What is the magnitude of the gravitational force between two 7 kg objects that are separated by 2 m

To see the relationship between G and g, start with the general gravitational force equation as in the previous replies:

F = Gm1m2/r² 

Suppose mass 1 is very large compared with mass 2 and that it has a very large radius (like mass1 is the Earth, say, and mass 2 is a ball near the surface of the Earth), so r is effectively just the radius of mass 1.

Then Gm1/r² = g is virtually constant when dealing with objects much smaller than mass1 and near the surface of mass1.  The force equation then simplifies to:

F = m2*g

or just F = m*g if we let the mass of the small object be m.

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G is called the gravitational constant, whereas g is the gravitational acceleration.

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$$\\F=\frac{Gm_1m_2}{r^2}\\\\ F=\frac{9.8*7*7}{2^2}\\\\$$

and I guess the units have to be

$$\frac{m}{s^2}\times\frac{kg^2}{m^2}=kg^2/(ms^2)$$

You can finish it :)

Right formula, but wrong G Melody!

G = 6.6742*10^-11 m³/(kg.s²)

so:

Force = 6.6742*10^-11*7*7/2² N

$${\mathtt{Force}} = {\frac{{\mathtt{6.674\: \!2}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left(-{\mathtt{11}}\right)}{\mathtt{\,\times\,}}{\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{7}}}{{{\mathtt{2}}}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{Force}} = {\mathtt{0.000\: \!000\: \!000\: \!817\: \!589\: \!5}}$$

Force ≈ 8.2*10^-10 N

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thanks Alan, I stand corrected.

What is that G?

thanks Alan,

I can see how that G is derived when you are talking about Earth and a small object close to the Earth's surface

BUT  why is it the same constant when you are talking about two equally sized objects that could be anywhere in the universe?

I don't get it.   

Newton's law of gravitational interaction says that the gravitational force between any two objects is proportional to the product of their masses divided by the square of the distance between them.  The "G" is just the constant of proportionality, which is a universal constant that has to be determined experimentally.

On the other hand "g" is not a universal constant, in fact, it varies from place to place even on Earth!

(Not sure if this answers your question.)

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Thanks Alan,

Yes I actually did understand that - I am just intrigued by the fact that this constant is the same all the time.

That is all