All bodies have gravity unto them. Not just the Earth and Sun and planets, but ALL bodies (including YOU). Of course, the gravity for all of these is not equal. Far from it. The force of gravity can be summarized in an equation:
F = G m1 m2 / d^2
or.... the force of gravitation is equal to a constant ("big G") times the product of the masses, divided by the distance between them (between their centers, to be precise) squared.
Big G = 6.67 x 10^-11 *, which is a tiny number - therefore, you need BIG masses to see appreciable gravitational forces. This number, the universal gravitation constant, can be thought of as a way of relating mass and distance to force, and arriving at measurable force values.
(Note that the unit for this quantity is Nm^2/kg^2 -- the result of this is that the unit for force works out to be a newton, which is roughly 1/4 of a pound.)
This is an INVERSE SQUARE law, meaning that:
- if the distance between the bodies is doubled, the force becomes 1/4 of its original value
- if the distance is tripled, the force becomes 1/9 the original amount
- etc.
Weight
Weight is a result of local gravitation. Since F = G m1 m2 / d^2, and the force of gravity (weight) is equal to m g, we can come up with a simple expression for local gravity (g):
g = G m(planet) / d^2
Likewise, this is an inverse square law. The further you are from the surface of the Earth, the weaker the gravitational acceleration. With normal altitudes, the value for g goes down only slightly, but it's enough for the air to become thinner (and for you to notice it immediately!).
Note that d is the distance from the CENTER of the Earth - this is the Earth's radius, if you're standing on the surface.
If you were above the surface of the earth an amount equal to the radius of the Earth, thereby doubling your distance from the center of the Earth, the value of g would be 1/4 of 9.8 m/s/s. If you were 2 Earth radii above the surface, the value of g would be 1/9 of 9.8 m/s/s.
The value of g also depends on the mass of the planet. The Moon is 1/4 the diameter of the Earth and about 1/81 its mass. You can check this but, this gives the Moon a g value of around 1.7 m/s/s. For Jupiter, it's around 25 m/s/s.
>
Newton is also remembered for his "laws of motion."
Newton, Philosophiae Naturalis Principia Mathematica (1687) Translated by Andrew Motte (1729)
- often called Principia.
Newton's 3 laws of motion:
1. Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.
2. The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
3. To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
In simpler language:
1. A body will continue doing what it is doing unless there is REASON for it to do otherwise. It will continue in a straight line at a constant velocity, unless something changes that motion. This idea is often referred to as INERTIA.
2. The second law is trickier:
An unbalanced force (F) causes a mass (m) to accelerate (a). Recalling that acceleration means how rapidly a body changes its speed (in meters per second per second, or m/s/s):
F = m a
There is a new unit here: the kg m/s/s - this is called a newton (N)
Note that a larger force gives a larger acceleration. However, with a constant force - the larger the mass is the smaller the acceleration. Imagine pushing me on a skateboard vs. pushing a small child with the same force - who would accelerate more rapidly?
3. To every action there is always opposed an equal reaction.
You move forward by pushing backward on the Earth - the Earth, in turn, pushes YOU forward.
A rocket engine pushes hot gases backward - the gases, in turn, push the rocket forward.
If you fire a rifle or pistol, the firearm "kicks" back on you.
No comments:
Post a Comment