Thomas J. Wdowiak is an Athena scientist who takes time out of his busy schedule to show kids how to do fun
science experiments at home. When he isn't teaching at the University of Alabama at Birmingham or training
at the Jet Propulsion Lab in California, he writes for the local newspaper in Birmingham in the "Just for
Kids" section. He goes by "Tommy Test Tubes," a nickname given to him when he was a kid. Now "Tommy Test
Tubes" contributes his experience and knowledge to the Athena web page with a new column. If you have a
question for Tom, click here.
What is the difference in gravity between Mars and Earth? Why is there
this difference?
You better get out your pencil and paper! A calculator, (I always have
one in my shirt pocket), can help. First you have to realize that
gravity is a consequence of things called mass and energy. Issac
Newton, hundreds of years ago figured out that mass was important, and
then almost a century ago Albert Einstein understood you needed both.
Earth and Mars have both of these things, therefore it makes good common
sense as a first step to compare what both world’s possess in that
regard.
Well Earth is “bigger” than Mars so it’s a good guess that it should
have more of mass and energy than Mars. How much more? Since Earth and
Mars are shaped like round balls, you can start by thinking about round
bowls. Yes bowls, the kind of things you put stuff in! A round bowl if
shaped right is really half a round ball, isn’t it?
If you have two round bowls, like mixing bowls, and the larger bowl is
twice as large across as the smaller one, you can do an interesting
experiment. How many full small bowls of water would it take to fill
completely the big bowl? Two small bowls? No! You would find that it
would take eight small bowls! Sounds like a cereal commercial.
The reason is that 2 X 2 X 2 equals 8, and of course 2 comes into the
picture because the bigger bowl is 2X across compared to the smaller
bowl. We say that the bigger bowl has 8 times the volume of the smaller
bowl. Since water (or other stuff like rock, etc) possess both mass and
energy, if the larger bowl has eight times the volume then it would have
eight times the mass and energy when filled to the brim.
Let’s apply this idea to Earth and Mars, both of which are really
“double bowls,” which of course would be a ball shape. First of all,
Earth is not twice as large across as Mars. It is a little less,
actually 1.8794 times larger across than Mars is.
So how do you figure out how much larger the volume of the Earth is than
that of Mars (and consequently how much more mass and energy)? You do
it the same way as for the two bowls – 1.8794 X 1.8794 X 1.8794.
Obviously this is where a calculator is called for! Taking mine out of
my shirt pocket and carefully pushing the right buttons in the right
order (of course the first button to push is the “on” button), I get
6.6383. Lets make it easy and just say that it’s about 6.64! This
means that Earth would have almost 7 times the amount of mass and energy
of Mars, and according to Newton and Einstein, almost 7 times the
potential for the creation of gravity.
But you have to remember this, when we played with bowls of water we had
the same “stuff” in each bowl – water. If the stuff of Earth and Mars
is different from each other, the answer would be different than what
we’ve just figured out. We’ll get to that later. To answer the original
question there is something else you have to first take into
consideration.
What people generally mean by gravity is how much of a “pull” there is
at the surface of the planet, after all, isn’t that where we are?
Gravity does of course pull things down. Since the Earth is larger than
Mars, the “pull” is spread out over a greater surface and you have to
take that into account (remember when accountants are dealing with
money, there’s always a catch). If you were to have to paint the
surface of both Earth and Mars, you would find it takes more paint to do
the Earth, a lot more!
Going back to the round bowls, one twice as large across as the other,
you would find that painting the outside of the larger bowl (or even the
inside) would take 4 times the paint necessary for doing the smaller
one. Well how do you get 4 from the number 2 which comes from the
larger bowl being twice as large across than the smaller bowl? Taking a
hint from what we did before, 4 = 2 X 2. Using the same idea for Earth
and Mars where Earth is 1.8794 times larger across than Mars is, 1.8794
X 1.8794 = 3.5321. So lets say that the answer is about 3.53! This
means Earth’s gravity is about 3 and a half times more “spread out” over the
Earth’s surface than Mars’ gravity would be over the surface of Mars.
Lets put this all together. If the more mass and energy of Earth ought
to cause about 6.64 times the gravity caused by the mass and energy of
Mars (assuming the same kinds of stuff), but it’s spread out about 3.53
times more at the Earth’s surface than would be for Mars, it would seem
the pull of gravity on Earth compared to on Mars, is 6.64 divided by
3.53 (get the calculator out again) which is about 1.88. In other words
the pull of gravity you feel now is about 1.88 times what you would feel
on Mars. Looking at it from the perspective of being a Martian, you
would feel about 53 percent of the gravity felt by a terrestrial (I’ll
let you figure out how to do this).



The core of Mars has less iron than that of the Earth.

The fact is that the measured pull of gravity at the surface of the
Earth is really about 2.6 times greater than that for Mars, not 1.88.
Does this mean we miscalculated after all that work? No! What it means
is that the stuff of Earth and Mars must be different. Remember I said
that this was possible. Thinking of both Mars and Earth as bowls it
means they are filled with different things. Actually rocky Earth has
something hidden inside that rocky Mars doesn’t have, a bunch of iron!
You probably have heard that Earth has an iron core. Well Mars has
considerably less of an iron core than not only Earth but also Venus and
Mercury as well.
Then how do we know what the pull of gravity is at the surface of Mars?
Mars has
two little moons
and by carefully watching how
these satellites go around in their orbits, you can measure their
speeds. This tells us what the strength of the Martian gravity is at
the distance of the orbit from the center of the planet. Then
calculating in the way we have done, think about it, the strength of
gravity at the Martian surface can be figured out. Having two moons to
work with, doublechecks the answer, which is a nice thing to be able to
do.
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