The total gravitational field at a point P due to all the masses is given by the vector sum of the gravitational field due to the individual masses.

**Superposition
principle ****for
Gravitational field**

Consider
â€˜nâ€™ particles of masses *m*_{1}
, *m*_{2} , .*m _{n}*, distributed in space at
positions

Instead
of discrete masses, if we have continuous distribution of a total mass M, then
the gravitational field at a point P is calculated using the method of
integration.

a)
Two particles of masses *m*_{1}
*and m*_{2} are placed along
the x and y axes respectively at a distance â€˜aâ€™ from the origin. Calculate the
gravitational field at a point P shown in figure below.

Gravitational
field due to *m*_{1} at a point
P is given by,

Gravitational
field due to *m*_{2} at the
point p is given by,

The
direction of the total gravitational field is determined by the relative value
of *m*_{1} and *m*_{2}.

When
*m*_{1} = *m*_{2} = *m*

(iË†
+ jË† = jË† + iË† as vectors obeys commutation law).

total points towards the
origin of the co-ordinate system and the magnitude of _{total}
is G_{m}/a^{2}.

Qualitatively
indicate the gravitational field of Sun on Mercury, Earth, and Jupiter shown in
figure.

Since
the gravitational field decreases as distance increases, Jupiter experiences a
weak gravitational field due to the Sun. Since Mercury is the nearest to the
Sun, it experiences the strongest gravitational field.

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11th Physics : UNIT 6 : Gravitation : Superposition principle for Gravitational field |

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