Taking the earth to be a uniform sphere of radius 6400 km and the value of g at the surface to be10 ms–2, calculate the energy needed (in × 1010J) to raise a satellite of mass 2000 kg to a height of 800 km above the earth’s surface and to set it into circular orbit at that altitude.

Initial energy of the satellite,E1=−GMmR( since initial KE=o)Final energy of the satelliteE2=−GMm2(R+h)Energy needed, ΔE=E2−E1=−GMm2(R+h)−−GMmR=GMm1R−12(R+h) But GM =R2gΔE=R2gM1R−12(R+h)=mgR⁡1−121+hRΔE=7.1×1010J

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Taking the earth to be a uniform sphere of radius 6400 km and the value of g at the surface to be
$10 {ms}^{- 2},$ calculate the energy needed (in $\times 10^{10} J)$ to raise a satellite of mass 2000 kg to a height of 800 km above the earth’s surface and to set it into circular orbit at that altitude.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

answer is 7.1.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Initial energy of the satellite,

$E_{1} = - \frac{GMm}{R} (since initial KE = o)$

Final energy of the satellite

$E_{2} = - \frac{GMm}{2 (R + h)}$

Energy needed, $ΔE = E_{2} - E_{1}$

$= - \frac{GMm}{2 (R + h)} - (- \frac{GMm}{R}) = GMm (\frac{1}{R} - \frac{1}{2 (R + h)})$

$But GM = R^{2} g$

$ΔE = R^{2} gM [\frac{1}{R} - \frac{1}{2 (R + h)}]$

$= mgR [1 - \frac{1}{2 (1 + \frac{h}{R})}]$

$ΔE = 7.1 \times 10^{10} J$

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!