Gravitation

Physics Part I

Physics

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How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of the earth around the sun is 1.5 × 10^{8} km.

Orbital radius of the Earth around the Sun,

Time taken by the Earth to complete one revolution around the Sun,

= 365.25 days

= 365.25 × 24 × 60 × 60 s

Universal gravitational constant, G = 6.67 × 10

Thus, mass of the Sun can be calculated using the relation,

=

= 2 × 10

Hence, the mass of the Sun is 2 × 10

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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.

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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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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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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.

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The position co-ordinates of two particles of masses m_{1} and m_{2}are (x_{1}, y_{1}, z_{1}) and (x_{2}, y_{2}, z_{2}) respectively. Find the coordinates of the centre of mass.

The position vectors of masses m

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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