Using Newton's second law and the universal gravitation law we find that the maximum acceleration response is
The universal law of Gravitation states that the force between two bodies is proportional to their masses and inversely proportional to the square of their distance
F = [tex]G \frac{M m}{r^2}[/tex]
Where G is the universal gravitation constant (G = 6.67 10-11 N m²/kg²), M and m the mass of the bodies and r the distance between them
Newton's second law indicates that the force is proportional to the masses and the acceleration of the bodies
F = m a
Where F is the force, m and a the mass and acceleration of the body
let's substitute
[tex]G \frac{Mm}{r^2}[/tex] = m a
a = [tex]G \frac{M}{r^2}[/tex]
In this case the acceleration is called centripetal since it corresponds to a circular motion of the Moon and the Earth.
In tables we can find the values:
Let's calculate the acceleration of the Moon around the Earth
a₁ = 6.67 10⁻¹¹ [tex]\frac{5.98 \ 10^{24}}{ (3.84 \ 10^8 )^2 }[/tex]
a₁ = 2.71 10⁻³ m / s²
The acceleration of the Earth around the Sun
a₂ = 6.67 10⁻¹¹ [tex]\frac{1.991 \ 10^{30} }{(1.496 \ 10^{11})^2 }[/tex]
a₂ = 5.93 10⁻³ m / s²
We can see that the acceleration around the Sun is twice the acceleration of the moon around the Earth
In conclusion they use Newton's second law and the universal gravitation law, we find that the maximum acceleration response is
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