In the years before Newton, a general belief prevailed that different laws governed objects in the sky than objects on Earth. When Kepler wrote down the three laws of planetary motion, explaining in detail the geometrical properties of the planetary orbits around the Sun, there was no immediate idea to discern their connection with more fundamental laws. It was Isaac Newton who, in 1665–66, figured out the connection between planetary motion, the motion of the moon around the Earth, and...

Since gravitational force is a conservative force, the amount of work done to move an object between two points in the gravitational field in which it resides is independent of the path taken. Thus, similar to the gravitational field, a gravitational potential energy function can be defined, which depends only on spatial coordinates.
Consider a mass gravitationally bound to another object. For example, the Earth is gravitationally bound to the Sun’s gravitational field. The potential...

Consider a system comprising several point masses. The coordinates of the center of mass for this system can be expressed as the summation of the product of each mass and its position vector divided by the total mass:

Gain and phase shift are properties of linear circuits that describe the effect a circuit has on a sinusoidal input voltage or current. The circuit's behavior that contains reactive elements will depend on the frequency of the input sinusoid. As a result, it is observed that the gain and phase shift will all be frequency functions.
Gain:
Suppose Vin is the input and Vout is the output signal to a circuit.

Potential energy is not just a property of each object, but also a property of the interactions between objects in a chosen system. For each type of interaction present in a system, there is a corresponding type of potential energy. The total potential energy of the system is the sum of the potential energies of all the objects. Potential energy can be classified into two major categories: gravitational potential energy and elastic potential energy. The potential energy associated with a...

Gravitation is one of the four fundamental forces in nature. The force between objects on Earth and Earth itself is called gravity.
Like other forces, gravity does work on an object if it displaces it toward the Earth's center. In this case, the work done by gravity is said to be positive. If an external force acts on the object against the pull of gravity and manages to lift it away from the Earth's center, work is done against gravity. In this case, the net work done is said to be...