Respuesta :
Answer:
[tex]a = 2.7\times 10^{-3} m/s^2[/tex]
Explanation:
As we know that moon is revolving around the Earth in circular path
Here the centripetal force on the moon is due to Earth and always towards the position of the Earth
This force is given as
[tex]F = \frac{GM_eM_m}{r^2}[/tex]
here we know that
[tex]M_e[/tex] = mass of Earth
[tex]M_m[/tex] = mass of moon
[tex]r[/tex] = distance between the center of moon and Earth
so we know by Newton's II law that
[tex]F = ma[/tex]
[tex]a = \frac{F}{M_m}[/tex]
[tex]a = \frac{GM_e}{r^2}[/tex]
[tex]M_e = 5.98 \times 10^{24} kg[/tex]
[tex]r = 384400 km[/tex]
now we have
[tex]a = \frac{6.67 \times 10^{-11} 5.98 \times 10^24}{(384400\times 10^3)^2}[/tex]
[tex]a = 2.7\times 10^{-3} m/s^2[/tex]
