The student is expected to describe and calculate how the magnitude of the gravitational force between two objects depends on their masses and the distance between their centers.
The gravitational force is one of the four fundamental forces of nature. It is always attractive and acts between all particles of matter. The gravitational force of one object on a second one acts in the opposite direction and is equal to the force exerted by the second object on the first one.
The gravitational force between two objects can be calculated. It is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Law of Universal Gravitation
Gravity is one of the fundamental forces of nature. In 1687, Sir Isaac Newton published his workPhilosophiæ Naturalis Principia Mathematica (“Mathematical Principles of Natural Philosophy”) in which he introduced the Law of Universal Gravitation. It states:
where:
Fg is the gravitational force between two objects,
G is the gravitational constant,
m1 and m2 are the masses of the two objects, and
d is the distance between the two objects.
This law says that any two objects with mass exert a gravitational force on each other. The force on each object has the same magnitude. The magnitude is proportional to the product of the objects' masses. It is inversely proportional to the square of the distance between them.
Gravitational Constant
Although the gravitational constant G was included in Newton’s formula, it was not measured until 70 years after his death by Henry Cavendish. Gravity is difficult to measure as it is weak and an experimental apparatus cannot be separated from the gravitational influence of other objects. The accepted value is 6.67 x 10-11 Nm2/kg2.
Gravitons
At least most of the carrier particles for the electromagnetic, strong nuclear and weak nuclear forces have been discovered. The properties of the carrier particles for gravity, gravitons, can be inferred from theory. However, gravitons have not been detected experimentally. Gravity is the only fundamental force not currently included in the Standard Model. Currently, it is unclear how, or even if gravity can be included with the other forces.
Importance of Newton’s Work
Newton made a huge step forward by finding a simple law and equation to describe gravity. Newton’s law of universal gravitation provided an explanation for processes ranging from ocean tides to the motion of comets, from falling apples to Earth’s orbit around the Sun. Before Newton, scientists had many different explanations for these different processes. Newton found a single equation to describe all of them.