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CBSE Class 9 Answered

the satellite of mass 1000 kg is supposed to orbit the earth at height of 2000 km about the Earth surface. the kinetic energy and potential energy respectively are
Asked by ambica.mallarapu | 30 Oct, 2023, 09:58: PM
answered-by-expert Expert Answer
Radius R of earth  = 6.371 × 106  m
 
If the satellite is at a distance h = 2000 km above earth surface , then centripetal force is calculated as
 
begin mathsize 14px style m space fraction numerator v squared over denominator R plus h end fraction space equals space G space fraction numerator M space space m over denominator left parenthesis R plus h right parenthesis squared end fraction end style
 
where m is mass of satellite , v is speed of satellite in its orbit , G is universal gravitational constant  and
M is mass of earth
 
from above expression , we get
 
begin mathsize 14px style v space equals space square root of fraction numerator G space M over denominator left parenthesis R plus h right parenthesis end fraction end root space equals space square root of fraction numerator 6.674 space cross times 10 to the power of negative 11 end exponent cross times 5.972 cross times 10 to the power of 24 over denominator 8.371 cross times 10 to the power of 6 end fraction end root space equals space 6900 space m divided by s end style
 
Kinetic energy K of satellite,  begin mathsize 14px style K space equals space left parenthesis 1 divided by 2 right parenthesis space m space v squared space equals space 0.5 space cross times space 1000 space cross times space left parenthesis 6900 right parenthesis squared space equals space 2.381 space cross times space 10 to the power of 10 space J end style
Potential energy U of satellite ,  begin mathsize 14px style U space equals space minus space G space fraction numerator M space m over denominator left parenthesis R plus h right parenthesis end fraction space equals space fraction numerator negative space 6.674 space cross times space 10 to the power of negative 11 end exponent space cross times 5.972 space cross times space 10 to the power of 24 over denominator 8.371 space cross times space 10 to the power of 6 end fraction space equals space minus 4.761 space cross times space 10 to the power of 7 space J end style
Answered by Thiyagarajan K | 31 Oct, 2023, 11:01: AM
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