Question

V2
Two satellites are at heights hı, h2 The ratio of their orbital angular speeds
is
3/2
3/2​

Answer 1

Answer:

Orbital velocity is given by:

$v = \sqrt{ \frac{gm}{r + h} }$

Where G is the Universal Gravitational constant, M is the mass of the Earth, h is the height of the satellite from the earth's surface and R is the radius of the earth.

$v \times \frac{1}{ \sqrt{r + h} } \\ \frac{ {v}^{1} }{ {v}^{2} } = { \frac{r + {h}^{2} }{r + {h}^{1} } }$

given:

$\frac{ {v}^{1} }{ {v}^{2} } = \frac{2}{1} \\ {h}^{1} = 100km \: and \: r = 6500km \\ = \frac{2}{1 } = \sqrt{ \frac{6400 + {h}^{2} }{6400 + 100} } \\ = 6400 + {h}^{2} =4 \times 6500 = 26000km \\ hence \: the \: height \: above \: the \: earth \: surface \\ {h}^{2} = 26000 - 6400 = 19600$