Lesser by a factor of 0.63
Time taken by the Earth to complete one revolution around the Sun, Te = 1 year
Orbital radius of the Earth in its orbit, Re = 1 AU
Time taken by the planet to complete one revolution around the Sun, \(T_p = \frac{1}{2} T_e = \frac{1}{2}\) year
Orbital radius of the planet = Rp
From Kepler’s third law of planetary motion, we can write:
\((\frac{R_p}{R_e})^3 = (\frac{T_p }{ T_e})^2\)
\(\frac{R_p}{R_e} = (\frac{T_p}{T_e})^{\frac{2}{3}}\)
\(=(\frac{\frac{1}{2}}{1} )^{\frac{2}{3}}= (0.5)^{\frac{2}{3} }= 0.63\)
Hence, the orbital radius of the planet will be 0.63 times smaller than that of the Earth.
Give reasons for the following.
(i) King Tut’s body has been subjected to repeated scrutiny.
(ii) Howard Carter’s investigation was resented.
(iii) Carter had to chisel away the solidified resins to raise the king’s remains.
(iv) Tut’s body was buried along with gilded treasures.
(v) The boy king changed his name from Tutankhaten to Tutankhamun.
Find the mean deviation about the median for the data
xi | 15 | 21 | 27 | 30 | 35 |
fi | 3 | 5 | 6 | 7 | 8 |
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]