A New Way for Measuring Earth’s Gravity from Italian Scientists

By Hannes Grobe, AWI [Public domain], via Wikimedia Commons

By Hannes Grobe, AWI [Public domain], via Wikimedia Commons

It may not be underestimation of the human intelligence to say that a significant number of the educated human population have no idea on the processing of measuring Earth’s gravity, even after graduating from college. There will be those who are familiar with Newton’s law of gravitation and the concept of acceleration due to gravity but not many will be able to offer a good answer or explanation when asked how strong the earth’s gravitational force is.

Well, here’s a bit of good news for those who have just realized that they don’t really know how strong Earth’s gravity is: even scientists are not sure about it as they can’t agree on an exact number. Scientists haven’t figured out yet how to measure the gravitational force constant. It is said that the only way to precisely measure Earth’s gravity is to observe how it moves when put side by side with another object that also has its own gravitational pull and another that may have very negligible gravity.

Gravity of Earth

Those who remember studying gravity in their Physics subject at school would probably remember gravity of Earth denoted by the letter “g,” referring to the acceleration that the Earth causes on objects on or near its surface. It is given the approximate value of 9.81 meters per square seconds. This means that if there is no air resistance and other factors preventing a straight-on fall to the Earth’s surface, objects will be accelerating at the speed of 9.81 meters for every second of fall. However, this does not really offer a precise measurement of gravitational pull.

On the other hand, Newton’s law of gravitation state that gravitational force is directly proportional to the product of the masses of two objects and inversely proportional to the square of the distance between their centers. However, the direct proportion isn’t a one-to-one relationship. There is another required to properly determine gravitational force. This number is similar to pi used in the formulas for solving the area and circumference of a circle, referred to as a proportionality constant. This figure is referred to as the big Ge

Stated in a mathematical formula, Newton’s law can be written as follows: F=Gm1m2, where F is the force of gravity, m1 and m2 are the masses of the two bodies being examined, and G is the gravitational constant. The big G number is what remains to be elusive until now. Scientists couldn’t come up with a precise number for it. What’s certain is that G is a very small number, somewhere near 0.0000000000667 cubic meters per kilogram per square second. Measuring it requires the use of very sensitive instruments

The Quest for G

Since the time British scientist Henry Cavendish tried measuring G, there have been over 300 similar attempts mostly involving the use of torsion balance devices or something similar. The figures arrived at varied wildly although many came close within 1% of the accepted (still an estimate) G value at present. These earlier measurement attempts relied on the measurement of the movements in hanging spheres as they are brought close to each other. Naturally, it will be quite difficult to come up with a precise figure to represent gravitational constant since the spheres are affected by external factors, including the gravitational pull of Earth itself.

In Italy, scientists want to make use of the “Quantum method” as a solution to finally determine the value of the Big G with greater precision.

Public domain, via Wikimedia Commons

Public domain, via Wikimedia Commons

The “Quantum” Method

A team of scientists from the University of Bologna and the University of Florence has come up with a new way to measure Earth’s gravity. This new approach involves the use of a 516-kilogram array of tungsten cylinders, cold rubidium atoms, and devices referred to as atom interferometers.

The rubidium atoms had to be kept cold to make their movements easily measurable. At room temperature, rubidium atoms have speeds reaching several kilometers per second. When cooled to near absolute zero, their movements can be limited to a few millimeters for every second.

The “Quantum” method the Italian scientists have developed aims to exploit the counterintuitive quantum nature of individual atoms or their ability to behave as waves. The cooled rubidium atoms were contained in a vacuum and were then zapped with laser pulses, making them bounce up and down. The laser pulses separate the “matter wave” identified with each atom into a superposition of two energy states. Every one of these energy states is observed to have a different velocity and maximum bouncing height. The differences in the rubidium atom movements (as influenced by Earth’s gravity and by the tungsten cylinders) are analyzed, including the interference pattern they create.

Two atom interferometers were used to cancel out the effects of Earth’s gravitational pull and the forces created by tides, the sun, and the moon. This was done to find out the extent of the movement changes in the rubidium atoms once Earth’s gravity and other external forces are eliminated. This allows the scientists to interpolate the value of G.

The Big G Value According to the “Quantum” Method

The Italian scientists have determined the Big G to be (6.67191 ± 0.00099) × 10−11 meters3 per kilogram per second2. This number is deemed to have a 0.015% uncertainty. This new measurement is lower than most of the values obtained by traditional G measurement methods.

Created by User:Johnstone using a 3D CAD software package and an image of planet earth from NASA's Galileo spacecraft.

Created by User:Johnstone using a 3D CAD software package and an image of planet earth from NASA’s Galileo spacecraft.

Even with all these developments in the attempt to determine G, it can be said that the scientific community still has not achieved an acceptable level of certainty to be able to pinpoint the real G value. Instead of narrowing down, the differences in the values of G measured by different scientists have even increased. There’s really no rush in trying to find out the real value of G but, hopefully, the question on the real value of Earth’s gravitational constant can be determined before the theory of relativity gets proven with certainty.