Question

A planet orbits a star, in a year of length 4.34 x 10^7 s, in a nearly circular orbit of radius 1.42 x 10^11 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.

Answer 1

Explanation:

It is given that,

Time taken by a planet to orbit a star, $T=4.34\times 10^7\ s$

Radius of circular orbit, $r=1.42\times 10^{11}\ m$

(a) Angular speed, $\omega=\dfrac{2\pi}{T}$

$\omega=\dfrac{2\pi}{4.34\times 10^7}$

$\omega=1.44\times 10^{-7}\ rad/s$

(b)  Tangential speed of the planet, $v=r\times \omega$

$v=1.42\times 10^{11}\ m\times 1.44\times 10^{-7}\ rad/s$

v = 20448 m/s

(c) Centripetal acceleration of the planet, $a=\dfrac{v^2}{r\\}$

$a=\dfrac{(20448)^2}{1.42\times 10^{11}}$

$a=0.0029\ m/s^2$

Hence, this is the required solution.