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

Step-by-step explanation:

It is given that,

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

Radius of circular orbit,
`r=1.42* 10^(11)\ m`

(a) Angular speed,
`\omega=(2\pi)/(T)`

`\omega=(2\pi)/(4.34* 10^7)`

`\omega=1.44* 10^(-7)\ rad/s`

(b) Tangential speed of the planet,
`v=r* \omega`

`v=1.42* 10^(11)\ m* 1.44* 10^(-7)\ rad/s`

v = 20448 m/s

(c) Centripetal acceleration of the planet,
`a=(v^2)/(r\\)`

`a=((20448)^2)/(1.42* 10^(11))`

`a=0.0029\ m/s^2`

Hence, this is the required solution.