86 PART 1^ |^ EXPLORING THE SKY
depends on how fast the planet moves, and the stored energy
depends on the size of its orbit. Th e relation between these two
kinds of energy is determined by Newton’s laws. Th at means
there has to be a fi xed relationship between the rate at which a
planet moves around its orbit and the size of the orbit—between
its orbital period P and the orbit’s semimajor axis a. You can even
derive Kepler’s third law from Newton’s laws of motion as shown
in the next section.Newton’s Version of Kepler’s Third Law
Th e equation for circular velocity is actually a version of Kepler’s
third law, as you can prove with three lines of simple algebra. Th e
result is one of the most useful formulas in astronomy.
Th e equation for circular velocity, as you have seen, is:Vc
√^____
GM____r
Th e orbital velocity of a planet is simply the circumference of its
orbit divided by the orbital period:V 2πr___
P
If you substitute this for V in the fi rst equation and solve for P^2 ,
you will get:
P^2 (4π(^2) )
(GM)
r^3
energy (Focus on Fundamentals 2). A planet orbiting
the sun has a specifi c amount of energy that depends only on its
average distance from the sun. Th at energy can be divided
between energy of motion and energy stored in the gravitational
attraction between the planet and the sun. Th e energy of motion
Energy
P
hysicists defi ne energy as the ability
to do work, but you might paraphrase
that defi nition as the ability to
produce a change. A moving body has energy
called kinetic energy. A planet moving along
its orbit, a cement truck rolling down the
highway, and a golf ball sailing down the
fairway all have the ability to produce a
change. Imagine colliding with any of these
objects!
Energy need not be represented by motion.
Sunlight falling on a green plant, on photo-
graphic fi lm, or on unprotected skin can
produce chemical changes, and thus light is a
form of energy. Batteries and gasoline are
examples of chemical energy, and uranium fuel
rods contain nuclear energy. A tank of hot
water contains thermal energy.
Potential energy is the energy an object
has because of its position in a gravitational
fi eld. A bowling ball on a shelf above your
desk has potential energy. It is only potential,
however, and doesn’t produce any changes
until the bowling ball descends onto your
desk. The higher the shelf, the more potential
energy the ball has.
Energy constantly fl ows through nature and
produces changes. Sunlight (energy) is
absorbed by ocean plants and stored as sugars
and starches (energy). When the plant dies, it
and other ocean life are buried and become
oil (energy), which gets pumped to the
surface and burned in automobile engines to
produce motion (energy).
Aristotle believed that all change origi-
nated in the motion of the starry sphere and
fl owed down to Earth. Modern science has
found a more sophisticated description of the
continual change you see around you. In a
way, science is the study of the way energy
fl ows through the world and produces change.
Energy is the pulse of the natural world.
Using the metric system (Appendix A),
energy is expressed in joules (abbreviated J).
One joule is about as much energy as that
given up when an apple falls from a table to
the fl oor.
2
MASS | ENERGY | TEMPERATURE AND HEAT | DENSITY | PRESSURE
Energy is the ability to cause change.■ Figure 5-7
Skaters demonstrate conservation of angular momentum when they spin
faster by drawing their arms and legs closer to their axis of rotation.