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Earth Satellites

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Earth Satellites:

  • Any object revolving around the earth.

Natural Satellite

  • Satellite created by nature.

  • Example: - Moon is the only natural satellite of the earth.

Artificial Satellites:

  • Humans built objects orbiting the earth for practical uses. There are several purposes which these satellites serve.

Example:- Practical Uses of Artificial satellites are

  • Communication

  • Television broadcasts

  • Weather observation

  • Military support

  • Navigation

  • Scientific research

Determining the Time period of Earth Satellite:-

Time taken by the satellite to complete one rotation around the earth is known as the time period of the satellite.

As satellites move in circular orbits there will be a centripetal force acting on it.

`"F"_c = "mv"^2/("R"_e + h)` it is towards the centre.

where,

h = distance of the satellite from the earth

`"F"_c` = centripetal force.

`"F"_G = ("GM"_e"m")/("R"_e + "h")^2`

where,

`"F"_g` = Gravitational force

m = mass of the satellite.

`"M"_e` = mass of the earth

`"F"_c = "F"_G`

`"mv"^2/("R"_e + "h")=("GM"_e"m")/("R"_e + "h")^2`

`"v"^2 = "GM"_e/("R"_e + "h")`

`"v" = sqrt("GM"_e/("R"_e +"h"))`     ...(1)

This is the velocity with which satellite revolves around the earth.

The satellite covers distance = `2pi("R"_e +"h")` with velocity v.

`"T"=(2pi("R"_e + "h"))/"v"`

`(2pi("R"_e+"h"))/((sqrt"GM"_e)/("R"_e+"h"))`      ...from(1)

`"T"=2pi("R"_e+h)^(3/2)/sqrt"GM"_e`

Special case:-

h << `"R"_e` (satellite is very near to the surface of the earth)

Then `"T"=2pisqrt("R"_e^3/"GM"_e)`

After calculating

`"T" = 2pisqrt("R"_e/"g")`

Shaalaa.com | motion of satellites

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