Express the constant k of Eq. (8.38) in days and kilometres. Given k = `10^(–13) s^(2) m^(–3)` . The moon is at a distance of `3.84 xx 10^5` km from the earth. Obtain its time-period of revolution in days.

Explanation

Given
K = `10^(-13) s^(2) m^(-3)`
`= 10^(-13) [ (1)/((24 xx 60 xx 60 )^(2))d^(2) ] [ (1)/((1 // 1000)^(3) km^(3)) ] `
`= 1.33 xx 10^(-14) d^(2) km^(-3)`
Using Eq. (8.38) and the given value of k, the time period of the moon is
`T^(2) = (1.33 xx 10^(-14)) (3.84 xx 10^(5))^(3)`
Not that Eq. (8.38) also holds for elltpttcal orbits If we replace `(R_(E) + h)` by the semi- major axis of the elltpse. The earth. will then the at one of the foct of this ellipse.