The Days (And Years) Of Our Lives
Looking at the numbers above, you'll immediately notice that you are
different ages on the different planets. This brings up the question of
how we define the time intervals we measure. What is a day? What is a
year?
The earth is in motion. Actually, several different motions all at once.
There are two that specifically interest us. First, the earth rotates on its axis, like a spinning top. Second, the earth revolves around the sun, like a tetherball at the end of a string going around the center pole.
The top-like rotation
of the earth on its axis is how we define the day. The time it takes
the earth to rotate from noon until the next noon we define as one day.
We further divide this period of time into 24 hours, each of which is
divided into 60 minutes, each of which is broken into 60 seconds. There
are no rules that govern the rotation rates of the planets, it all
depends on how much "spin" was in the original material that went into
forming each one. Giant Jupiter has lots of spin, turning once on its
axis every 10 hours, while Venus takes 243 days to spin once.
The revolution of the earth around the sun is how we define the
year. A year is the time it takes the earth to make one revolution - a
little over 365 days.
We all learn in grade school that the planets move at differing rates
around the sun. While earth takes 365 days to make one circuit, the
closest planet, Mercury, takes only 88 days. Poor, ponderous, and
distant Pluto takes a whopping 248 years for one revolution. Below is a
table with the rotation rates and revolution rates of all the planets.
Planet
|
Rotation Period
|
Revolution Period
|
Mercury
|
58.6 days
|
87.97 days
|
Venus
|
243 days
|
224.7 days
|
Earth
|
0.99 days
|
365.26 days
|
Mars
|
1.03 days
|
1.88 years
|
Jupiter
|
0.41 days
|
11.86 years
|
Saturn
|
0.45 days
|
29.46 years
|
Uranus
|
0.72 days
|
84.01 years
|
Neptune
|
0.67 days
|
164.79 years
|
Pluto
|
6.39 days
|
248.59 years
|
Why the huge differences in periods? We need to go back to the time of
Galileo, except that we're not going to look at his work, but rather at
the work of one of his contemporaries, Johannes Kepler (1571-1630).
Kepler briefly worked with the great Danish observational astronomer,
Tycho Brahe. Tycho was a great and extremely accurate observer, but he
did't have the mathematical capacity to analyze all of the data he
collected. After Tycho's death in 1601, Kepler was able to obtain
Tycho's observations. Tycho's observations of planetary motion were the
most accurate of the time (before the invention of the telescope!).
Using these observations, Kepler discovered that the planets do not move
in circles, as 2000 years of "Natural Philosophy" had taught. He
discovered that they move in ellipses. A ellipse is a sort of squashed
circle with a short diameter (the "minor axis") and a longer diameter
(the "major axis"). He found that the Sun was positioned at one "focus"
of the ellipse (there are two "foci", both located on the major axis).
He also found that when the planets were nearer the sun in their orbits,
they move faster than when they were farther from the sun. Many years
later, he discovered that the farther a planet was from the sun, on the
average, the longer it took for that planet to make one complete
revolution. These three laws, stated mathematically by Kepler, are known
as "Kepler's Laws of Orbital Motion." Kepler's Laws are still used
today to predict the motions of planets, comets, asteroids, stars,
galaxies, and spacecraft.
Here you see a planet in a very elliptical orbit.
Note how it speeds up when it's near the Sun.
(Requires QuickTime Plugin)
Kepler's third law is the one that interests us the most. It states
precisely that the period of time a planet takes to go around the sun
squared is proportional to the average distance from the sun cubed.
Here's the formula:
Let's just solve for the period by taking the square root of both sides:
Note that as the distance of the planet from the sun is increased, the
period, or time to make one orbit, will get longer. Kepler didn't know
the reason for these laws, though he knew it had something to do with
the Sun and its influence on the planets. That had to wait 50 years for
Isaac Newton to discover the universal law of gravitation.
The Gravity Of The Situation
Closer planets revolve faster, more distant planets revolve slower. Why?
The answer lies in how gravity works. The force of gravity is a measure
of the pull between two bodies. This force depends on a few things.
First, it depends on the mass of the sun and on the mass of the planet
you are considering. The heavier the planet, the stronger the pull. If
you double the planet's mass, gravity pulls twice as hard. On the other
hand, the farther the planet is from the sun, the weaker the pull
between the two. The force gets weaker quite rapidly. If you double the
distance, the force is one-fourth. If you triple the separation, the
force drops to one-ninth. Ten times the distance, one-hundredth the
force. See the pattern? The force drops off with the square of the distance. If we put this into an equation it would look like this:
The two "M's" on top are the sun's mass and the planet's mass. The "r"
below is the distance between the two. The masses are in the numerator
because the force gets bigger if they get bigger. The distance is in the
denominator because the force gets smaller when the distance gets bigger.
Note that the
force never becomes zero no matter how far you travel. Knowing this law
helps you inderstand why the planets move faster when they are closer to
the sun - they are pulled on with a stronger force and are whipped
around faster!
LINKS
Your Weight On Other Worlds
Build A Solar System
The Exploratorium's "Observatory"
The Nine Planets
Other nerdy dates you should celebrate!
Views of the Solar System
NSSDC Photo Gallery
NASA Jet Propulsion Laboratory, Pasadena, California
Astronomy Picture
of the Day
|
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