Gravitational Field theory

Gravitational Field, Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their masses.

The gravitational interaction between two bodies can be expressed by a central force which is proportional to the mass of bodies and inversely proportional to the square of the distance that separates them.

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The gravitational field is a physical property that is communicated to the space by a mass M. This field is characterized by:

• To be conservative
• To be steady.

Fields as the gravitational field that are defined at each point of space by a vector quantity are called vector fields. These fields can be represented by lines of force. A line of force has the characteristic of being tangent at all its points to the direction of the field at that point and its meaning is the same as the field has.

Superposition principle.

In the case of a field which is created by several bodies we use the superposition principle to know the aggregate field at a given point. The principle of superposition tells us that the gravitational field created by a body at a point is independent from gravitational fields which are created by other bodies. We will operate by finding out the field created by each body at the point in question and we will add all of them (vector sum) for the total field.

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Escape velocity is the minimum speed that a body should be thrown to escape from the gravitational pull of the Earth or other celestial body. This means that the body or projectile will not fall on Earth or starting astro, leaving at rest on a sufficiently large (in principle infinite) distance from Earth or the star.

This speed explains why some planets have atmospheres and others not. According to the kinetic theory of gases, the gas molecules move at a speed:

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A black hole is a finite region of space within which there is a mass concentration high enough to generate a gravitational field such that no material particle, not even light, can escape from it.
The gravity of a black hole, or “curvature of space-time,” causes a singularity surrounded by a closed surface, called the event horizon.

FORMULA SUMMARY:

Newton’s Law of Universal Gravitation

(G = universal gravitational constant)

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The minus sign means that the gravitational field is directed in the opposite direction to the unit vector that it points the direction from the Earth to the point in question.

Kepler’s Third Law

(T = orbital period of each planet ; R = is the semi-major axis of the orbit)

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Orbital period of a planet

(M = Mass of the Sun ; R = distance between the center of the Sun and the planet’s center)

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Gravitational acceleration

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Gravitational acceleration depending on the height

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Gravitational potential energy

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Orbital velocity of a projectile

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Escape velocity of a projectile

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Equipotential surfaces

An equipotential surface is formed by points that all of them have the same gravitational potential. Since all points are at the same height, from the ground, all have the same gravitational potential, we may consider that gravitational equipotential surfaces as parallel to the surface of the earth planes. The surface formed by all these points is called equipotential surface.

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