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

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 = (2\pi)/(T)=(2\pi)/(3.37* 10^(7))`

`\omega = 1.864* 10^(-7)\ rad/s`

b) tangential speed

`v = r \omega = 1.04* 10^(11)* 1.864 * 10^(-7)`

v = 1.94 x 10⁴ m/s

c) centripetal acceleration magnitude

`a = (v^2)/(r)= ((1.94* 10^4)^2)/(1.04* 10^(11))`

a = 3.62 x 10⁻³ m/s²