Gravitation

Physics Part I

Physics

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Let us assume that our galaxy consists of 2.5 Ã— 10^{11}stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be 10^{5}Â ly.

Mass of our galaxy Milky Way,Â

Solar mass = Mass of Sun = 2.0 Ã— 10

Mass of our galaxy,Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 5 Ã— 10

Diameter of Milky Way,Â

Radius of Milky Way,Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â 1 ly = 9.46 Ã— 10

âˆ´ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 4.73 Ã—10

Â

A star revolves around the galactic centre of the Milky Way.

Time period is given by the relation,Â

Â Â =Â Â

Â Â = Â

Â Â = 1.12Â Ã—Â 10

1 year = 365Â Ã—Â 324Â Ã—Â 60Â Ã—Â 60 sÂ

Â Â Â Â 1s = yearsÂ

Therefore,

1.12Â Ã—Â 10

Â Â Â Â Â Â Â Â Â Â Â =Â 3.55Â Ã—Â 10

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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 theÂ celestial sphere.

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The position co-ordinates of two particles of masses m_{1}Â 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, Â Â

Â

Comparing the coefficients of Â , we get

Â

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Is Geodesic always a straight line?

No, Geodesic is a straight line if and only if, Â 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 Heliocentric theory?

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

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