Instead of doing the above $v$ and spending a significant part of your mass on

propellant, you decide to use the space elevator that a colleague of yours just

designed. It allows to bring payloads up to an altitude of ${55}^{\text{'}}000km.$

$4-$ At what altitude should be the center of mass of the elevator system $($as always,

assume that center of mass $=$ center of gravity$)?$

${35}^{\text{'}}784km$

${35}^{\text{'}}788km$

Using the space elevator, you decide to bring your spacecraft at an altitute of

${55}^{\text{'}}000km.$ Once there, you simply release the spacecraft.

$5-$ What is the speed of the spacecraft just after the release $($in $k\frac{m}{s})?$

$10\mathrm{.}78$

$6-$ What is the $v$ you need to provide to your spacecraft in order to reach the desired

hyperbolic departure excess velocity $($in $k\frac{m}{s})?$

$3\mathrm{.}6$

$7-$ How much propellant $($in $kg)$ will you have to use to provide that $v?($Isp$=350$s$)$

$2793\mathrm{.}39$