ï»¿ Â Does the escape speed of a body from the earth depend on:Â (a) the mass of the body,Â (b) the location from where it is projected,Â (c) the direction of projection,Â (d) the height of the location from where the body is launched? from Physics Gravitation Class 11 Manipur Board

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Â Does the escape speed of a body from the earth depend on:Â
(a) the mass of the body,Â

(b) the location from where it is projected,Â

(c) the direction of projection,Â

(d) the height of the location from where the body is launched?

The escape velocity is independent of the mass of the body and the direction of projection. It depends upon the gravitational potential at the point from where the body is launched. Gravitational potential depends slightly on the latitude and height of the point, therefore, the escape velocity dependsÂ on these factors.Â
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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.Â
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The position co-ordinates of two particles of masses m1Â and m2are (x1, y1, z1) and (x2, y2, z2) respectively. Find the coordinates of the centre of mass.

The position vectors of masses m1Â and m2Â 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, Â  Â

Â

Comparing the coefficients of Â , we get

Â

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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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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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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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