Monday, August 28, 2017

newtonian gravity - Pluto's gravitational pull on a person on the Earth's surface?


My physics teacher stated that Pluto has a gravitational pull on objects on Earth, namely humans. Is this true? What is the free-fall acceleration of Pluto with respect to being on the Earth's surface (i.e. the Earth's free-fall acceleration is $9.8$ m/s$^{2}$)?



Answer



This is true. Newton's law of universal gravitation says everything attracts everything. To get the free-fall acceleration of some object on Earth towards Pluto, take Newton's law and divide by the object's mass to get $$a=\frac{F}{m}=\frac{GM}{r^2}.$$ Subbing in reasonable values - $M=0.002$ Earth masses, and $r$ between 29 and 49 AU you get something like $10^{-14}\textrm{ m s}^{-2}$.


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