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A satellite is a taken to a height equal...

A satellite is a taken to a height equal to the radius of the Earth and then projected horizontally with a speed of 7km/s . State the nature of its orbit.

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Data : `h= R_(E), G = 6.67 xx 10^(-11) N.m^(2)//kg^(2), M_(E) = 6xx 10^(24)` kg,
` R_(E) = 6.4 xx 10^(6)` m
Critical speed at an altitude h =` R_(E)`is
`v_(c)=sqrt((GM_(E))/(R_(E)+h))=sqrt((Gm_(E))/(2R_(E)))`
` = sqrt((6.67 xx 10^(11))(6xx10^(24)))/(2(6.4 xx 10^(6)))= sqrt((200.1 xx 10^(6))/(6.4))`
= `5.591 xx 10^(3) m//s = 5.591 ` km/s
And the escape speed from an orbit at that altitude,
` v_(c)=sqrt(2)v_(c)`
= 1.414 `xx` 5.591= 7.905 km/s
Since 7.905 km/s gt 7 km /s gt 5.591 km/s
` v_(e) gt v gt v_(c)`
Teh satellite's orbit will be elliptical.
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