Gravitational Force: Mass & Distance Impact

[LoveKnowledge]

1. Show that the gravitational force between two planets is quadrupled if the masses of both planets are doubled but the distance between them stays the same.



2. F = G m1m2/d2 ??



3. confused...

 

[Sabrewolf]

Okay let's say that we have the following:

G (Gravitational constant) = 6.67E-11
mass of planet 1 = 200,000 kg
mass of planet 2 = 40,000 kg
lets say that the distance r = 10,000 m
all are numbers I just randomly made up

Using the equation: $$F_{g} =$$ $$\frac{Gm_{1}m_{2}}{r^{2}}$$

we just plug in and find that the Force of gravity is:

$$\frac{(6.67E-11)(200000)(40000)}{(10000)^{2}}$$ which gives 5.336E-9

If we double the masses but keep the distance between them the same:

$$\frac{(6.67E-11)(400000)(80000)}{(10000)^{2}}$$ gives the value 2.1344E-8


If we divide the force with the doubled masses by the original force:

$$\frac{2.1344E-8}{5.336E-9}$$ = 4

Thus the gravitational force has been increased by a factor of 4, and quadrupled. HOWEVER THIS IS ONLY AN EXAMPLE, AND PROBABLY NOT WHAT THE QUESTION IS ASKING.


Most likely, the question is asking for some algebra actually showing that doubling the masses results in quadrupled force.


Start with

$$F_{g}$$ = $$\frac{Gm_{1}m_{2}}{r^{2}}$$

the question asks you to show that if the masses are doubled, then the force of gravity
quadruples

so just double the masses and do some algebra to show that either:
a)the second force is 4 times greater than the original force or
b)the original force is 1/4 the second force

Here I'll even get you started:

$$F_{g2}$$ = $$\frac{G(2m_{1})(2m_{2})}{r^{2}}$$ = ?

 

[LoveKnowledge]

thx so much!