Gravitation- interesting question..please explain why the answer is 1/4 not 1/2 G see below?

Question

If the gravitational attraction between two 1-kilogram objects 1 meter away from each other is defined as 1G, the gravitational attraction between those same 1-kilogram objects now 2 meters apart from each other would be 1/4G"

For the life of me I cannot see why it' s not 1/2 G as a proportion . Author states 1/4 2:1?? 1G=1/2G??HELP!!

Answer 1

Gravity varies as the inverse square of distance

See

http://hyperphysics.phy-astr.gsu.edu/Hba...

Answer 2

First response is correct.  The formula for gravitational force F is F = G m1 m2/r^2, where the m's are the masses of the objects in kilograms, G is the universal gravitational constant, and r is the distance between the objects.  This is more satisfying intellectually if you view gravity as a field; the density of the flux lines across a spherical surface is inversely proportional to the area of the surface -- which is, of course, proportional to the square of the radius.  Mathematically, there is a thing called Green's theorem which formalizes this.

Answer 3

I can see how this throws you off, it seems odd at first.

The force of gravity is given as this equation:

F = G(M1*M2) / R²

where G is the gravitational constant, M1 is mass of object 1, M2 is mass of object 2, and R is the radius.

if each object is 1kg, then the numerator is 1.

if they are 1m apart, then R = 1

so F = G [(1*1 / (1)²] = 1G

but if they are 2m apart, then denominator is now 2² = 4

so F = G (1 / 4) = (1/4)G

i hope this explanation helps!  it seems odd until you notice thw equation deals with 1² = 1 and 2² = 4.