Respuesta :
Answer:
The minimum launch speed is 13366.40 m/s.
Explanation:
Given that,
Mass of planet [tex]M=15\times10^{24}\ kg[/tex]
Radius [tex]R= 9.6\times10^{6}\ m[/tex]
Height = 6R
We need to calculate the speed
Using relation between gravitational force and total energy
[tex]-\dfrac{GMm}{6R+R}=\dfrac{1}{2}mv^2-\dfrac{GMm}{R}[/tex]
[tex]\dfrac{}{}mv^2=\dfrac{GMm}{7R}-\dfrac{GMm}{R}[/tex]
[tex]\dfrac{1}{2}mv^2=\dfrac{6GMm}{7R}[/tex]
[tex]v^2=\dfrac{2\times6GM}{7R}[/tex]
Put the value into the formula
[tex]v=\sqrt{\dfrac{2\times6\times6.67\times10^{-11}\times15\times10^{24}}{7\times9.6\times10^{6}}}[/tex]
[tex]v=13366.40\ m/s[/tex]
Hence, The minimum launch speed is 13366.40 m/s.
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