Is a Helicopter on a Geostationary Orbit?

[FactChecker]

No, they don't always act along the same line. The gravitational force is not perpendicular to the surface (except at the poles and equator). The rest of your argument is based on this misconception.

The force from the chair includes a static friction force that opposes any component of gravity or centripetal force that is tangent to the Earth's surface. The result is that the chair does exert a force exactly opposite to all other lateral forces on your body.

 

[A.T.]

The force from the chair includes a static friction force that opposes any component of gravity or centripetal force that is tangent to the Earth's surface. The result is that the chair does exert a force exactly opposite to all other lateral forces on your body.

No matter how you decompose them into components, the vector sum of gravity and chair force on you is not zero. If it was, you would move in a straight line in the inertial frame, but you move in a circle.

So no, the component of gravity tangent to the surface is not canceled by static friction. And neither is the component of gravity normal to the surface completely canceled by the normal force. These unbalanced components provide together the centripetal force to keep you on a circular trajectory.

 

[FactChecker]

So no, the component of gravity tangent to the surface is not canceled by static friction. And neither is the component of gravity normal to the surface completely canceled by the normal force. These unbalanced components provide together the centripetal force to keep you on a circular trajectory.

Regarding the lateral force: The reason a person does not slide laterally is that the static friction exactly cancels any lateral force. Static friction does that. I know. I have gotten it wrong in simulations and watched as the simulated object of interest slowly started to slide laterally.

Regarding the normal force: You are right about there being some acceleration. At no point does a person come closer to the center of the earth. The chair provides the exact force necessary to make that happen. All the forces are constantly rotating except at the geographical poles.

 

[MikeGomez]

A body in orbit is in free fall.

 

[A.T.]

The reason a person does not slide laterally is that the static friction exactly cancels any lateral force.

No, the component of gravity tangent to the surface is not exactly canceled by static friction.

 

[FactChecker]

No, the component of gravity tangent to the surface is not exactly canceled by static friction.

In a perfect world, the surface of the Earth is an equipotential surface where both gravity and centripetal force are take into account. In that case there is no lateral force component tangent to the surface. In a realistic world, there are small lateral forces but static friction stops things from sliding around. The force from static friction is the exact amount needed to counteract other forces that are too small to overcome the static friction. But this is digressing from the OP.

 

[Vanadium 50]

Can we focus on the original question, please?

 

[Integral]

I am surprised that no one has used Keplers law to compute the orbital period for a orbit at the Earth's surface.

 

[D H]

Can we focus on the original question, please?

Since that apparently could not be done, thread closed.