Standing on a Round Object [Earth]
My student asked this question in class, and I couldn't answer it.
We were talking about how the earth spins on its axis. We live in New
York and a student asked, "If we're on an angle, why do we stand straight
up and are not standing at an angle?"
The earth's gravity pulls us directly toward the earth's center. Because
the earth is round, the earth's center is straight down from wherever you
are. Straight down for you in New York is at an angle to straight down for
me in Chicago, but both point to the center of the earth.
Richard Barrans Jr., Ph.D.
Chemical Separations Group
--I went to HS in New York city. The reason people in New York
do not fall over is that there is so much trash on the streets that you
cannot help but stand up straight!! (ONLY KIDDING-but at least you guys
have Mayor Giulani instead of Ed Koch and the garbage strikes to deal with).
Serious answer--as best I remember basic gravitational theory. The earth is
roughly a sphere. Think of the mass being concentrated at a point in the
center of the earth. Gravity acts outward perpendicular to the source.
Gravity acts, therefore, radially out from the center of the earth (really
simplistic model here) and is constant along those radial lines. A human is
on average between 5 and 6 feet tall. The action distance out from the
theoretical center of the earth is several thousand miles compared to the
final 5-6 feet of the human's height at the surface. That is why you do not
feel any perceptible difference on your body whether you are standing
upright or reclining on your side (if you were in a centrifuge machine like
they use to test astronauts and pilots, you would easily see the difference
in body orientation) at the earth's surface. People are normally upright at
the earth's surface due to gravity tending to keep them in a perpendicular
orientation to the center of the earth along the radial gravity lines.
This is not an exact scientific answer, and I defer to experts on the
subject. It should suffice for a grade school or HS class explanation. You
can consult the physics dept. at Columbia or Princeton if you wish for a
more detailed answer or you can try the Goddard Space Flight center of NASA
in Greenbelt, MD, etc. Hope this helps a little.
The earth's axis is tipped relative to its orbit around the sun. The earth
also rotates around its axis, and this tends to try and throw us off the
earth. There is also the gravitational force of the moon which tries to
pull us off the earth. In fact there are so many different forces acting on
us I couldn't name them all.
However, the overwhelming force that acts on us is the gravitational force
of the earth. This force is so strong compared to all the other forces that
a lot of the time, we simply ignore the other forces completely.
This gravitational force acts on all objects and is fairly uniform around
the whole earth. There are minor variations in the strength of the force of
gravity at different locations around the earth, but humans are generally
not sensitive enough to actually feel these variations.
Also, the force of gravity is always pulling us toward the center of the
earth. That is why we don't fall off the bottom or anything like
that--gravity always looks the same to us because we are on the top of a
sphere being pulled to the center.
Anyway, I suppose the short answer to your question is that the earths axis
may be on an angle, but gravity is not, and it is gravity that holds us to
We are standing at an angle. A line starting at our head and running through
our feet continues on through the center of mass of the earth. From space,
people in New York appear to be leaning at something like a 45-degree angle
with respect to an axis through the poles. That polar axis in turn makes
an angle with the plane defined by the average orbit of the planets in the
solar system because earth's spin axis is tilted.
We feel like we're standing straight up because our notion of up and down
is defined by the direction of the gravitational force on us.
In the big picture, we do stand at an angle.
In the short run, though, we see ourselves as perpendicular to the horizon,
so we see ourselves as standing straight up.
A good way to picture the situation on a larger scale would be the seeds of
a dandelion. The seeds radiate around a seed head with each seed, per
small area of the total seed head, appearing to be horizontal to that seed
head surface. Those on the bottom appear to be perpendicular to the seed
head itself. Those on each side are also perpendicular to the seed head,
but in this case they point outward from the base of the seed head.
In pictorial form, we can depict a cross section:
Because gravity effectively pulls us toward
the center of the earth, people on each side of the earth see what they call
'UP' as up or away from the ground, and "down" as down towards the ground.
Simply put, we do seem to stand straight up, but if you see each human on
the earth while in a spaceship distant from the earth, you would see humans
radiating from the earth similar to the simple drawing on the left. With
respect to another's 'horizon', others ARE standing at an angle; for them,
however, they feel they are standing straight up, perpendicular to the
ground, and everyone else is standing at some angle to their horizon.
Thanks for using NEWTON!
Click here to return to the General Topics Archives
Update: June 2012