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Class 10 Class 12
A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is 1.50 ×108 km away from the sun?

Distance of the Earth from the Sun, re = 1.5 × 108 km
= 1.5 × 10
11 m

Time period of the Earth =

Time period of Saturn, Ts = 29. 5 T

Distance of Saturn from the Sun = r

From Kepler’s third law of planetary motion,

T = (4π2r3 / GM)1/2

For Saturn and Sun,

rs3 / re3  =  Ts2 / Te

rs = re(Ts / Te)2/3

= 1.5 × 1011 (29.5 Te / Te)2/3

= 1.5 × 1011 (29.5)2/3

= 14.32 × 1011 m

Hence, the distance between Saturn and the Sun is 1.43 × 1012 m.
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What is the celestial sphere?

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.
661 Views

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.
1256 Views

What is Heliocentric theory?

According to the Heliocentric theory, the sun is at the centre and various planets revolve around the sun at their axis.
907 Views

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.
609 Views

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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