Mass of our galaxy Milky Way, M = 2.5 × 1011
solar mass Solar mass = Mass of Sun = 2.0 × 1036 kg
Mass of our galaxy, M = 2.5 × 1011 × 2 × 1036 = 5 ×1041 kg
Diameter of Milky Way, d = 105 ly
7 Radius of Milky Way, r = 5 × 104 ly
1 ly = 9.46 × 1015 m
∴ r = 5 × 104 × 9.46 × 1015
= 4.73 ×1020 m
Since a star revolves around the galactic centre of the Milky Way, its time period is given by the relation:
\(T = (\frac{4π^2 \,r^3 }{ GM})^{\frac{1}{2}}\)
\(= (\frac{4 × (3.14)^2 × (4.73)^3 × 10^{60} }{6.67 ×10 ^{-11 }× 5 × 10^{41}}) ^{\frac{1}{2}} =\frac{ 39.48 × 105.82 ×10^{30} }{33.35 }) ^{\frac{1}{2}}\)
\(=(125.27 × 10^{30} )^{\frac{1}{2}} = 1.12 × 10^{16}\) s
1 year = 365 x 324 x 60x60 s
\(1s = \frac{1}{365 ×324 × 60×60}\) year
\(∴ 1.12 × 10^{16}s = \frac{1.12 × 10^{16} }{365 × 324 × 60×60}\)
\(= 3.55× 10 ^8 \) years
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: The kinetic energy needed to project a body of mass $m$ from earth surface to infinity is $\frac{1}{2} \mathrm{mgR}$, where R is the radius of earth. Reason R: The maximum potential energy of a body is zero when it is projected to infinity from earth surface.
take on sth: | to begin to have a particular quality or appearance; to assume sth |
take sb on: | to employ sb; to engage sb to accept sb as one’s opponent in a game, contest or conflict |
take sb/sth on: | to decide to do sth; to allow sth/sb to enter e.g. a bus, plane or ship; to take sth/sb on board |
Gravitational force is a central force that depends only on the position of the test mass from the source mass and always acts along the line joining the centers of the two masses.
According to Newton’s law of gravitation, “Every particle in the universe attracts every other particle with a force whose magnitude is,
By combining equations (1) and (2) we get,
F ∝ M1M2/r2
F = G × [M1M2]/r2 . . . . (7)
Or, f(r) = GM1M2/r2 [f(r)is a variable, Non-contact, and conservative force]