Question

A planet orbits a star, in a year of length 3.37 x 107 s, in a nearly circular orbit of radius 1.04 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.

Answer 1

Answer

Given,

Time period of star,T = 3.37 x 10⁷ s

Radius of circular orbit,R = 1.04 x 10¹¹ m

a) Angular speed of the planet

   $\omega = \dfrac{2\pi}{T}=\dfrac{2\pi}{3.37\times 10^{7}}$

   $\omega = 1.864\times 10^{-7}\ rad/s$

b) tangential speed

   $v = r \omega = 1.04\times 10^{11}\times 1.864 \times 10^{-7}$

       v = 1.94 x 10⁴ m/s

c) centripetal acceleration magnitude

      $a = \dfrac{v^2}{r}= \dfrac{(1.94\times 10^4)^2}{1.04\times 10^{11}}$

          a = 3.62 x 10⁻³ m/s²