Approximate orbital period for earth's moon

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SUMMARY

The approximate orbital period for an object, such as an apple, placed in orbit around Earth at the moon's distance is equivalent to that of the moon itself. This is derived from the formula for orbital period, where the distance from the Earth (RMoon) and the gravitational influence dictate the orbital velocity (vorbital). According to the Newtonian approximation, the orbital period (Porbital) can be calculated using the equation Porbital = (2πRMoon) / vorbital, confirming that both the apple and the moon share the same orbital characteristics at that distance.

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jaypee
Does anyone know what would be the approximate orbital period (time for one complete orbit) for an apple placed in orbit around Earth at the moon’s distance from Earth?
 
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Orbital period depends strictly on distance (for relatively small objects). The apple would have the same period as the moon.
 
GMEarthmapple or Moon/(RMoon)2=mapple or Moon(vorbital)2/RMoon

so vorbital is the same for both Moon and apple, since mapple or Moon cancels (Newtonian approximation as Russ pointed out), and Porbital=(2[pi]RMoon)/vorbital
 

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