I understand that when someone is in low earth orbit, the "pull" of their inertia is equal to the pull of gravity. However, the force of gravity is still acting on them. However, if they are in outer space there the pull in any direction is miniscule, they should feel different that the way they feel in orbit, because you feel forces on your body and in outer space there is no net force while in orbit there is. Am I correct?
[Physics] How you feel in outer space vs. orbit
centrifugal forcecentripetal-forceequivalence-principlenewtonian-gravitynewtonian-mechanics
Related Solutions
As many others said, the Sun feels the same force towards Earth as the Earth feels towards the sun. That is your equal and opposite force. In practice though the "visible" effects of a force can be deduced through Newton's first law, i.e. ${\bf F} = m{\bf a}$. In other words, you need to divide the force by the mass of the body to determine the net effect on the body itself.
So:
${\bf F_s} = {\bf F_e}$
${\bf F_s} = m_s {\bf a_s}$
${\bf F_e} = m_e {\bf a_e}$
therefore,
$m_s {\bf a_s} = m_e {\bf a_e}$
and
${\bf a_s} = {\bf a_s} \frac{m_e}{m_s}$
Now, the last term is $3 \cdot 10^{-6}$! This means that the force that the Earth enacts on the sun is basically doing nothing to the sun.
Another way of seeing this:
$F = \frac{G m_s m_e}{r^2}$
$a_s = \frac{F}{m_s} = \frac{G m_e}{r^2}$
$a_e = \frac{F}{m_e} = \frac{G m_s}{r^2}$
$\frac{a_s}{a_e} = \frac{m_e}{m_s} = 3 \cdot 10^{-6}$
Again, the same big difference in effect.
Regarding the centripetal force, it is still the same force. Gravity provides a centripetal force which is what keeps Earth in orbit.
Note
It's worth pointing out that the mass that acts as the charge for gravity, known as gravitational mass is not, a priori, the same mass that appears in Newtons's law, known as inertial mass. On the other hand it is a fact of nature that they have the same value, and as such we may use a single symbol $m$, instead of two, $m_i$ and $m_g$. This is an underlying, unspoken assumption in the derivation above. This is known as the weak equivalence principle.
There are three misconceptions that I can see in your reasoning.
The poles are the only places on Earth where you are not accelerating due to the Earth's rotation, so you have that backwards.
You seem to think that the normal force has to be the same at the poles and the equator, which isn't true. Finding the normal force at the poles does not give you the normal force at the equator.
The forces involved are vectors, not scalars, and they are not collinear (except for the special case of the equator). The gravity and normal force are approximately collinear with the Earth's radius everywhere, but the centripetal (or centrifugal) force is not; it points towards (away from) the axis of rotation. So you need to do some vector math/trigonometry to get the actual values.
You seem to be struggling with the distinction between the centripetal force and the centrifugal force. It seems like you have the right idea, but its hard to tell due to the other issues. Let me try to explain what those are.
The centrifugal force is a "fictitious force" (meaning there is no object that exerts this force) that appears to arise in a rotating coordinate system; considering the centrifugal force in a rotating coordinate system maintains the usefulness of Newton's 2nd law.
The centripetal force is the required amount & direction of force that the net force on an object must satisfy in order for the object to move in a circle of a certain radius at a certain speed.
Best Answer
They should feel the same. You only feel forces in orbit if there is something causing sensations, and nothing does in either case. Even on earth, you don't feel the "force" of gravity; you feel the force of the floor pushing you up so that you don't start falling under gravity's influence. In orbit, there is no floor, so you don't feel gravity.
You might imagine a force pushing on your spacesuit which then pushes against you. But in orbit, the force on your spacesuit causes an acceleration of the spacesuit that's exactly the acceleration that your body experiences, so there will be no relative difference in the motion of your body and your spacesuit, so you won't feel anything.
Or you might imagine your left arm feeling a different force than your right, and so feeling pulled apart. But the accelerations they experience in orbit will be the same, so their relative positions won't change, and you won't feel any difference.
(Technically, there might be minuscule differences referred to as tidal forces. These should be measurable by extremely sensitive instruments, but not by humans orbiting anything humans are likely to orbit any time soon.)