The radius of the earth\'s orbit around the sun (assumed to be circular) is \\(1

Question

The radius of the earth's orbit around the sun (assumed to be circular) is (1.50 imes 10^{8}; { m km}), and the earth travels around this orbit in 365 days.

Part A

What is the magnitude of the orbital velocity of the earth in ({ m m/s})?

Part B

What is the radial acceleration of the earth toward the sun?

Part C

What is the magnitude of the orbital velocity of the planet Mercury (orbit radius (=5.79 imes 10^{7}; { m km}), orbital period = 88.0 days)?

Part D

What is the radial acceleration of the Mercury?

Explanation / Answer

Apply the formula for Orbital Speed Vo^2 = GM/R

part A :

Vo^2 = 6.67 e -11 * 1.99 e30/(1.5 e 11)

Vo^2 = 8.848 e 8

Vo = 29.74 km/s

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part B :

Radial Acceleration a = V^2/R

a = (29.74 e 3 * 29.74 e 3)/(1.5 e 11)

a = 0.00589 m/s^2

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part C :

Vo^2 = 6.67 e -11 * 1.99 e 30/(5.79 e 11)

Vo^2 = 2.92 e 8

Vo = 15.14 km/s

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part D:

a = v^2/R

a = 15.14 e3 * 15.14 e 3/(5.79 e 11)

a = 0.000395 m/s^2

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