What is Gravitational field strength exactly

[isyang94]

Hello, I just read a book reagarding Newton and his laws and had few questions about it.
What is Gravitational field strength exactly and what is Newton's universal gravitational constant? Aren't they the same thing?
please explain these two concepts simple enough for me to understand and to be able to explain it to my brother who also doesn't understand it
thanks

 

[isyang94]

Newton

Is gravitational field strength same as Newton's universal constant?
If not how exactly are they different?
please explain simply
thanks

<Moderator's Note: Multiple Threads Merged>

 

[Mentz114]

Newton's realized the force between two bodies of mass m and M and separation r is proportional to the product of the masses divided by the square of the distance.

$$F \propto \frac{m\ M}{r^2}$$

The dimensions (Mass=M, length=L, time=T) on the left of the proportionalty sign are [ML²T^-2] and on the right [M²L^-2]. To make physical sense we need to multiply the RHS by a constant of dimension [L³M^-1T^-2] to make them the same. This is metres³Kg^-1sec^-2 in MKS. It is assumed usually that the constant G has the same value everywhere.

We can work out the value of G by experiment and observation.

Gravitational field strength caused by a single point mass is ( I think), the potential GM/r.

 

[Naty1]

A "field" such as electrical or gravitational is a convenient mathematical approach for determining forces...such as electrical charge forces or gravitational mass forces. With this approach one first determines the field, then the force that the field imparts on a particle.

None of this obvious at first exposure. People likely tried a lot of approaches and this is the one that seemed to work for a variety of problems. It's a bit like asking "why do we use the convention that 1 + 1 equals 2..? " I don't know, but for thing, it's a lot better than roman numerals!

The gravitational field strength g is a vector (has a magnitude AND a direction in which it acts) : g = F/m where F is a vector force and m the scalar mass. g is the acceleration of a body arising from the Earth's gravitational pull. g varies with altitude but is usually taken as about 9.8m/sec² near the surface of the earth.

As noted above, G is a constant having the same value for all pairs of particles.

Since F = mg, and F = GmM_e/r² where M_e is the mass of the earth...
so you can calculate g for different separations (different r's, like different altitudes).

more here:
http://en.wikipedia.org/wiki/Gravitational_field

 

[mathman]

f=Gm/r², where f is field strength, G is grav. constant, m is mass of body determining gravity, and r is distance from center of body to point in space.

 

[AlexChandler]

Gravitational field strength caused by a single point mass is ( I think), the potential GM/r.

Actually the field strength is:

$$g = \frac{GM}{r^2}$$

 

[granpa]

you can visualize the field with flux lines.