Why is gravity, on earth, approximatley 9.81 m/s[SUP]2[/SUP].What

1. Sep 19, 2010

jsmith613

why is gravity, on earth, approximatley 9.81 m/s2.

What causes it to be so?

thanks

2. Sep 19, 2010

zhermes

Re: Gravity

Well, its an observational property of all matter in the universe that it attracts other matter by an equation which newton found (http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation)
$$F_G = G \frac{m_1 m_2}{r^2}$$
For two masses (m1 and m2), separated by a distance (r); given 'newton's gravitational constant' (G).

Now, according to one of newton's other laws
$$F = ma$$
If you combine these equations you find out that the acceleration due to gravity only depends on the mass of the earth and your distance away from its center.... if you plug in the values you get ~9.81 m/s^2

3. Sep 19, 2010

jensel

Re: Gravity

Mass of the earth and the Newton law that F=m a=-G m M/R^2. In classical physics the acceleration does depend only on the distance to the center of the earth. (This means that the acceleration is on a mountain smaller.)
That m does cancel out in this equation is very important, it is unique in physics and let Einstein think about the General Theory of Relativity.

Best regards,
Jens

4. Sep 20, 2010

jsmith613

Re: Gravity

So essetisally, because the earth's mass is so large, the mass of the other objects is next to insignificant. Because the value of r is also large, changing the value by an amount will make little differernce.

Therefore will the value of gravity be in the range 9 - 10

(M1 = earth, M2 = object)

correct?

5. Sep 20, 2010

zhermes

Re: Gravity

Not quite; it doesn't matter how large one body's mass is---because it cancels out in the equations, it has no influence on the acceleration.

That's exactly right. The earth's radius is something like 6000km, while the highest mountain is only about 10km... so the change in gravity will be about 0.3% (or something like that, so very small).

Yeah, if you plug in the usual values, thats what you get.

6. Sep 20, 2010

jsmith613

Re: Gravity

I don't quite understand what you mean. Please explain

Question 2: Using the equation G = M1 * M2 / r^2 does that mean I cause the earth to accelerate upwards at a rate of 9.81 m/s^2. If this is the case, why does the earth not move upwards dramatically due to the upward accealration of every landmass on earth.

7. Sep 20, 2010

Staff: Mentor

Re: Gravity

No. That equation gives you the force. Acceleration is a=f/m so the larger the mass, the smaller the acceleration for the same force.

8. Sep 20, 2010

jsmith613

Re: Gravity

Does that not mean, therefore that Gravity should change based on force and mass for each object, if we assume a = f/m

9. Sep 20, 2010

Rebound

Re: Gravity

Simply put, the only variables in the calculation are the masses of the 2 objects and the distance between them. (Of course, this assumes an isolated system or one in which other objects are too distant to influence it.)

Other forces may act to overcome some or all of the influence of gravity, say a velocity of one object greater than the escape velocity of the larger object, but otherwise, that's really and truly all there is to it.

10. Sep 20, 2010

Staff: Mentor

Re: Gravity

Note that Russ said 'for the same force'. The force of gravity does change based on the mass. In fact the force is proportional to the mass, which makes the acceleration of a free falling object due to gravity the same for all masses, since the mass drops out of the equation.

11. Sep 20, 2010

Re: Gravity

The acceleration gravitational field depends only on the mass of the "source".

Given Earth with mass M and body on its surface with mass m, the force between them is:
$$F = G\frac{Mm}{r^2}$$

Now to calculate the acceleration of Earth you divide the force by Earth's mass
$$a = \frac{F}{M}$$
which is
$$a = G\frac{m}{r^2}$$

The body feels acceleration
$$a = \frac{F}{m}$$
$$a = G\frac{M}{r^2}$$

Now you see that acceleration of bodies on surface of Earth is in fact the same because it does not depends on body's mass.

Gravity is really nice force!

12. Sep 20, 2010

Staff: Mentor

gravitational force, yes: that's what you measure with a bathroom scale.

13. Sep 20, 2010

jsmith613

Re: Gravity

Why is this so,

14. Sep 20, 2010

Drakkith

Staff Emeritus
Re: Gravity

Does all this mean that no matter the mass of the smaller object, it will always have the same acceleration?

15. Sep 20, 2010

jsmith613

Re: Gravity

I understand it know

THanks everyone

16. Sep 20, 2010

zhermes

Re: Gravity

Yes it does.

17. Sep 20, 2010

Drakkith

Staff Emeritus
Re: Gravity

Is this because as the mass increases, the attraction due to gravity increases as well, but so does the amount of force required to move it? I think thats right, just wanting to make sure.

18. Sep 20, 2010

zhermes

Re: Gravity

Yes! That's exactly it.

And as someone said above, this is a very interesting feature of the laws of physics, in newton's force equation there is an inertial mass
$$F_{net} = m_{inertial} a$$
and in his gravitational equation, there is a gravitational mass
$$F_g = G\frac{M m_{grav}}{r^2}$$

And it turns out, they seem to be the same.
$$m_{inertial} = m_{grav}$$

That's what einstein called the "Equivalence principle," which led to his formulation of 'general relativity.' These days we take it for granted that those two masses are equal, but there is no fundamental physical law that says it has to be so, its an observational fact.

19. Sep 20, 2010

Drakkith

Staff Emeritus
Re: Gravity

Awesome.