The earth's velocity is expressed as:

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

Angular velocity is:

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

Centripetal acceleration:

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

**(a)**

The Gravitational constant, G = 6.67 × 10^{-11} N·m^{2}/kg^{2 }and the mass of the sun, M = 1.99 × 10^{30} kg.

Substituting into the first equation:

The radius of the earth's very nearly circular orbit around the sun is 1.5×10^{11} m.**(a)** Find the magnitude of the earth's velocity as it travels around the sun. Assume a year of 365 days.**(b)** Find the magnitude of the earth's angular velocity as it travels around the sun. Assume a year of 365 days.**(c)** Find the magnitude of the earth's centripetal acceleration as it travels around the sun. Assume a year of 365 days.

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