Gravity among objects

[TouK]

A friend of mine said to me that every object has gravity and as a result if u place a man and a pen close to each other in the space then the pen will come closer to the man beacuse his gravitational force will effect it. Such an information seems really interesting to me and i would be grateful if someone could explain me what really happens.

-Please explain them simply(15 years old)

-Sorry for any english mistakes..didnt take the proficiency yet!

[elfmotat]

Your friend is right. There is a gravitational force between any two massive objects. So yes, if you put any two objects relatively close to each other in deep space then they will eventually come together under gravity. The equation that tells us this is called "Newton's Universal Law of Gravitation:"

 

[math]F=\frac{Gm_1 m_2}{r^2}[/math]

 

where [math]F[/math] is the force on one object due to the other, [math]G[/math] is the gravitational constant (it's just a number that's always the same), [math]m_1[/math] is the mass of object 1, [math]m_2[/math] is the mass of object 2, and [math]r[/math] is the distance between the two objects.

 

What this says is that larger masses create larger gravitational forces (which should make sense), and that the farther away two objects are, the smaller the force between them (which should also make sense).

[swansont]

However, gravity is quite weak. If you are measuring masses in kg and distance in meters, G will have a value of 6.67 x 10^-11, which means that the force each feels is very, very, very small. You would not notice the motion that resulted from the gravitational attraction without some sensitive instruments to help you measure it.

[TouK]

Thank you very much!!!!
I am going to say it to my friend beacuse he wasnt sure too!

In addition, is it true that we affect each other beacuse of our gravity here on earth too?(well such force will be tiny,otherwise we would stick together).

[swansont]

Gravity affects everything, really. We notice the attraction of the earth because it is so massive

[TouK]

Yes of course..is there any specific range in which an object affects others?

[swansont]

Yes of course..is there any specific range in which an object affects others?

 

No specific range. The size of the effect varies — that's what the equation tells you. If you double the mass, you double the force. If you cut the distance in half, the force goes up by a factor of 4. But it's always there.

[Enthalpy]

Cavendish measured directly the force between objects of a size manageable by humans

http://en.wikipedia.org/wiki/Cavendish_experiment

with an elegant and refined setup (designed by Michell) in 1798.

 

Presently, accelerometers used for geologic prospection detect the presence of a few kg at several metres.

http://en.wikipedia.org/wiki/Gravimeter

"The superconducting gravimeter achieves sensitivities of one nanogal, one thousandth of one billionth (10^-12) of the Earth surface gravity."

Gravity gradiometers must be more sensitive to local objects

http://en.wikipedia.org/wiki/Gravity_gradiometry

 

At least one detector shown 20 years ago made from 1/2m distance a picture of where mass is in a piece of luggage - at about 3*3 pixels resolution.

 

So it's possible and it's done... but consider that these setups and apparatus are among those that most exaggerate the performance as compared with anything reasonable.

[Janus]

Just as an added tidbit. It would also be possible to have the pen orbit you like a moon. As an example, if the pen had an average distance of one meter (as measured from the center of your body), and you had a mass of 70 kg, the pen would take over 25 hrs to complete on orbit. If the pen started ar rest with respect to you, it would take ~12.5 hrs before it reaches you.

[elfmotat]

You would not notice the motion that resulted from the gravitational attraction without some sensitive instruments to help you measure it.

 

The time for two point masses to come together under gravity from rest is:

 

[math]T=\frac{\pi}{2}\frac{r_0^{3/2}}{\sqrt{2G(m_1+m_2)}}[/math]

 

For two 1-kg masses starting out 5 meters apart, time time for them to come together is about 12 days, so you'd definitely notice if you were patient enough.

[swansont]

The time for two point masses to come together under gravity from rest is:

 

[math]T=\frac{\pi}{2}\frac{r_0^{3/2}}{\sqrt{2G(m_1+m_2)}}[/math]

 

For two 1-kg masses starting out 5 meters apart, time time for them to come together is about 12 days, so you'd definitely notice if you were patient enough.

 

I'm going to count 12 days of no perturbations as a sensitive measurement.

[TouK]

What a great forum ...thank you guys!