Are you Galilean?

Classical Mechanics Level 3

In the Laws of Gravity by Galileo, we say that every object take equal time to fall if there's no air resistance. We always ignore that The Earth will also have acceleration due to that object also !

So, if we don't ignore that concept, Are Galileo's Laws of Gravity correct? Think once again, can you explain your logic behind your opinion?

Make some theoretical calculations, consider both acceleration , and make a decision on this million dollars problem(!) - Are Galileo's Laws Accurately Correct?

Depends on Mass of the object Yes! No!

Muhammad Arifur Rahman by Muhammad Arifur Rahman , 23, Bangladesh

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1 solution

Traditionally, g = GM r 2 g=\frac{\text{GM}}{r^2} Where, M=Mass of earth r=Distance between the object and the center of the earth

But in reality, earth will also have the acceleration due to the object of mass m . In that case, resultant acceleration, g = g o + g e g=g_o+g_e Here, g e g_e = Acceleration due to earth (for the object) And, g o g_o = Acceleration due to object (for the earth!) So, g o = Gm r 2 g_o=\frac{\text{Gm}}{r^2} g e = GM r 2 g_e=\frac{\text{GM}}{r^2}

Then, assume the earth is still . So, Relative (Actual) Acceleration of the object g = g o + g e g=g_o+g_e = G r 2 (M+m) =\frac{\text{G}}{r^2}\text{(M+m)}

The equation says that Heavy objects have greater relative acceleration compared to lighter objects . So, heavy objects falls earlier !

So, in reality, in actuality, Galileo's Laws aren't perfect!

But most of the time we ignore acceleration of the earth (Acceleration due to object) , which makes calculations simpler!

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Are the 2 accelerations in the same direction? ??? How do you add them algebraically rather than vectorially? ??

Istiak Reza - 5 years, 8 months ago

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Hopefully you're familiar with Relative Velocity . And in this case, its Relative Acceleration . It makes nasty calculations easier.

Its better you follow this Note . Do You Think Galileo Is Right!

Muhammad Arifur Rahman - 5 years, 8 months ago

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