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# Problem: The radius of the earth's very nearly circular orbit around the sun is 1.5x1011m.A. Find the magnitude of the earth's velocity as it travels around the sun. Assume a year of 365 days. (km/s)B. Find the magnitude of the earth's angular velocity as it travels around the sun. Assume a year of 365 days. (rad/s)C. Find the magnitude of the earth's centripetal acceleration as it travels around the sun. Assume a year of 365 days (m/s2)

###### FREE Expert Solution

The earth's velocity is expressed as:

$\overline{){\mathbf{v}}{\mathbf{=}}\sqrt{\frac{\mathbf{G}\mathbf{M}}{\mathbf{r}}}}$

Angular velocity:

$\overline{){\mathbf{\omega }}{\mathbf{=}}\frac{\mathbf{v}}{\mathbf{r}}}$

Centripetal acceleration:

$\overline{){{\mathbf{a}}}_{{\mathbf{c}}}{\mathbf{=}}\frac{{\mathbf{v}}^{\mathbf{2}}}{\mathbf{r}}}$

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###### Problem Details

The radius of the earth's very nearly circular orbit around the sun is 1.5x1011m.

A. Find the magnitude of the earth's velocity as it travels around the sun. Assume a year of 365 days. (km/s)

B. Find the magnitude of the earth's angular velocity as it travels around the sun. Assume a year of 365 days. (rad/s)

C. Find the magnitude of the earth's centripetal acceleration as it travels around the sun. Assume a year of 365 days (m/s2)

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