The planet XYZ traveling about the star ABC in a circular orbit takes 24 hours to make an orbit. Assume that the orbit is a circle with radius 89 comma 000 comma 00089,000,000 mi. Find the linear speed of XYZ in miles per hour.

v = 2.33 10⁷ mi / h

Explanation:

For this exercise we must observe that the velocity module is constant, so we can use the kinematic relation

v = d / t

The distance traveled in each orbit is the length of the circle

L = 2π r

The time it takes in orbit is called period (T)

Let's reduce the quantities

r = 8.9 10⁷ mi

t = 24 h (3600s / 1 h) = 86400 s

We replace

v = 2π r / T

Let's calculate

v = 2π 8.9 10⁷/86400

v = 6.47 10³ mi / s

v = 6.47 10³ mi / s (3600 s / 1h)

v = 2.33 10⁷ mi / h

linear speed v = 23303166.67 mi/h

Explanation:

From linear speed v = angular speed w * radius r

And we have angular speed w = 2*pi/T

where T is the period

hence, v = 2*pi*r/T

Given:

r = 89,000,000 mi, T = 24 hours

Hence v = 2*3.142*89000000/24

linear speed v = 23303166.67 mi/h