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Physics

Mechanics

Easy

Question

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is v. For a satellite orbiting at an altitude of half of the earth's radius, the orbital velocity is

$\frac{3}{2} v$
$\sqrt{\frac{3}{2}} v$
$\sqrt{\frac{2}{3}} v$
$\frac{2}{3} v$

The correct answer is: $square root of 2 over 3 end root v$

$v equals square root of fraction numerator G M over denominator R plus h end fraction end root table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em rowspacing 3 pt end attributes row blank row cell text For first satellite end text h equals 0 comma v subscript 1 equals square root of fraction numerator G M over denominator R end fraction end root end cell end table text For second satellite end text h equals R over 2 comma v subscript 2 equals square root of fraction numerator 2 G M over denominator 3 R end fraction end root v subscript 2 equals square root of 2 over 3 end root v subscript 1 equals square root of 2 over 3 end root v$

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