By what factor would your weight change if Earth’s diameter were tripled and its mass were tripled?
February 20th, 2023
My weight would decrease by 3 times than when I stand on the Earth’s surface.
The force of gravity##(F)## of earth is given by## (GMm)/r^2 ##, if I stand on the surface of Earth.
Where ##G## is universal gravitational constant and ##d/2=r##
##M## is the mass of Earth, ##m## is my mass, ##d## the diameter where ##r## is raduis.
if the parameters( ##M## and ##d## ) are tripled,
##M->3M## and ##d->3d=>r->3r##
The gravity would be
##(G(3M)m)/((3*r)^2)= (3GMm)/ (9r^2)= 1/3*(GMm)/(r^2 )##
##:.##My weight would decrease by 3 times the original if the Earth’s mass and diameter would be tripled