

Gravity

Gravity is the attraction of every body to every other
body due to the masses of each body. The larger the mass, the greater the
force. It also depends on the distances: the closer the bodies, the greater
the force. Gravity is directed toward the center of a body, and the distance
is measured from the center. Gravity keeps the moon going around the Earth,
the Earth going around the Sun, and the Sun going around the center of the
Milky Way. Gravity is the weakest of the four fundamental forces of nature
(electromagnetic, weak nuclear, and strong nuclear are the other three),
yet it is the force that governs motion in the universe. 
2. What factors
determine the force of gravity between two bodies? 
The force of gravity (F) depends on the masses of the
two bodies (m_{1}, m_{2}) and the distance between the bodies' centers (r).
There is a direct proportion between mass and gravitational force: If
you double the mass of one body, the gravitational force between them
is also doubled. The gravitational force is inversely proportional to
the square of the distance: If you double the distance between the two
bodies, the force of gravity is reduced to onefourth its original value.
The equation relating these ideas is: F = G(m_{1}m_{2})/r^{2}, where G is the
universal gravitational constant equal to 6.67 x 10^{11} Nm^{2}/kg^{2} or m^{3}/s^{2}kg). 
3. What keeps
objects in orbit? (What keeps the moon from falling to Earth or the Earth
from falling into the Sun?) 
Objects remain in orbit around a massive body due to
gravity and their sideways motion. Objects in orbit are moving sideways,
approximately at right angles (90 degrees) to the force of gravity. An
object would travel in a straight line with a constant speed if it were
not for the gravitational attraction of a massive body. The attractive
force changes the motion of the object from a straight line to a closed
curve, as it begins orbiting the massive body. In effect, the object is
"falling" around the massive body. 
4. What is an unbalanced
force? 
An unbalanced or net force causes changes in an object's speed and/or
direction. Only one force acting on a body is unbalanced because there
is no counterforce to cancel the force's effects. A person remains
at rest when sitting in a chair because there are two balanced forces
acting on that person. One of those forces is gravity, which pulls the
person downward. The other force is the chair pushing upward on the
person. The two forces are equal in magnitude (size) and opposite in
direction. So they balance each other, and the person doesn't change
direction or speed.
On the other hand, Earth's gravitational influence on the moon is unbalanced.
The moon is constantly changing its direction of motion, so it is experiencing
acceleration. Any time there is an unbalanced force, the object will
undergo a change in direction or speed. So, a change in direction or
speed means there is an unbalanced force at work.

5. How does a large
body (like a planet) capture a small body (like a comet)? 
According to Newton's First Law of Motion, an object in motion tends
to remain in straightline motion at a constant speed unless acted upon
by an external, unbalanced force. When a comet or asteroid comes close
to a body with a large gravitational force (a planet, for example),
the path of the comet or asteroid is altered due to the unbalanced force
of gravity on the body. It moves toward the planet as described in Newton's
Second Law: When an unbalanced force acts on a body, the body experiences
acceleration in the direction of the force. A force that tends to make
a body move in a curved path is called a centripetal force.
Occasionally, the comet will be close enough to the planet to become
trapped by the gravitational force and will begin orbiting the planet.
The comet would like to continue traveling in a straight line, but the
planet is pulling the smaller body toward its center, making it travel
in a curved path around the planet.

6. Why does
the angle of approach affect the ability of a planet to capture a comet?

The more direct the approach, the easier it is for the
planet to capture a comet because the comet comes closer to the planet.
As discussed in question 5 above, the closer the objects come to each
other, the stronger the force of gravity. 
7. What role
does speed play in the capture of a comet by a planet? 
The faster an object is moving, the greater the kinetic energy. In
order for an object to be trapped by the gravity of a planet, the object's
kinetic energy (E_{k} = 1/2 mv^{2} where E_{k}
= kinetic energy, m = mass of comet, and v = speed) must be less than
the gravitational potential energy (U = GMm/r where U = potential energy,
G = gravitational constant, M = mass of planet, m = mass of comet, and
r = distance from the center of the planet to the center of the comet).
The comet's total energy is equal to the kinetic plus potential energies.
But the potential energy is negative, so a comet can only escape a planet's
gravitational pull if the kinetic energy is larger than the gravitational
potential energy.


