- #1

chis

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What is the equation for calculating a single bodies gravity?

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In summary, the equation for calculating a single body's gravity is g(r)=-G\frac{m}{r^{2}}\hat{r} for a uniform spherical mass distribution, where G is the gravitational constant, m is the mass of the object, r is the distance from the center of the object, and \hat{r} is the unit vector in the radial direction. This equation only applies for distances outside of the object and assumes a spherically symmetric mass distribution. As you approach the center of the object, the gravitational force decreases and reaches zero at the center. This can be represented by the equation g(r)=-\frac{Gm_{0}}{r_{0}^{3}}r\hat

- #1

chis

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What is the equation for calculating a single bodies gravity?

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- #2

mgb_phys

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(in classical gravity - it's a bit more complicated in general relativity)

It's really just a different way of writing the equation in the other thread for the force on a 1kg object placed at a distance 'r'

- #3

chis

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Thanks by the way

Chris

- #4

mgb_phys

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The Earth could actually be hollow and as long as it had the same total mass you wouldn't be able to tell - gravity would work just the same.

- #5

chis

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So at the centre of an object the value r = 0

- #6

Nabeshin

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- #7

chis

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Is there an equation tht reflects this?

- #8

Doc Al

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Furthermore, it's only valid for spherically symmetric mass distributions.Nabeshin said:While in Newtonian gravity you treat all an object's mass as if it were located at the center, this assumption is only valid while you are outside of the body.

- #9

Nabeshin

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chis said:Is there an equation tht reflects this?

Assuming a uniform spherical mass distribution, we have the following equations:

[tex]g(r)=-G\frac{m}{r^{2}}\hat{r} ; r>r_{0}[/tex]

[tex]g(r)=-\frac{Gm_{0}}{r_{0}^{3}}r\hat{r} ; r<r_{0}[/tex]

The equation for calculating the gravity of a single body is F = (G * m1 * m2)/r^2, where F is the force of gravity, G is the gravitational constant (6.67 x 10^-11 m^3/kg*s^2), m1 and m2 are the masses of the two bodies in kilograms, and r is the distance between the two bodies in meters.

The force of gravity is inversely proportional to the square of the distance between two bodies. This means that as the distance between two bodies increases, the force of gravity decreases. For example, if the distance between two bodies is doubled, the force of gravity between them is decreased by a factor of four.

The gravitational constant, denoted by G, is a fundamental constant in physics that represents the strength of the gravitational force between two objects. It is important in the equation for calculating the gravity of a single body because it determines the magnitude of the force of gravity and ensures that the units of the equation are consistent.

Yes, the equation for calculating the gravity of a single body can be used for any two bodies. However, it is most accurate for two point masses (objects with negligible size) and becomes less accurate for larger or irregularly shaped objects.

The force of gravity is directly proportional to the masses of the two bodies. This means that as the masses of the two bodies increase, the force of gravity between them increases as well. For example, if the mass of one body is doubled, the force of gravity between it and the other body will also double.

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