Physics: Aplanet orbits a star, in a year of length 2.27 x 107 s, in a nearly circular orbit of radius 3.99 x 1011 m. with respect to the star, determine (a) the angular speed of the planet, (b) the tangential speed of the planet, and (c) the magnitude of the planet s centripetal acceleration.

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Aplanet orbits a star, in a year of length 2.27

meechristianp

31.12.2021

Explanation:

It is given that,

Radius of circular orbit, $r=3.99\times 10^{11}\ m$

Time taken, $t=2.27\times 10^{7}\ m$

(a) Angular speed of the planet is given by :

$\omega=\dfrac{2\pi}{t}$

$\omega=\dfrac{2\pi}{2.27\times 10^{7}\ m}$

$\omega=2.76\times 10^{-7}\ rad/s$

(b) The tangential speed of the planet is given by :

$v=r\times \omega$

$v=3.99\times 10^{11}\times 2.76\times 10^{-7}$

v = 110124 m/s

$a=\dfrac{v^2}{r}$

$a=\dfrac{(110124)^2}{3.99\times 10^{11}}$

$a=0.0303\ m/s^2$

Hence, this is the required solution.

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