Quote:
Originally Posted by island911
I get that people call out centrifugal force as a force, even though it is not a force. Yet it is handy to have that relative reference frame.
But what is this about inertial spin at the equator changing the gravitational (or space-time) field?
Seems an asteroid pulled into a pole or the equator would 'see' the same planetary mass-induced acceleration.
No?
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again don't confuse forces and accelerations
any change of motion can
only be caused by a force,
change of motion aka acceleration can be speeding up, slowing down or changing direction
net acceleration is always in the same direction as and proportional to net force applied
net force is the summation of all the forces acting on the body
the force between the asteroid you mention and Earth is defined by this formula
F = Gm
1m
2/r
2
F is the force acting to pull the 2 masses together
G is the universal gravitational constant
m
1 is the Earth's mass here or any other generic mass
m
2 is the asteroids mass here or any other generic mass
r is the distance between the gravitational centers of the 2 masses, which in the case of a homogeneous masses is also their geometric center
That formula also applies to the person standing at the N pole or at the equator, but that is not the only force being applied to a person standing on the surface of the Earth, Such a person is also having the direction of his motion continuously being changed by an additional force, in this case the friction( + less important forces like air resistance) between the person and the surface he/she is standing on. The net Force applied is the summation of all the forces being applied and again will be aligned the direction of the summation
In the case of the person on the equator there is a considerable change in the direction of motion, w/o G the person would continue to go in a straight line at ~460 m/s soon leaving the Earth on a tangent, w/o friction the person would be stationary and slam in to any any on coming vertical surface connected to the Earth at ~ 450m/s, The summation of all the forces keep the person planted moving along at ~450 m/s w/ a path the curves parallel to the Earths surface
as one approaches either pole the spin velocity of the Earth's surface asymptotically approaches 0, so the net acceleration asymptotically approaches g caused by G(capitol G, Earths force gravity) and the person's weight adjusts correspondingly
The analogy of a car going around a curve is apt, w/o a force to change direction, the car or you will go straight off the road, the tires generate a friction force(the basis of which is mostly electro-magnetic force, remember there are only 4 fundamental forces) this additional force alters the straight line inertia(aka momentum) to change the direction of motion. You as a passenger cannot sense any difference between this phantom inertial force and gravity other than the direction of action