Compare planets farther from the Sun to those nearer the Sun. (a) Do the farther planets have (greater or lesser) orbital velocity than the nearer ones? greater or lesser?

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meep26wesley

High School

Compare planets farther from the Sun to those nearer the Sun. (a) Do the farther planets have (greater or lesser) orbital velocity than the nearer ones?
greater or lesser?

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skyluke89

Verified answer

Answer:
Lesser
Explanation:
The gravitational pull between a planet orbiting the Sun and the Sun is equal to the centripetal force keeping the planet in circular motion:
$G\frac{mM}{r^2}=m\frac{v^2}{r}$
where
$G=6.67\cdot 10^{-11} m^3 kg^{-1} s^{-2}$ is the gravitational constant
$M$ is the mass of the Sun
$m$ is the mass of the planet
$r$ is the distance between the Sun and the planet
v is the orbital velocity of the planet
We can re-arrange the formula to solve for v, the orbital velocity of the planet:
$v=\sqrt{\frac{GM}{r}}$
We see that the velocity is inversely proportional to the square root of the distance, r: therefore, the farther the planet from the Sun, the lesser the orbital velocity of the planet.
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