Because of the effects of air drag abandoned satellites, at the end of their usual lives lose energy in the upper layers of atmosphere, before finally burning up when they reach the denser lower layer

Question

Because of the effects of air drag abandoned satellites, at the end of their usual lives lose energy in the upper layers of atmosphere, before finally burning up when they reach the denser lower layers. It can be shown that satellites originally moving along circular trajectories will continue to travel in approximately circular orbits, with their orbital radii slowly decreasing. Drag force acting an satellite can be expressed as $F_{drag} = C ρ v^{2}$ where $ρ$ is density of air at the altitude of satellite and v is the speed of satellite, C is a constant. Mark the correct statement(s) :-

Options:(select one or more)

Answer:

A, C

Solution:

$\frac{GMm}{2 r ^{2}} Δ r = CPv^{2}; 2 π r (where, v = \frac{GM}{r}) ρ = \frac{m Δ r}{4 π r ^{2} C}$

TestHub · Accepted Answer

​ 2 r 2 GMm ​ Δ r = CPv 2 ; 2 π r ( where, v = r GM ​ ​ ) ​ ρ = 4 π r 2 C m Δ r ​ ​

Physics - Gravitation Question with Solution | TestHub

Options:(select one or more)

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