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A satellite of mass 1000 kg is supposed ...

A satellite of mass 1000 kg is supposed to orbit the earth at a height of 2000 km above the earth's surface. Find a. its speed in the orbit b. its kinetic energy. c. The potential energy of the earth satellilte system and d. it time period. Mass of the earth `=6xx10^24kg`.

Text Solution

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The correct Answer is:
A, B, C, D
`V=(sqrt(GM)/(r+h))=(sqrt(gr^2)/(r+h))`
`(sqrt(9.8xx(6400xx10^3)^2))/(10^6xx(6.4+2)))`
`(sqrt(9.8xx6.4xx6.4xx10^6)/8.4)`
`=6.9xx1063m/s=6.9km/s`
b. K.E. =1/2mv^2`
`=1/2xx1000xx(47.6xx10^6)`
`=2.38xx10^10J`
c. P.E. `=(GMm)/(-(R+h))`
`=-(6.67xx10^-11xx6xx10^24xx10^3)/((6400+2000)xx10^3)`
`=(40xx10^13)//400=-4.76xx10^10J`
d. `T=(2pi(r+h))/V`
`=(2xx3.14xx8400xx10^3)/(6.9xx10^3)`
`=(6.28xx8xx10^2)/6.9`
`=76.6xx10.2sec`
`=2.1hours`
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