Calculate the area covered per second (m²/s
) by the Moon for one
complete revolution round the Earth
(distance of Moon from
Earth = 3.845x10⁸m and period of revolution of Moon = 27⅓
days).
Answers
Given :-
Distance of Moon from earth = 3.845 × 10⁸ m and period of revolution of moon = 27⅓ days .
To Find :-
The area covered per second metre square by the moon for one complete revolution around the Earth .
Solution :-
For diagram refers to the attachment .
It is clear from the attachment that the radius of the circle is the distance between Earth and Moon i.e 3.845 × 10⁸ m .
At first , we will find the total area i.e πr² for a circle .
Here , r = 3.845 × 10⁸ m
We will use π = 3.14
Now , πr² :-
=> 3.14 × 3.845 × 10⁸ × 3.845 × 10⁸
=> 46.4 × 10¹⁶
=> But according to the rule of standard and usual forms we need the decimal before 6 . So , Multiplying and dividing by 10 we get ,
=> 464 × 10¹⁶ × 10 / 10 × 10
=> 4.64 × 10¹⁷ m²
Now , Lets convert the time into seconds that moon take to complete a revolution of Earth i.e 27⅓ days
=> 81 + 1/3
=> 82/3 days
Now , 1 day = 24 hours
=> 82/3 days = 24 × 82/3 = 656 hours
=> 1 hour = 3600 second
=> 656 hours = 3600 × 656 = 2361600 seconds
Now , The area covered per second metre square by the moon for one complete revolution around the Earth :-
=> Total area/Total time
=> 4.64 × 10¹⁷/2361600
=> 464 × 10¹⁷/23616 × 100 × 100
=> 464 × 10¹³/23616
=> 10¹³ × 0.0196
=> 196/10000 × 10¹³
=> 196 × 10⁹
=> Multiplying and Dividing by 100 we get ,
=> 196 × 10⁹ × 100/100
=> 1.96 × 10¹¹ m²/s
Henceforth, The required answer is
1.96 × 10¹¹ m²/s .
Calculate the area covered per second (m²/s
) by the Moon for one
complete revolution round the Earth
(distance of Moon from
Earth = 3.845x10⁸m and period of revolution of Moon = 27⅓
days).
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