A planet orbits a star, in a year of length 2.35 x 107 s, in a nearly circular orbit of radius 3.49 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.

a) w = 9.599 10⁴ rad / s, b) v = 3.35 10¹⁶ m / s, c) a = 3.22 10²¹ m / s²

Explanation:

For this exercise we must use the relation of angular kinematics

a) angular velocity, the distance remembered in orbit between time (period)

w = 2π r / T

w = 2 π 3.59 10¹¹ / 2.35 10⁷

w = 9.599 10⁴ rad / s

b) linear and angular velocity are related by the equation

v = w r

v = 9,599 10⁴ 3.49 10¹¹

v = 3.35 10¹⁶ m / s

c) the centripetal acceleration is

a = v² / r = w² r

a = (9,599 10⁴) ² 3.49 10¹¹

a = 3.22 10²¹ m / s²