Astronauts in the International Space Station (ISS) are just under 700 km above the earth's surface.  While this seems like a long way off, that's only approximately 1/10 of earth's radius.  Gravity there is 89% as strong as it is where you're reading this, yet clearly their experience looks different than yours and mine.  Why?  We will address that in this chapter.

We discussed in our section on kinematics that velocity cannot be felt, and can only be measured relative to some other object.  So there is no preferred reference frame for velocity in a fundamental sense.  This just means that measuring velocity relative to one object as compared with another is no more right or wrong. Another way of saying the same thing is that there simply is no unique answer to the question: "How fast is the car really moving?" So without a universal reference frame against which we should measure velocity, we need a reference frame. Commonly we just tend to use our planet as that reference frame because it's convenient.  So we say things like "a car is driving at 30m/s" when we really mean "a car is driving at 30m/s relative to a fixed point on planet earth's surface".[br][br]If we have a similar discussion, except not about velocity, but about acceleration, our conclusions will be different.  If asked "Can you tell (measure) the difference between being inside different elevator cars undergoing different rates of acceleration?", the answer is yes.  It's odd though, because you'd need to know one other thing to specify how you'd feel or what you'd measure.  You'd need to know if gravity is also present to the same degree in each elevator car?  That's because [b]the feeling of accelerating is identical to the feeling (and measurement) of gravity[/b].  So an elevator accelerating at 10m/s[sup]2[/sup] in interstellar space far away from any source of gravity feels exactly the same as a resting elevator in the physics building on campus.  This really means that what you are feeling right now is the feeling of accelerating UPWARD at around 10m/s[sup]2[/sup]!  Notice I said upward, not downward.  [br][br]Back to the elevators:  The difference in elevators undergoing different rates of acceleration is that they all would feel like gravity of a different strength got mixed in with any actual gravity nearby.  So in principle they all do feel different.  The most common choice of reference frame in physics is to use one that is not undergoing any acceleration. A non-accelerating reference frame is called an[b] inertial reference frame[/b]. We have only dealt with inertial reference frames until now. [b] In general, the choice of reference frame used to solve a problem matters, since the way the physics looks and the behavior of objects changes in accelerated reference frames.  [/b][br][br]In this chapter we will discuss one way we can use this to our advantage for problem solving.  In many ways if you understand what you are doing, it is easier to solve certain problems when taking the viewpoint of an accelerated reference frame rather than an inertial one. It is also worth mentioning that your life experience is from an accelerated reference frame like when you ride a bike or drive in a car. Even sitting or standing still on earth's surface is actually an accelerated reference frame since earth is spinning and orbiting. We'll talk about those details in this chapter.

If gravity is the only force affecting an object like a human while in free fall (before air drag is significant), what is the feeling?  The answer which I'm sure experience will confirm is that you have the sensation of weightlessness.  There is no distinction of how you feel in free fall from how you'd feel while floating in interstellar space far from gravitational sources, or from how you'd feel as an astronaut at the ISS relatively close to home but in orbit!  [br][br]If you tried to measure your weight on a scale as you jump off a ledge the scale would fall right along with you and you'd weigh nothing.  [b]Your sensation of weight is really due to the normal force pushing up against you, and not because of gravity pulling downward on you[/b].  If the normal force is removed, your sense of weight and the your ability to feel the force of gravity, or even measure its effect, is gone.  You'd be like the astronauts in orbit. What's strange about this is that the gravitational force is just as strong as always for you in free fall, or equal to [math]\vec{F_g}=m\vec{g}.[/math]  Even for the astronauts in the ISS, they feel 89% of that. So, in a very real sense, we don't feel gravity's force, but just the forces of surfaces or objects pushing on us - like the chair on your butt that prevents you from freely falling.  This is my major reservation about calling the force of gravity your weight, as introductory physics books often do.    [br][br]Your head feels weighted down really because your butt is pushed by the chair, which in turn pushes on other parts of you via third law pairs in a chain reaction, until your shoulders and spine - being supported by tissues below them - are pushing upward on your head.  All of that disappears in free fall while the force of gravity remains the same.[br][br]I need you to see the difference. Gravity is not why your head seems heavy. It’s rather the upward force of supporting tissues… the normal forces that give rise to the sensation of weight. Do away with normal forces and your weight is gone such that no instrument (nor your senses) can measure it.

So if we can feel weightless right in the midst of a gravitational field, what other odd effects can occur?  I'm sure you've noticed when you take an elevator that the moment it starts accelerating upward you feel heavier for a moment.  You've certainly also noticed that when an elevator accelerates downward that you feel lighter.  If you had a scale with you in the elevator you'd weigh more while accelerating upward due to an increased normal force (keep repeating if you need to that [b]the normal force is really the measure of your weight[/b]), and you'd weigh less while accelerating downward, likewise due to a decreased normal force.  [b]So the normal force, which we use to infer how strongly gravity pulls on us, changes based on the acceleration we are undergoing[/b].[br][br]Hopefully it's clear then, that while physics books often refer to the force of gravity as weight, really weight is a measure of normal force.  As mentioned briefly above, we don't even measure our true weight while standing still on a bathroom scale because the normal force is affected by earth's rotational motion and the associated centripetal acceleration![br][br]These facts taken together lead to a term called the [b]effective gravitational field[/b], or [math]\vec{g}_{effective}.[/math]  This term accounts for the combination of actual gravitation as well as any acceleration that is being experienced, which is indistinguishable from gravity. In an upward accelerating elevator, for instance, your keys would fall to the ground faster, balls would fly along more curved arcs, scales would indicate you weigh more, etc.  [i]Effectively[/i] gravity would have changed.

To find out what the effective gravitational field is for a given circumstance, all you need to know is the acceleration of the system.  The equation is simple: [br][br][center][math]\vec{g}_{effective}=\vec{g}-\vec{a}.[/math][/center]This equation works regardless of the direction of the acceleration, since it's a vector.  Whatever the vector subtraction leads to is the direction that feels like "downward" in that scenario.  Whatever the magnitude of the effective gravitational constant, it indicates how strong gravity feels.[br][br]Look back at free fall, for example.  While in free-fall, we know that [math]\vec{a}=\vec{g}[/math], so [math]\vec{g}_{effective}=\vec{0}.[/math]  In other words it is as if there is no gravity if you are the one falling.  If you let go of your keys as you fall, they go nowhere with respect to you.  [br][br]It is worth briefly mentioning that the air drag a sky diver feels would quickly detract from the weightless feeling of free-fall. That is because with air drag your downward acceleration does not equal 'g' for very long. After seconds, you are nearly at terminal speed and all you get is the sensation of a very strong upward wind instead of weightlessness. In the indoor skydiving facilities (if you've seen them) you never get the sensation of weightlessness, only the wind part.