# Physics gravitational constant

February 24, 2017

In 1665, Isaac Newton recognized that all matter attracts all other matter, but he also recognized that the gravitational attraction of everyday objects for each other was far too small to be measured in his time. Newton tested his theory of gravitation with the large masses of astronomical objects like the moon, Earth, and sun.

In 1797, Henry Cavendish succeeded in measuring the tiny gravitational force between two metal spheres. He fastened small spheres on the ends of a rod and hung it from a wire. Then he brought up two larger spheres, as shown in the schematic drawing, so that the gravitational forces twisted the wire slightly. The forces between a small and large sphere are only about a billionth of their weight. Nevertheless, from the amount of twist in the wire, and the physical properties of the wire and suspended spheres, Cavendish measured the tiny force, and it agreed with Newton's prediction. (See drawing at right)

Dependence on mass and separation

Photo of University of Washington experiment showing polished spheres

Newton discovered that all matter in the universe attracts all other matter, with a force that decreases with the square of the separation. If you double the separation of two objects, the force they exert on each other is divided by four.

The force is proportional to the mass of each object. Double the mass of one object, and the gravitational force doubles, too.

We make an equation.

So far we have that for the force of gravity F between two objects, 1 and 2,

 F is proportional to M1M2 R2

In the above relationship, M1 and M2 are masses, R is the separation between them. To make this relationship into an equation, we need a constant, fondly known as “Big ‘G’”. Here's the equation:

Notice that if R gets big, the value of F gets small.

Why “Big ‘G’” is important

If we know "G" from lab measurements, we can find the mass of Earth by measuring the radius of the moon's orbit and the length of the month, or by measuring the acceleration of gravity on Earth's surface. Likewise, we can find the mass of the sun by measuring Earth's orbit and determining the length of the year.

We expect measurements to get more and more accurate over time, as physicists improve experiments and employ new technologies. With "Big 'G'", however, for a while the accuracy was going down, and fast. Prior to 1987, "Big 'G'" was taken to be accurate to 0.013%. Subsequently, two research groups made measurements that were tenths of a percent from the then-accepted value, and in different directions! Consequently the accepted uncertainty was raised by more than a factor of ten. This unfortunate situation galvanized several other groups into action, including one at the University of Washington, whose measurements are accurate to 0.0015%, nearly 10 times more accurate than the 1987 value.

### Measuring Big 'G'

Big news at an April 2000 scientific meeting was the announcement of a long-awaited higher precision measurement of the gravitational constant (affectionately known as “Big ‘G’”among physicists) by Jens Gundlach of the University of Washington. Although G has been of fundamental importance to physics and astronomy ever since it was introduced by Isaac Newton in the seventeenth century (the gravitational force between two objects equals G times the masses of the two objects and divided by their distance apart squared), it has been relatively hard to measure, owing to the weakness of gravity.

Steve Merkowitzz (l) and Jens Gundlach (r) with the Cavendish apparatus developed at the University of Washington. (Credit: Mary Levin, University of Washington)

Source: www.physicscentral.com