Tag: geostationary orbits

Questions Related to geostationary orbits

Geostationary satellite

evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

  1. is situated at a great height above the surface of the Earth.

  2. moves in the equatorial plane.

  3. have time period of $24$ hours.

  4. have time period of $24$ hours and moves in the equatorial plane.

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Correct Option: D
Explanation:
Geostationary satellite is used for communication purpose.
Thus, geostationary satellites are placed at an altitude of 36,000 kms and moves in the equatorial plane in the same direction as the Earth rotates. Hence, its time period is 24 hours.

The distance of a geostationary satellite from the centre of earth (radius R = 6400 Km) is nearly.

evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

  1. 18 R

  2. 10R

  3. 7R

  4. 5R

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Correct Option: C
Explanation:

A geostationary satellite is placed at an altitude of about 36000 km  from the earth surface.

So, its distance from centre of earth, $r= 36000+6400   km=  42400    km$ 
$d= \dfrac{42400}{6400}  R  \approx  7R$

A satellite launching station should be

evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

  1. near the equatorial region.

  2. near the polar region.

  3. on the polar axis.

  4. all locations are equally good.

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Correct Option: A
Explanation:
At equator, $g$ is minimum relative to all the other points on the surface of the Earth. When a spacecraft is launched into the orbit, it should end up spinning around the Earth quickly enough not to be pulled back in by the Earth's gravity. If a ship is launched from the equator, it goes up into space, and it is also moving around the Earth at the same speed it was moving before launching. This is because of inertia. This speed will help the spacecraft keep up a good enough speed to stay in the orbit.

A communication satellite of earth which takes $24 hr$. to complete one circular orbit eventually has to be replaced by another satellite of double mass. If the new satellites also has an orbital time period of $24 hrs$, then what is the ratio of the radius of the new orbit to the original orbit ?

evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

  1. $1 : 1$

  2. $2 : 1$

  3. $\sqrt 2 : 1$

  4. $1 : 2$

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Correct Option: A
Explanation:
Time period of revolution of satellite,  $T= \sqrt{\dfrac{r^3}{GM _e}}$    where $r$ and $M _e$  are the radius  of the orbit and mass of earth.

Thus time period doesn't depend on the mass of satellite.

$\implies $ for same time period, radius of the orbit will be same.
Hence  $r' : r= 1:1$  

The minimum number of satellites needed to be placed for world-wide communication between any two locations on earth's surface  is:

evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

  1. 6

  2. 4

  3. 3

  4. 5

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Correct Option: C
Explanation:

For a world-wide communication between any two locations of the earth, minimum 3 satellites must be placed such that each pair of  the satellites subtend angle of $120^o$ at the centre of earth. 

A body is dropped by a satellite in its geo -stationary orbit.

evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

  1. it will burn on entering in to the atmosphere

  2. it will remain in the same place with respect to the earth

  3. it will reach the earth is $24$ hours

  4. it will perform uncertain motion

Show answer
Correct Option: B
Explanation:

Geo-stationary satellite are those which have same angular velocity as that of earth, so they appear stationary with respect to earth. A body dropped off from satellite would also have same velocity as that of satellite, and so the angular velocity of the body would be same as that of earth also. So it would also seem stationary with respect to earth.

The earth satellite can move in an orbit the plane of which coincides with.

evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

  1. The plane of any great circle round the earth

  2. The plane of any latitude circle of the earth

  3. Any plane not containing the centre of the earth

  4. The plane of tropic of cancer

Show answer
Correct Option: A
Explanation:

Such is the case of a geo-stationary satellite, the angular velocity of satellite must be same as that of earth in any circular path around the earth.

If $R$ is the average radius of earth, $\omega $ is its angular velocity about its axis and $g$ is the gravitational acceleration on the surface of earth then the cube of the radius of orbit of a geostationary satellite will be equal to.

evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

  1. $\dfrac {R^2g}{\omega }$

  2. $\dfrac {R^2\omega^2 }{g}$

  3. $\dfrac {Rg}{\omega^2 }$

  4. $\dfrac {R^2g}{\omega^2}$

Show answer
Correct Option: D
Explanation:
As, $mr\omega^2=\dfrac{GMm}{r^2}$

$\implies r\omega^2=\dfrac{GM}{r^2}$

$\therefore r^3=\dfrac{GM}{\omega^2}=\dfrac{GM}{R^2}\dfrac{R^2}{\omega^2}=g\dfrac{R^2}{\omega^2}$

Motion of artificial earth satellites around the earth is powered by

evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

  1. Liquid fuel

  2. Solar batteries

  3. Atomic energy

  4. None of the above

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Correct Option: D
Explanation:

 A satellite orbits Earth when its speed is balanced by the pull of Earth gravity. Without this balance, the satellite would fly in a straight line off into space or fall back to Earth.

So, the the motion of satellites around the earth is powered by the gravitational pull of the earth, which provides the necessary centripetal force for the satellite to orbit the earth.

The moon waxes and wanes while going around the earth and hence it has circular motion

evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

  1. True

  2. False

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Correct Option: A
Explanation:

The moon waxes and wanes while going around the earth, because the terrestrial viewpoint of the moon changes relative to the moon's source of light. Hence it has a circular motion.