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A satellite orbits at height $h$ from Earth's surface where $h \ll R$ ($R$ = Earth's radius). The minimum increase in speed for the satellite to escape Earth's gravitational field is:
For $h \ll R$, orbital radius $\approx R$:
Orbital speed: $v_o = \sqrt{gR}$
Escape speed from surface (approximately same radius): $v_e = \sqrt{2gR}$
Minimum increase: $\Delta v = v_e - v_o = \sqrt{2gR} - \sqrt{gR} = \sqrt{gR}(\sqrt{2}-1)$
Overlap occurs when $n_1 \lambda_1 = n_2 \lambda_2$.
$n_1(650) = n_2(520) \implies \frac{n_1}{n_2} = \frac{520}{650} = \frac{4}{5}$.
Distance $y = \frac{n_1 \lambda_1 D}{d} = \frac{4 \times 650 \times 10^{-9} \times 1.5}{0.5 \times 10^{-3}} = 7.8 \times 10^{-3} \text{ m} = 7.8 \text{ mm}$.
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