1© Manhattan Press (H.K.) Ltd. 6.5 Satellite system of the earth Orbital motion of satellite...

© Manhattan Press (H.K.) Ltd. 1

6.5 Satellite system of the 6.5 Satellite system of the earthearth

• • Orbital motion of satelliteOrbital motion of satellite• • Synchronous satellite and Synchronous satellite and

parking orbitparking orbit

• • Energy of satelliteEnergy of satellite

• • WeightlessnessWeightlessness


Orbital motion of satellite

6.5 Satellite system of the earth (SB p. 227)

Moon – only natural satellite of earthArtificial satellites – man put them around earth

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More to Know 20More to Know 20




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launching speed of satellite at its orbital height




Paths of satellite:

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Example 9Example 9


Synchronous satellite and parking orbit


Synchronous satellites – move around earth at the same as the rotation of earth about its axis

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(a) period = 24 hours (appear stationary seen from earth), no relative displacement, called geostationary satellites

(b) orbit around earth in same direction as rotation of earth (west to east)

(c) plane containing orbits of synchronous satellites = plane containing the equator




(c) its radius of orbit and height

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Example 10Example 10


Energy of satellite


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Energy of satellite


Closer to earth’s surface, satellite loses energy (due to atmospheric friction) and moves to lower orbit

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Energy of satellite


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Example 11Example 11


Weightlessness


Weightlessness occurs when- we are in free-falling motion- in spacecraft moving in circular orbit around earth

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Types of artificial satellites

Communication satellites are always used for transmitting of television or telephone signals between two places.Weather satellites are used for transmitting the pictures of cloud pattern for weather forecasting.

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Paths of satellite for different speed (v)1. A part of ellipse for v < 2. A circle for v = 3. An ellipse for > v > 4. A parabola for v = 5. A hyperbola for v > where is the launching speed required for a circular orbit near the earth and is the escape speed of the earth.

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Launching a satellite

(a) Normally, we use a two-stage rocket to (i) raise a satellite to the desired height, and(ii) give the satellite the correct speed and direction by the launching rocket.(b) At lift off, the rocket with spacecraft on top is held down by clamps on the launching pad for a few seconds until the exhaust gases have built up an upward thrust which exceeds the rocket’s weight. The rocket rises vertically initially and after this is gradually tilted by the guidance system. The first-stage rocket lifts the spacecraft with the second-stage rocket to the desired height, then separates and falls back to the earth.



Launching a satellite (cont’d)

(c) The spacecraft with the second-stage rocket casts in free flight to its orbital height where it is momentarily moving horizontally. The second-stage rocket then fires and increases the speed to that required for a circular orbit at the height. Then the spacecraft is separated from the second-stage rocket with the launching speed required.


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Q:Q: For a satellite which is close to the earth’s surface, its radius of orbit may be assumed to be equal to the earth’s radius = 6.38 × 106 m.Estimate(a) the speed, and(b) the periodof the satellite.

Solution



Solution:Solution:

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Synchronous satellite is also known as geostationary satellite or communication satellite.


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Synchronous satellites

Most of communication satellites are synchronous satellites.


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Q:Q: Two widely-separated planetary systems, whose suns of masses S1 and S2, planet P1 of mass M1 and planet P2 of mass M2 are observed to have circular orbits of equal radii. What are the relationship between S1 and S2 if P1 completes one orbit in half the time taken by P2?

Solution



Solution:Solution:

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Loss in total energy of satellite

If the total energy of the satellite reduces, the radius of orbit (r) decreases. However, the kinetic energy of the satellite increases because the increase in the gravitational force by the earth (F = ) accelerates the satellite towards the earth. Hence, the satellite moves faster.

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Q:Q: A body of mass m is released from rest at a height h above the earth’s surface of mass ME and radius RE.(a) (i) Derive an expression for the speed (v) with

which the body will strike the earth’s surface in terms of h, ME, RE, and the gravitational constant (G).

(ii) Hence, estimate the speed with which a meteorite will strike the earth’s surface.

(b) (i) If h is small compared to RE, derive an expression for the gravitational potential energy (U) of the body when it is at a height (h) above the earth in terms of m, h, ME, RE, and G. (Neglecting terms in h/RE of powers greater than one)

(ii) If the gravitational potential energy of the body is redefined as V = mgoh where go is the acceleration due to gravity on the earth’s surface, express U in terms of V.[Mass of earth (ME) = 5.98 × 1024 kg; radius of earth (RE) = 6.38 × 106 m]

Solution



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Solution (cont’d):Solution (cont’d):

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Feeling of weight in space

The astronaut experiences reaction when the spacecraft is launching or moving from one orbit to another orbit.


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1© Manhattan Press (H.K.) Ltd. 6.5 Satellite system of the earth Orbital motion of satellite...

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