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Question
Solve the following problem.
Calculate the speed of a satellite in an orbit at a height of 1000 km from the Earth’s surface.
(ME = 5.98 × 1024 kg, R = 6.4 × 106 m)
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Solution
Given: h = 1000 km = 1 × 106 m, ME = 5.98 × 1024 kg, R = 6.4 × 106 m, G = 6.67 × 10–11 N m2/kg2
To find: Speed of satellite (vc)
Formula: `"v"_"c" = sqrt("GM"/"r")`
Calculation: From formula,
`"v"_"c" = sqrt("GM"/(("R + h")))`
`= sqrt((6.67 xx 10^-11 xx 5.98 xx 10^24)/([(6.4 xx 10^6) + (1 xx 10^6)]))`
`= sqrt((6.67 xx 5.98 xx 10^7)/7.4)`
`= sqrt("antilog"{log (6.67) + log(5.98) - log(7.4) xx 10^7})`
`= sqrt("antilog"{0.8241 + 0.7767 - 0.8692} xx 10^7)`
`= sqrt("antilog"{0.7316} xx 10^7)`
`= sqrt(5.391 xx 10^7)`
`= sqrt(53.91 xx 10^6)`
= 7.343 × 103 .....[Taking square root value]
= 7.343 × 103 m/s
Speed of the satellite at height 1000 km is 7.343 × 103 m/s.
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