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# Problem: The radius of the earth's very nearly circular orbit around the sun is 1.5×1011 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.

###### FREE Expert Solution

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·m2/kgand the mass of the sun, M = 1.99 × 1030 kg.

Substituting into the first equation:

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###### Problem Details

The radius of the earth's very nearly circular orbit around the sun is 1.5×1011 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.