The moon orbits the earth - Leaving Cert Physics - Question b - 2009
Question b
The moon orbits the earth. What is the relationship between the period of the moon and the radius of its orbit?
Worked Solution & Example Answer:The moon orbits the earth - Leaving Cert Physics - Question b - 2009
Step 1
Identify the relationship
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Answer
The period of the moon's orbit (T) is related to the radius of its orbit (R) according to Kepler's third law of planetary motion. This law states that the square of the period of the orbit is directly proportional to the cube of the semi-major axis of its orbit.
Step 2
Establish the proportionality
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Answer
This relationship can be expressed mathematically as:
T2∝R3
indicating that the period squared is proportional to the radius cubed.
Step 3
Include gravitational constant
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For more precise calculations, this relationship can also be expressed as:
T2=GM4π2R3
where G is the gravitational constant and M is the mass of the Earth.
Step 4
Final conclusion
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Answer
In summary, the period of the moon's orbit increases with the radius of its orbit according to the cube root relationship, illustrating how larger orbits require longer periods to complete their revolution.
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