Respuesta :
escape velocity moon:
[tex]v = \sqrt{ \frac{2 mG}{r} } [/tex]
escape velocity earth:
[tex]v = \sqrt{ \frac{2 mG}{R} } [/tex]
difference:
[tex]v = \sqrt{ \frac{2 mG}{R - r} } [/tex]
r radius moon
R radius earth
m mass spaceship
G gravitational constant
[tex]v = \sqrt{ \frac{2 mG}{r} } [/tex]
escape velocity earth:
[tex]v = \sqrt{ \frac{2 mG}{R} } [/tex]
difference:
[tex]v = \sqrt{ \frac{2 mG}{R - r} } [/tex]
r radius moon
R radius earth
m mass spaceship
G gravitational constant
Escape speed is the minimum speed required for a free, non-propelled object to escape from the gravitational pull. The escape speed will be [tex]\rm v=\sqrt{\frac{2mG}{R-r} } \\\\[/tex].
What is escape speed?
Escape speed is the minimum speed required for a free, non-propelled object to escape from the gravitational pull of the main body and reach an infinite distance from it in celestial physics.
It is commonly expressed as an ideal speed, neglecting atmospheric friction.
The formula for the escape speed of the moon is;
[tex]\rm v=\sqrt{\frac{2mG}{r} } \\\\[/tex]
The formula for escape speed of the earth is;
[tex]\rm v=\sqrt{\frac{2mG}{R} } \\\\[/tex]
If a spacecraft is launched from the moon at the escape speed of the earth then the value of escape speed will be the difference of both the velocities;
[tex]\rm v=\sqrt{\frac{2mG}{R-r} } \\\\[/tex]
Hence the escape speed will be [tex]\rm v=\sqrt{\frac{2mG}{r} } \\\\[/tex].
To learn more about the escape speed refer to the link;
https://brainly.com/question/14178880
