Low mass is important when calculating the behavior of objects, such as the Earth and Moon, rotating around each other. Sir Isaac Newton’s Second Law of Mechanics can be used to calculate the forces between objects based on their mass and distance, but reduced mass must be taken into account for objects in motion. The reduced mass is calculated by multiplying the mass of both objects and dividing by their sum, and can be used to calculate the effects of force and gravity as if there were a single mass at a point called the center of rotation. This concept can also be applied to small atomic particles.
When observing particles as small as an atom or objects as large as the Earth and moon, low mass can be an important consideration when calculating the behavior of objects moving around each other. A proton and an electron or the Earth and the Moon rotate each other with very different masses, or the amount of each object affected by the force of gravity. Using a low mass equation can simplify calculations of how each will behave in different situations.
Because two objects rotate around each other, they have a force that can be calculated from Sir Isaac Newton’s Second Law of Mechanics, which calculates the forces between objects based on their mass and distance. Newton (1642-1727) was a mathematician, chemist and physicist who formulated many concepts on planetary motion and gravity. His second law describes the forces that occur between two objects, but assumes that the objects are stationary. The reduced mass takes into account each object and their distance from each other, providing a value that can be used in Newton’s equation and other calculations for gravity and acceleration.
The Earth and the Moon are very different in size, and it could be assumed that the Earth is the center of rotation of the two bodies. This isn’t exactly true, because the Moon affects the rotation point, called the center of rotation, due to its distance from the Earth and its mass. Using the center of the Earth would create errors in the calculation if not corrected for the mass of the Moon.
The reduced mass is calculated from the mass of both objects multiplied together, then divided by the sum of the masses of the two objects. The result can then be used to calculate the effects of force and gravity as if there were a single mass at a point called the center of rotation. An example of this is connecting two balls with a string, with the balls having different weights. Attempting to spin the balls by holding the string in the middle would have been unsuccessful. The experimenter should hold the string closest to the heavier ball, which is the center of rotation of the two balls.
Calculations for low mass can also be used for small atomic particles. When electrons rotate around an atomic nucleus, they create a center of mass and spin at points other than the center of the nucleus. Solving for reduced mass creates values that can be used for other molecular forces.
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