Question

The radius of the earth's very nearly circular orbit around the sun is 1.5 x 10^11 m. find the magnitude of the earth's velocity as it travels around the sun. assume a year of 365 days. find the magnitude of the earth's angular velocity as it travels around the sun. assume a year of 365 days. find the magnitude of the earth's centripetal acceleration as it travels around the sun. assume a year of 365 days.

Answer 1

In 1 year, 365 days, each day 24 hours, each hour 60 minutes and each minute 60 seconds.

OR

`1 \ year = 365 \ days = 365 * 24 * 60 * 60 = 3.15  * 10^7 seconds`.

As the radius of the earth's very nearly circular orbit around the sun is 1.5 x 10^11 m.

Therefore, the magnitude of the earth's velocity

`v = (2\pi r)/(T) = (2*3.14* 1.5 * 10^(11)  m)/(3.15 * 10 ^7 \ s) =2.99 * 10^4 m/s \approx 3 *  10^4 m/s`.

The magnitude of the earth's angular velocity is

`(v)/(r) = (3 *  10^4 m/s)/(1.5 * 10^(11)  m) = 2 * 10^(-7) rad/s`.

The magnitude of the earth's centripetal acceleration is

`a_(c) =(v^2)/(r) = ((3 *  10^4 m/s)^2)/(1.5 * 10^(11)  m) = 6 * 10^(-3) \ m/s^2`