Paul Bloomer, age 11, of Rochester, N.Y., for his question:
How can the earth be weighed?
On a summer night you can look up and see a starry constellation called libra, the scales. But this celestial balance cannot be used to it1easure the weight of the world. However, this weighty problem can be solved with equations of force, distance and matter.
If you knew the right figures to use you might be able to perform a tricky experiment and solve this problem for yourself. The actual measuring job requires patience and unusual skills, but at least you could figure out how and why the experiment works. First, the job requires a thorough knowledge and understanding of the laws of gravitation.
These laws immediately put us right on the difference between weight and mass. Mass is the amount of matter packed into the volume of an object. Weight is the force exerted upon the object by the attraction of gravity between it and its planet. A 100 pound earth boy would weigh 25 pounds on little mercury and 264 pounds on giant Jupiter; but his mass, the amount of material in his body, would not change.
A ton can be a measure of weight or mass, but we measure the earth in mass tons. We can estimate its mass from the laws of gravitation figured out and precisely stated by young Isaac Newton. The force of gravity is interrelated with mass and distance. When you know three factors of this equation you can figure out the fourth, which should give you the mass of the earth two objects are attracted by the gravitational force from their exact centers.
This force diminishes at a set ratio and the distance between their two centers increase.
If you know the mass of the two objects and the distance between them you can figure the gravity.
A neat equation of this sort can be turned around. If you know the distance, the amount of gravitational force and the mass of one object, you can figure the mass of the second body. You could, for example, measure the exact mass of a metal sphere and use a complex instrument to measure the force between it and the giant earth. If you happen to be a trained and skilled physicist you could figure the missing factor of the equation and find out that the mass of the earth is more than 6.5 sextillion tons or roughly 6,600 followed by 18 zeros.
The instrument for the job is a delicate balance of two metal balls suspended like a dumbbell. The gravitational force is measured from their attraction toward two suspended larger balls. This gadget was originated by the eccentric english scientist, Lord Cavendish, in 1798. He was the first to measure the earth's mass. More refined instruments of the same kind are used to get a more exact estimate of the so called weight of the world.