What is Gravitational Field of a Point Mass?

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One of the more important concepts in Physics is the concept of gravitational force. This concept affects all of us in our daily lives and is basically something that allows staying on Earth! Learn more about this in your school learning and Physics tuition to find out how it can be applicable in your examinations. To start off, what is gravitational force?

Any two bodies that are sufficiently close to each other attract each other with a force which increases as their mass increases and decreases as the distance between them increases. This force is called gravitational force. It is this force that makes our Earth and all the other planets of the solar system revolve around the Sun.

Gravitational force between point masses

To explain this phenomenon, Sir Isaac Newton proposed the law of universal gravitation, which states that a point mass will attract another point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Mathematically, this law is represented by the following equation:

F = G * m1 * m2 / r2

 

Where, F is the force of gravitation, m1 is the mass of the first particle, m2 is the mass of the second particle, r is the distance between the two particles, and G is the universal gravitational constant.

The value of G is about 6.67 x 10-11 m3 kg-1 s-2 in SI units. The universal gravitational constant, represented by capital ‘G’, should not be confused with the small ‘g’, which is the acceleration due to gravity.

This above equation works correctly only for spherical objects with a uniform density. For non-spherical objects with varying density, you will have to resort to calculus to derive the value of F.

A point mass should not be misunderstood as the mass of a point. Every spherical body with a uniform density can be considered a point mass. Not only that, mass of any shape and size can be considered a point mass if it is studied from a distance that is larger than the size of the body.

Gravitational field of a point mass

Now that we know the gravitational force between point masses, we can derive the formula for the gravitational field strength, which is defined as the force per unit mass exerted on a point mass placed at that point.

Since F = m * g, where m is the mass of the body and g is the force of gravitation, we can replace the F in the above equation with m * g.

m * g = G * M * m / r2

Where M is the mass of the body exerting the gravitational field force and m is the mass of the object on which the force is exerted. Note that we have replaced m1 and m2 with M and m respectively.

Cancelling the two small ‘m’, we get the following equation:

g = G * M / r2

 

The gravitation field strength, g, tells us how strong the gravitational field of a body is at that point. You may be aware that the value of g near the earth’s surface is 9.81 m/s2. What it means is that any object falling towards earth near the earth’s surface falls with an acceleration of 9.81 m/s2.

Thus, we can say that the gravitational field strength of a point mass is the acceleration another object will experience within the first object’s gravitational field. If you are having problems with understanding this concept, you should seek extra consultations in school or approach a Physics Tuition centre for help. With extra practice, you will be able to understand this concept much better.