The speed of the moon in its orbit is 1011 m/s
Explanation:
The gravitational force exerted by the Earth on the Moon is given by
[tex]F=G\frac{Mm}{r^2}[/tex]
where
[tex]G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}[/tex] is the gravitational constant
[tex]M=5.98\cdot 10^{24} kg[/tex] is the mass of the Earth
m is the mass of the moon
[tex]r=3.9\cdot 10^8 m[/tex] is the Earth-moon distance
This force provides the centripetal force that keeps the Moon in circular orbit, and this centripetal force is
[tex]F=m\frac{v^2}{r}[/tex]
where v is the orbital speed of the moon.
Therefore, we can equate the two forces:
[tex]G\frac{Mm}{r^2}=m\frac{v^2}{r}[/tex]
Re-arranging the equation and solving for v, we find:
[tex]v=\sqrt{\frac{GM}{r}}=\sqrt{\frac{(6.67\cdot 10^{-11})(5.98\cdot 10^{24})}{3.9\cdot 10^8}}=1011 m/s[/tex]
Learn more about gravitational force:
brainly.com/question/1724648
brainly.com/question/12785992
#LearnwithBrainly
