Graviational Fields

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Weight

Weight is the non-contact force acting on objects due to gravity. It is equal to the product of an object’s mass and the gravitational field strength at the object's location. Weight can act over very large distances.

The graviational field strength can be through of as the acceleration of an object at that position.

$$W=mg$$

For a uniform field $g$, the graviational field strength, is a constant and at the surface of the Earth is approximately $9.81N{kg}^{-1}$

Weight and Mass Compared
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Weight and Mass Song
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Questions
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Newton's Law of Gravity

$$F=\frac{G{m}_1{m}_2}{r^2}$$

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Graviational Potential Energy

Using the above and $E=Fs$ where $F$ and $s$ are parallel. We get,

$$E_{\mathrm{Grav}}=mgh$$

• where
• $E_{\mathrm{Grav}}$ is the gravitational potential energy, $J$,
• and
• $h$ is the height gain, $m$.

This is the gravitational potential energy for a uniform field $g$ is a constant.

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The above works well for a small volume of space say near the surface of a planet. For greater distances we need to think of the graviational field as spherically symmetric, perhaps around a planet. Then $g$ is given by

$$g=-\frac{GM}{r^2}$$

• where
• $g$ is the gravitational field strength, $N{\mathit{kg}}^{-1}$ (or $m{s}^{-1}$)
• $G$ is the universal gravitation constant
• $M$ is the mass of the object creating the field, $\mathit{kg}$
• and
• $r$ is the distance from the centre of the mass to the point of interest, $m$

Now $g$ is not constant and is described at the ration of the graviational force acting on an object of small mass to the objects mass.

Orbital motion

Planets move in approximately circular orbits about a star, in the case of are solar system this is the Sun. Around planets, in a similar way, orbit satelites. Other objects may orbit too: minor planets, asteroids, comets, etc. These, however, may have orbits that are not circular. These orbits are elongated into elipses or hyperbolae.

$$\frac{m{v}^2}{r}=\frac{GMm}{r^2}$$
$$v=\sqrt{\frac{GM}{r}}$$

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Questions:

Circular Motion [ MS ]

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A formula for Weight

Prerequesite Materials

Mass

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Describing Weight

$$W=mg$$

• where
• $W$ is the weight, $N$
• $m$ is the mass, $\mathit{kg}$
• and
• $g$ is the gravitational field strength, $N{\mathit{kg}}^{-1}$ (or $m{s}^{-2}$)

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The rearrangements

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Related Equations

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