Using Math To Calculate Your Weight In Outer Space
Introduction
Newton's Law of Universal Gravitation states:
If
F is the force due
to gravity, G
the Universal Gravitational Constant (6.67x10^{11} N^{.}m^{2}/kg^{2}),
m_{1}
and
m_{2}
are masses in kg, and
r the
distance between two objects in meters, then
The
The Weight of an Object On The Face Of The Earth
On the face of the earth, the value of r is the radius of the earth in
meters, m1 is the mass of the earth, and m2 is the mass of the object.
The force obtained is in Newtons. We may convert this force of Newtons
into pounds and may also use miles instead of meters by including a
conversion factor k. The weight on the surface of the earth is then
The Weight of an Object Above The Face Of The Earth
Above the face of the earth, the value of r is the radius of the earth
plus however many miles above the earth the object resides. The new
weight is given by the formula below. Note that the value of the
conversion factor k remains the same.
The Ratio W_{o}/W_{e}
The Ratio W_{o}/W_{e} gives the ratio of the
weight above the surface of the earth to the weight on the surface.
The formula for this ratio is given below. Notice that
everything but the ratio of the squared radiuses cancels out.
How Much Does a 180 lb Astronaut Weigh When Orbiting The Earth
220 Miles Above The Surface?
The typical distance from the earth
while orbiting is 220 miles. Using the formula above, we get a
ratio of W_{o}/W_{e} = 3963.17^{2}/(3963.17 +
220)^{2} = 0.898 . So an astronaut weighing 180 pounds
on the surface of the earth will weigh 180 x 0.898 = 161.6 pounds
while in orbit.
I Thought Astronauts Were Weightless While in Orbit?
They are in a state of weightlessness, but that is due to a
constant state of falling towards earth in a path that stays
equidistant from the earth (orbit). Their weight is still near
90% of that on the earth's surface if they are only 220 miles up. For
more information on this, see
This Article
A Weightlessness Calculator!
This Weightlessness Calculator calculates your reduced weight when
above the surface of the earth.
Enter the top 2 values on the right and click on CALCULATE.
