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"That their main business was not put into the mind knowledge which was not there before, but to turn the mind's eye towards light so that it might see for itself." ...Plato's advice to educators(429-347BC)

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 Author Topic: Space shuttle in a circular orbit with a small satellite held above  (Read 4618 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
ahmedelshfie
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 « Embed this message on: March 03, 2011, 05:42:20 pm » posted from:Uberaba,Minas Gerais,Brazil

Applet design by prof Hwang, Modified layout by Ahmed.
Original Applet Space shuttle in a circular orbit with a small satellite held above

a space shuttle is in a circular orbit at a height H above the Earth.A small satellite is held above the shuttle(i.e directly away from the Earth) by means of a rod of length h.i.e with a total height H+h above the Earth. The satellite is then released . The heights of the new orbit of the space shuttle and the satellite are R and r respectively.

Compare R and r with H and H+h.

Assume mass of shutter is $M_s$, mass of satellite is m_s, Mass of earth is $M$.
The tension along the rode is $T$. The radius of earth is $R_e$.
Let $r=R_e+H$, the angular velocity is $\omega$

Before the satellite is released.
For space shutter: $M_s r \omega^2+T = \frac{G M M_s}{r^2}$

For satellite: $m_s (r+h) \omega^2 -T =\frac{G M m_s}{(r+h)^2}$

From the above two equations:
$\omega =\sqrt{\frac{G M(M_s/r^2+m_s/(r+h)^2)}{M_s r+m_s(r+h)}}$

When the satellite is released, tension T become zero.
For space shutter: the gravitation force $\frac{G M M_s}{r^2}> M_s r \omega^2$ , so space shutter move inward.
For satellite: the gravitation force$\frac{G M m_s}{(r+h)^2}< m_s (r+h) \omega^2$, so satellite move outward.
Both of them become an ellipse orbit.

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 applet pic.jpg (41.06 KB, 625x578 - viewed 404 times.) « Last Edit: March 03, 2011, 05:44:51 pm by ahmedelshfie » Logged
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"That their main business was not put into the mind knowledge which was not there before, but to turn the mind's eye towards light so that it might see for itself." ...Plato's advice to educators(429-347BC)