# Gravitational acceleration (g) is used as constant, but is it?

1. Nov 4, 2015

### vishnu kumar

Acceleration due to gravity is used as a constant throughout the massive body,but it varies due to height and depth & also varies from equator to pole,so it affect the rotational speed of planet from equator to pole.So, why would it takes as a constant.

2. Nov 4, 2015

### andrewkirk

It is referred to as a constant in problems where all motion takes place within a small volume, so that the variation of the gravitational acceleration is small enough to be regarded as constant within that area.

3. Nov 4, 2015

### Grinkle

(G x M1 x M2) / (r-squared) is the acceleration due to gravity.

As you point out, if any of M1, M2 or r are changing over time, the acceleration will change over time. G is the only constant. You can decide if you need more complex models than purely constant numbers for M1, M2 and r depending on the specifics of your problem. You are quite correct in your thinking that for some problems they should be considered non-constant (varying wtth time, usually) in order to get accurate-enough results.

For instance, if you launch a model rocket and you want to accurately calculate the time it will take that rocket to reach zero velocity in the air before it begins to fall back to earth, you need a model of the rocket mass that is decreasing with time as the rocket burns fuel and exhausts mass.

You might decide you need a time varying model of r as well for this problem, but for a small toy rocket that is only going to climb a few hundred feet at most, you will probably choose not to bother and just use a constant r value. It depends on how much accuracy you require in your answer.

Last edited: Nov 4, 2015
4. Nov 4, 2015

### vishnu kumar

Yaa I agree but when we analyze astronomical model which varies a lot with time and rotation both.So, we should use such constant as a variable.

5. Nov 4, 2015

### Staff: Mentor

What do you mean by "astronomical model"? For motin of the planets, we use the universal gravitational constant, G, not the Earth's gravitational acceleration, g.

6. Nov 4, 2015

### Grinkle

Vishnu -

I think you need to study / think about the difference between G, the gravitational constant, and g, the approximation used to model the acceleration due to earths gravity imposed upon objects at the surface of the earth. G is thought to be universal. g is not thought by anyone to be a universally applicable constant, it only applies to simple situations on the surface of the earth.

7. Nov 4, 2015

### sophiecentaur

g is not treated as a constant. The approximate value for g is used for 'rough' calculations. Otoh, G is the constant that is assumed to be that, everywhere in the Universe.

8. Nov 4, 2015

### Grinkle

Sorry, Vishnu. I should have said force, and the acceleration comes from dividing out the mass of the object which is how one arrives at g. I shouldn't post before noon, I guess.

9. Nov 4, 2015

### vishnu kumar

Hi grinkle
I just want to figure out that only earth hasn't acceleration due to gravity, any massive bodies have, just like sun has 272 m/s^2 acc^n due to gravity. So, I only want to know that why should we take g as constant for higher massive body(large dia).

10. Nov 4, 2015

### ZapperZ

Staff Emeritus
11. Nov 4, 2015

### sophiecentaur

Who does?

12. Nov 4, 2015

### Grinkle

We shouldn't and we don't. You are, I think, confusing G with g.