This force contributes to the net force acting on the person. To understand it we must consider Newton's 2nd law, $\vec{F}_\mathrm{net} = m \vec{a}$. If the person is not accelerating, they have zero net force acting on them. All of the forces in a Newton's 2nd law statement act on the same object.

$$ \vec{F}_\mathrm{Earth\rightarrow person} + \vec{N}_\mathrm{ground\rightarrow person} = m_\mathrm{person}\, \vec{a}_\mathrm{person} = 0 $$

$$ \vec{F}_\mathrm{Earth\rightarrow person} = - \vec{N}_\mathrm{ground\rightarrow person} \quad (2^\mathrm{nd}\,\mathrm{law})$$

The equality of the normal force and the gravitational force depends on there being zero acceleration. If the person is accelerating, then the normal force is not equal to the gravitational force. You can experience this at the start or end of an elevator ride, when you speed up and slow down.

By Newton's third law the ground pushes with a normal force on the person, so the person pushes with a normal force on the ground.

$$ \vec{N}_\mathrm{ground\rightarrow person} = -\vec{N}_\mathrm{person\rightarrow ground} \quad (3^\mathrm{rd}\,\mathrm{law})$$

It's worth noting that the name 'normal force' refers to forces that push perpendicularly to a surface. 'Normal' is a mathy word for perpendicular. The ground pushes perpendicularly relative to the surface of contact (the person's feet). Anytime you push on something, you apply a normal force to the surface.

Paul T.
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