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What is The Gravitational Constant?

Wherever we observe that there are two objects with a certain mass, these two objects are gravitationally attracted to one another with a proportionality constant known as the gravitational constant, G. The gravitational constant appears in both classical and modern physics. In Newton's law of universal gravitation, it is known as Newton's constant, or Big G (not to be confused with a local acceleration due to gravity). Einstein's theory of general relativity also makes mention of G.

According to the classical definition found in Newton's law of universal gravitation, there is an attractive force between two objects of mass m1 and m2 that is proportional to the product of these masses and inversely proportional to the square of the distance between these two objects. Mathematically, this is described as:

F = G.(m1.m2)/r2

where F is the attractive force between the two objects, G is the gravitational constant, and r is the distance between the objects. G is has a measured value of 6.67428x10-11 m3/kg.s2. Though the units assigned to the gravitational constant appear to be out of the ordinary, they are the units necessary to cancel out the units it is being multiplied by in order to produce force units on the other side of the equation (kg.m/s2).

In celestial mechanics, the product of G and the mass of the Earth, M, is known as the Standard Gravitational Parameter, which is denoted by μ. In other words,

μ = GM = 398600.4418 km3/s2

Unfortunately, because the value of G is not known with a high degree of certainty, this uncertainty level carries over to the Standard Gravitational Parameter. This uncertainty has a value of +/- 0.0008.

The history of the measurement of G is a rather simple one. It took another 71 years after Sir Isaac Newton's death for G to finally be measured by Henry Cavendish. Cavendish used a torsion balance with lead balls to measure G implicitly. He was able to determine the inertia of the balls in relation to the torsion constant by timing the oscillation of the beam. In this way, he was able to measure G by determining the deflection of the beam caused by the faint attraction between the two balls. According to the Cavendish experiment, the value of G is 6.754x10-11.

Ever since this experiment, the value of G has only increased slightly in accuracy. Because the gravitational force is much weaker compared to other forces in the universe, it is incredibly difficult to measure. Aside from this fact, it is also very difficult to create a perfectly isolated system in which the value of G can be measured without the influence of the apparatus used to measure it. This could be considered a similarity to the Heisenberg uncertainty principle insofar as the experiment itself is so tainted by the presence of the experimenter that the accuracy of the experiment decreases significantly.

Having said this, modern science is coming up with new ways of measuring G with more accuracy. One of them is the Atom Interferometer, which has reported a value of G at 6.693x10-11 with a standard error of the mean of +/- 0.027x10-11 along with a systematic error of +/- 0.021x10-11.

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