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a.Find the radius of the circular orbit ...

a.Find the radius of the circular orbit of a satellite moving with ab angular speed equal to the angular speed of earth's rotation. b. If the satellite is directlly above the north pole at some instant find the time it takes to come over the equatorial plaen. Mass of the earth `=6xx10^24kg`

Text Solution

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The correct Answer is:
A, B, C, D
Angulr speed of earth and the satellite will be same
`(2pi)/T_e=(2pi)/T_s`
or `1/(24xx3600)=1/(sqrt2pisqrt((R+h)^3/gh^2))`
or `12xx3600=3.14 sqrt(((R+h)^3)/(gR^2))`
or `((R+h)^3)/(gR^2)=((12xx3600)62/((3.14)^2)`
`or ((6400+h^3)xx10^9)/(9.8xx(6400)^2xx10^6)=((12xx3600)^2)/((3.14)^2)`
or `((6400+h)xx10^9)/(6272xx0^9)=432xx10^4`
or `(6400+h)^3=6272x432xx10^4`
or `6400+h=(6272xx432xx10^4)^(1/3)-6400`
b. Time taken from north to equator
`=1/2T`
`=1/2xx6.28(((42300+6400)^3)/(10xx(6400)^2xx10^6))`
`=3.14(sqrt((479)^3xx10^6)/((64)^2xx10^11))`
`=3.14 sqrt((497xx497xx497)/(64xx64xx10^5))`
`=6 hours`
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