The moon revolves around the earth in almost a circle of radius 382400 km in 27.3 days. What is centripetal acceleration? (ac = 0.00271 m s⁻¹)


Given:

Radius of the moon orbit = r = 382,400 km = 3.8 ｘ10⁵ｘ10³ m = 3.8 ｘ10⁸ m
Time = t = 27.3 days = 27.3 ｘ 24 ｘ60 ｘ 60 s = 2358720 s = 2.359 ｘ10⁶ s

To Find:

Centripetal acceleration = ac = ?

Solution:

The formula for centripetal acceleration is 

ac  = r Ѡ² ---------(1)

But Ѡ = `\frac {2π}{t}` we have the equation (1)

ac  = r ( `\frac {2π}{t}` )²

ac  = r `\frac {4π²}{t²}`

putting values

ac  = 3.8 ｘ10⁸ m ｘ `\frac {4(3.1416)²}{(2.359 ｘ10⁶ s)²}`

ac  = 3.8 ｘ10⁸ m ｘ `\frac {39.478}{5.565 ｘ10¹² s²}`

ac  = 3.8 ｘ10⁸ m ｘ 7.094 ｘ10⁻¹² s⁻²

ac  = 26.957 ｘ10⁻⁴ m s⁻²

ac  = 0.0026957 m s⁻²

or

ac  = 0.0027 m s⁻² ---------------Ans.



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