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# 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.m2/kg2), m1 and m2 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  Wo/We
The Ratio  Wo/We 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 Wo/We = 3963.172/(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.

Value Type Enter TheTop 2 Values
Miles From Earth