**Newton's Law of gravitation** states that every particle in the universe attracts every other particle with a force which is directly proportional to the mass of each particle and inversely proportional to the square of the distance between them. If two particles 1 and 2 have masses m_{1} and m_{2}, and, the distance between them is r, the magnitude of the gravitational force between them is:

```
F
```

_{g} = Gm_{1}m_{2} /r^{2}

The constant of proportionality G is called **universal gravitational constant**,
and its value is 6.67 × 10^{-11} N-m^{2}/ kg^{2}.

**Force of gravity** is the special name given to the gravitational force exerted by the earth on any body on or
near its surface.
This force produces an **acceleration due to gravity**, **g**, in the body.
The vector **g** is always directed towards the centre of the earth and its standard value at sea
level at 45° latitude is 9.81 m/s^{2} . **Variation of acceleration due to gravity** happens due to a number of factors such as
altitude, depth, earth's rotation and its non-spherical shape.

A body possesses two types of mass: **inertial mass** and **gravitational mass**.
The concept of **inertial mass** comes from **Newton's second law of motion**.
It gives a measure of resistance to any change of state of rest or motion under an external force.
The concept of **gravitational mass** arises from **Newton's Law of gravitation**.
It gives a measure of the force experienced by the body in a given **gravitational field**.
Experiment shows inertial mass and gravitational mass of a body are the same.

**Kepler's laws of planetary motion**, as published by Johannes Kepler between 1609 and 1619, are as follows:

- The planets move in planar elliptical orbits with the sun situated at one focus.
- The radius vector from the sun to the planet sweeps equal areas in equal times.
- The square of the period of revolution of any planet about the sun is proportional to the cube of the length of the semimajor axis.

The **gravitational field** at a point in space is the gravitational force experienced by a unit mass placed at
that point. The dimensions of gravitational field are [LT^{-2}], and its SI unit is newton per kilogram (N/kg).

The gravitational potential energy of a system comprising two particles of masses m_{1} and m_{2} separated by distance r is:

```
U = - G m
```

_{1}m_{2} / r

This is a negative quantity, which becomes zero if the particles are at infinite separation.

The **gravitational potential** at a point due to a particle is the gravitational potential energy of a system comprising the particle in question and a unit mass placed at the given point.
The dimensions of gravitational potential are [L^{2}T^{-2}], and its SI unit is joule per kilogram (J/kg).

The minimum speed with which a particle must be projected so that it may escape the gravitational attraction of the earth is called the **escape speed** for the earth.
It is given by the formula:

```
v
```

_{esc} = √(2GM_{E} /R_{E})

where M_{E} and R_{E} are the mass and radius of the earth respectively.
Its value is 11.2 km/s, independent of the angle of projection of the particle.
Other heavenly bodies such as the sun, other planets and their moons also have their respective escape speeds.
**Escape speed** assigned with a specific direction is called **escape velocity**.

Just like the planets revolve round the sun, many of the planets have one or more natural **satellites** revolving round them.
A natural **satellite** is also called a "**moon**".
The earth's moon is its only natural satellite. However, man has launched many **artificial satellites** in orbits round the earth.
The **orbital speed** of a satellite in a circular orbit round the earth is given by:

```
v
```

_{orb} = √(GM_{E} / r)

Here r = R_{E} + h is the orbit radius, h being the height of orbit above earth's surface.
** Orbital velocity** at a given point on the orbit has magnitude equal to **orbital speed** and direction along the tangent to the orbit at the given point.

A **geostationary satellite** is an artificial satellite which always remains above the same spot on the equator.
Its orbit is called **geosynchronous orbit** or **parking orbit**.

The total **mechanical energy of satellite-earth system** is given by:

`E = - GM`

_{E} m / 2r

where M_{E} is earth's mass, m is satellite's mass, and r is orbit radius.

Since a satellite revolving round the earth is in a state of free fall, the satellite and its occupants must also be weightless.
An astronaut, like any other human, feels comfortable with the sensation of weight. Therefore, **weightlessness** of an astronaut during their long stay in an orbiting satellite is an unpleasant feeling and may cause medical symptoms.

Newton's Law Of Universal Gravitation
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Problems On Newton's Law Of Gravitation
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Determination Of Gravitational Constant G
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Gravity
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Variation Of Acceleration Due To Gravity I
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Variation Of Acceleration Due To Gravity II
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Problems On Variation Of Acceleration Due To Gravity
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Kepler's Laws Of Planetary Motion
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Gravitational Field
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Gravitational Potential Energy
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Gravitational Potential
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Gravitational Field And Potential Due To Some Extended Bodies
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Gravitational Field And Potential Due To Some Extended Bodies II
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Problems On Gravitational Field And Potential Due To Extended Bodies
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Escape Speed
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Problems On Escape Speed
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More Problems On Escape Speed And Gravitational Potential
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Natural And Artificial Satellites Of Planets
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Problems On Orbital Motion Of Satellites
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Mechanical Energy Of Satellite-Earth System
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More Problems On Mechanical Energy Of Satellite-Earth System
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Advanced Level Problems On Gravitation I 1:10:40

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