Isaac Newton is credited with first putting gravity on the scientific map with his universal law of gravitation.
According to Newton, “every particle in the universe exerts an attractive force on every other particle.” A particle by definition is “a piece of matter, small enough in size to be regarded as a mathematical point.”[1]
Newton called this attractive force gravity and discovered that for two masses (1&2) separated by a distance (radius r) the gravitational force is:
F=G(m1m2/r²)
F is the magnitude of the force of gravity between masses 1 and 2, G is the universal gravitational constant, first discovered by Henry Cavendish to be 6.673E-11, and r is the distance between the center of mass of the two masses in question. The gravitational force acts along this “axis” with each particle pulling on the other.
Later, Einstein would develop his general theory of relativity where gravity is not considered a force acting across a distance but represents the effects of local space-time geometry (curvature).[2]
We often think of gravity as something massive objects like the Earth and the Sun have (gravity causes things to fall down; gravity keep’s the Earth in its orbit).
In fact, like the definition above states, every particle exerts this attractive force.
You, therefore, possess a gravitational force.
What is it’s magnitude?
First let’s figure out what the gravitational force due to Earth’s gravity for an object resting on the surface of the Earth (known as g) is.
This force is what gives all of us weight and why, if you go to the moon, you’ll weigh about 1/6 of what you weigh on Earth: your mass will remain the same but the force of gravity on the moon is 1/6th’s of the Earth’s.
Side note: if you’re on a diet you’re not trying to loose weight; you’re trying to loose mass.
If you want to loose weight go to the moon.
On Earth g=G (Mass of the Earth)/r²
If you solve this equation, on the surface of the Earth g equals the familiar 9.80m/s² where the G is 6.673E-11, the mass of the Earth is 5.98E24 kilograms, and the radius from the center of the Earth to the surface is, on average at the equator, 6.38E6 meters.
In other words, if you weigh 200 pounds (or 90.7 kilograms; 1kg=2.205lb) you only have 9.26 kilograms of mass (90.7/9.8) or 20.41 pounds of mass.
No matter where you go in the universe (theoretically) your mass will remain constant (unless your diet really works or you eat too much) but your weight will change depending on the strength of the gravitational forces you encounter.
Now, speaking in Newtonian terms, while the Earth pulls down on you with its gravitational force, you pull up on it with yours.
The magnitude of your gravitational force pulling up on the Earth is so small that for all practical purposes it is ignored.
That, however, does not mean that you don’t have a “personal gravitational force.”
To calculate it you need to figure out 1) how much mass you have and 2) what your radius is.
To figure out your mass divide your weight in pounds by 2.205 (those on the metric system can skip this step).
Then divide the result by 9.8.
The solution will be the amount of mass you have as a person.
Not much is it. And then to think that 60% of the human body is water![3]
Our 200lb person has a mass of 9.26kg.
Figuring out an appropriate “radius” for a human being is trickier.
You could measure the difference between your navel and your back and divide by 2.
That would give you a larger answer.
For simplicity’s sake, we’ll assume this 200lb fellow is 1.7 meters or 5’6’’ tall and that his “radius” is ½ that or .85 meters.
Now you just plug all these numbers into the same equation we used to figure g for Earth except now we’re figuring your personal g (ypg):
ypg=G (Your Mass)/(Your Radius)²
For our hypothetical person this comes to…drum roll please.
8.55E-10 m/s² or .000000000855 m/s²
As you can see, nothing to write the Nobel committee about but a 200lb person does exert a gravitational force on everything he or she encounters.
It’s just so small that it can be ignored in almost all situations.
But it is real: in a sense, the “standard” gravitational acceleration caused by Earth (g=9.80m/s²) is the “net” figure after all the smaller masses throw their 2 cents (actually much much less than that) into the mix.
[1] See any standard physics textbook. The one I have is a 7th edition of Cutnell and Johnson’s Physics. Pages 95-99.
[2] See Wheeler, John Archibald. A Journey into Gravity and Spacetime. (New York: Scientific American Library, HPHLP, 1990).
[3] http://ga.water.usgs.gov/edu/propertyyou.html
