Jumping on Moving Earth
Would a person jumping on the ground have any effect
what-so-ever on the movement of the earth? My friend has stated that it
would move the earth beacuse of Newton's Law (actions having equal). My
argument is that the earth is not a stationary dead object, it is living
with millions of events happening all the time ie volcanoes, etc., and it
is also moving through space.
All this would mean an action by one timy object such as a person jumping
would have almost 0 effect, perhaps
According to Newton's Law of action-reaction, the earth will necessarily
accelerate in response to a person jumping. This acceleration is very
small. Since your number does not have a unit, it is difficult to
determine just what you mean. The accerlation of the earth can simply be
calculated using Newton's Second Law, f=ma. Here, f is the net force, m is
the mass, and a is the acceleration. Since the forces acting on the person
and the earth, we have:
f earth = f person
By substitution, it follows that:
(ma) earth = (ma) person
In a pictorial way, since the mass of the earth is huge, the acceleration
of the person must be huge, or:
(Ma) earth = (mA) person
Numerically, we have:
(5.97 * 10^24 kg)a = (50 kg)(2 m/s/s)
This gives the acceleration of the earth as about 1.68 * 10^-23 m/s/s
Clearly this is a very small number, and with current technology cannot
even be detected.
I would suggest that you look at the discussion in Paul Hewitt's
_Conceptual Physics_ book, in his discussion on Newton's Laws. The web sites:
may also help you.
Nathan A. Unterman
You and your friend are both right. As your friend understands, when you
jump away from the earth, you are also pushing the earth away from you. As
you understand, this effect is extremely small. Both you and the earth
will be given the same change in momentum, in opposite directions.
Momentum is equal to mass times velocity. Let's estimate the mass of a
human as about 70 kg (about 154 lb). The mass of the earth is about 6 x
10^24 kg. So, the mass of the earth is around 10^23 times more than the
mass of a human. This means that when you jump, you push the earth away
from you at 1/10^23 the velocity that you are moving. This is not a big
effect, and it's probably not a measureable effect, but it's bigger than
the approximately 1/10^100 difference that you estimated.
Richard Barrans Jr., Ph.D.
Physics would state that momentum is conserved in a closed system. If you
up, you must push the earth back the "other way". However the effect is so
ridiculously small as to be impossiible to measure, so in a sense you are
correct as well. I guess if something really big was thrown off the earth,
the earth would change in its orbit, say something the size of the moon. So
don't worry to much about jumping!
Dr. S. Ross
Your friend's argument is simple, to the point, and correct.
Furthermore, his key statement -- that every force generates an
opposing force -- is experimentally verified by your daily
experiences. If you catch a ball, doesn't your hand move backward?
When the cat jumps off your lap, don't you feel a downward push?
Your argument is a red herring. What I mean by that
is that you have filled in the blank in an argument like ``you're
wrong because ______'' with a statement that is true but has nothing
to do with the subject. Kind of like filling in the blank in ``You
should vote for George Bush in the 2000 Presidential election because
______'' with ``petunias are pretty'' or ``a quarter equals 25
Dr. C. Grayce
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Update: June 2012