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A planet orbits a star, in a year of length $3\mathrm{.}87{10}^{7}s,$ in a nearly circular orbit of radius $3\mathrm{.}42{10}^{11}m.$ With respect to the star, determine $($a$)$ the angular speed of the planet, $($b$)$ the tangential speed of the planet, and $($c$)$ the magnitude of the planet's centripetal acceleration.

$($a$)$ Number $$ Units

$($b$)$ Number $$ Units

$($c$)$ Number $$ Units $$

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