NCERT Physics Class 11 Exemplar Ch 8 Gravitation Part 6

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Q. 36 A satellite is to be placed in equatorial geostationary orbit around earth for communication.

(a) Calculate height of such a satellite.

Answer:

(b) Find out the minimum number of satellites that are needed to cover entire earth so that at least one satellites is visible from any point on the equator.

Answer:

Hence minimum number=3.

Q. 37 Earth’s orbit is an ellipse with eccentricity . Thus, earth’s distance from the sun and speed as it moves around the sun varies from day to day. This means that the length of the solar day is not constant through the year. Assume that earth’s spin axis is normal to its orbital plane and find out the length of the shortest and the longest day. A day should be taken from noon to noon. Does this explain variation of length of the day during the year?

Answer: Angular momentum and areal velocity are constant as earth orbits

the sun.

At perigee at apogee.

If ‘a’ is the semi-major axis of earth’s orbit, then and

Let be angular speed which is geometric mean of and and corresponds to mean solar day,

Conservation of angular momentum

Conservation of Angular Momentum

Conservation of angular momentum

If corresponds to per day (mean angular speed), then per day and per day. Since mean solar day, we get which corresponds to 24 hrs. 8.14″ (8.1″ longer) and corresponds to 23 hrs. 59 min 52″ (7.9″ smaller).

This does not explain the actual variation of the length of the day during the year.

Q.38 A satellite is in an elliptic orbit around the earth with aphelion of 6R and perihelion of 2 R where R= 6400 km is the radius of the earth. Find eccentricity of the orbit. Find the velocity of the satellite at apogee and perigee. What should be done if this satellite has to be transferred to a circular orbit of radius 6R?

Answer:

Conservation of angular momentum:

angular momentum at perigee = angular momentum at apogee

Conservation of Energy:

Energy at perigee = Energy at apogee

For

Hence to transfer to a circular orbit at apogee, we have to boost

the velocity by This can be done by

suitably firing rockets from the satellite.

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