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 x× 105 kmfrom the earth. Obtain its time-period of revolution in days.

Express the constant k of Eq. (8.38) in days and kilometres. Given k =

1.	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 x× 105 kmfrom the earth. Obtain its time-period of revolution in days.
Answer» Solution :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.