The Moon’s Mass Is 735 × 10²² Kg And It Moves In A Near Circ

The Moon’s Mass Is 735 X1022 Kg And It Moves In a Nearly Circular

The Moon’s mass is 7.35 x 10^22 kg, and it moves in a nearly circular orbit with radius 3.84 x 10^8 m. The period of its motion is 27.3 days. Use this information to determine the Moon’s (a) orbital speed and (b) acceleration.

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The Moon’s motion around the Earth offers a compelling application of classical mechanics, particularly orbital dynamics. By examining its orbital parameters, we can determine its orbital velocity and acceleration.

(a) Orbital Speed: The orbital speed (v) can be calculated using the relation between the circumference of the orbit and the period of revolution:

v = (2πr) / T

Where:

  • r = 3.84 x 10^8 m (radius of the Moon’s orbit)
  • T = 27.3 days = 27.3 x 24 x 3600 seconds = 2,359,680 seconds

Calculating the orbital speed:

v = (2 π 3.84 x 10^8 m) / 2,359,680 s

v ≈ (2 3.1416 3.84 x 10^8) / 2,359,680

v ≈ (2.412 x 10^9) / 2,359,680

v ≈ 1022 m/s

Therefore, the Moon’s orbital speed is roughly 1022 meters per second.

(b) Orbital Acceleration: The centripetal acceleration (a) is given by:

a = v^2 / r

Using the calculated velocity:

a = (1022)^2 / (3.84 x 10^8)

a ≈ 1,044,484 / 3.84 x 10^8

a ≈ 0.00272 m/s^2

This acceleration is significantly less than Earth's gravity, illustrating the gentle inward pull maintaining the Moon’s orbit.

References

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