﻿ The figure shows elliptical orbit of a planet m about the sun S. The shaded are SCD is twice the shaded area SAB. If t1 is the time for the planet to move from C to D and t2 is the time to move from A to B then, from Physics Gravitation Class 11 Manipur Board

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The figure shows elliptical orbit of a planet m about the sun S. The shaded are SCD is twice the shaded area SAB. If t1 is the time for the planet to move from C to D and t2 is the time to move from A to B then,

• t1 > t2

• t1 =4 t2

• t1 = 2t2

• t1 = t2

C.

t1 = 2t2

Apply Kepler's law of area fo planetary motion.

The line joining the sun to the planet sweeps out equal areas time interval ie, areal velocity is constant.

Apply Kepler's law of area fo planetary motion.

The line joining the sun to the planet sweeps out equal areas time interval ie, areal velocity is constant.

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Is Geodesic always a straight line?

No, Geodesic is a straight line if and only if,  the two points lie on the flat surface. If the two points lie on the curved surface then it is a curved line.
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The position co-ordinates of two particles of masses m1 and m2are (x1, y1, z1) and (x2, y2, z2) respectively. Find the coordinates of the centre of mass.

The position vectors of masses m1 and m2 are respectively,

Let the position coordinates of the centre of mass be (X, Y, Z).

Therefore the position vector of centre of mass is,

Since,

Comparing the coefficients of  , we get

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At night, if we see the planets and the stars in the sky, all appear to lie in the hemisphere (rest of the hemisphere we are unable to see because of being on the other side of the earth). This sphere is called the celestial sphere.
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What is Geocentric theory?

According to the geocentric theory, all the astronomical bodies like the moon, the sun and stars revolve around the earth, and the earth is at the centre of the universe.
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According to the Heliocentric theory, the sun is at the centre and various planets revolve around the sun at their axis.
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