Q26 of 38 Page 61

Out of aphelion and perihelion, where is the speed of the earth more and why?

Aphelion is the positon of earth from where it has the greatest distance from the sun and perihelion is the position from where it has the shortest distance. Now since the angular momentum of earth about the sun is conserved then we have:


Where m is the mass of the earth, rap is the earth - sun distance at the aphelion and rpe is the earth - sun distance at the perihelion.




Since rap > rpe, vpe > vap, therefore the velocity at the perihelion is greater than the velocity at the aphelion.


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An astronaut inside a small spaceship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size, can he hope to detect gravity?

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The gravitational force between a hollow spherical shell (of radius R and uniform density) and a point mass is F. Show the nature of F vs r graph where r is the distance of the point from the centre of the hollow spherical shell of uniform density.

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What is the angle between the equatorial plane and the orbital plane of

(a) Polar satellite?


(b) Geostationary satellite?


 28

Mean solar day is the time interval between two successive noon when sun passes through zenith point (meridian). Sidereal day is the time interval between two successive transit of a distant star through the zenith point (meridian). By drawing appropriate diagram showing earth’s spin and orbital motion, show that mean solar day is four minutes longer than the sidereal day. In other words, distant stars would rise 4 minutes early every successive day.

(Hint: you may assume circular orbit for the earth).