pinkharrier wrote:I'm still curious about the gravity assuming it has the same consistency as Earth. It may have a radius 2.4 greater but that would mean someone on the surface of that planet would be 2.4 times further away from the centre of it. So the gravity experienced shouldn't be 2.4g. Hmmmmm.

This is oversimplified.

The critical thing is the amount of mass between the surface and the centre. The gravity experienced at the summit of Everest is greater than that felt at similar latitudes at sea level.

hackenslash wrote:The gravity experienced at the summit of Everest is greater than that felt at similar latitudes at sea level.

But why then do we weigh more on the poles than on equator? Is that because of the centripetal acceleration?

renekawa wrote:

hackenslash wrote:The gravity experienced at the summit of Everest is greater than that felt at similar latitudes at sea level.

But why then do we weigh more on the poles than on equator? Is that because of the centripetal acceleration?

Because of rotation, the Earth is not a sphere, but it's a bit squashed at the poles. So the distance between the centre of Earth and the poles is less than the distance between the centre of the Earth and the Equator. Since gravity is given by the mass and distance, we have greater gravity at the poles. Greater gravity, more weight, as weight is W=mg where m=mass and g=acceleration of gravity. At the poles g will be greater, and so W will be increased.

Darkchilde wrote:
Because of rotation, the Earth is not a sphere, but it's a bit squashed at the poles. So the distance between the centre of Earth and the poles is less than the distance between the centre of the Earth and the Equator. Since gravity is given by the mass and distance, we have greater gravity at the poles. Greater gravity, more weight, as weight is W=mg where m=mass and g=acceleration of gravity. At the poles g will be greater, and so W will be increased.

But here your and hack's explanations contradict. Hack's example was that on Mt Everest one weighs more than on sea level because of that extra mass between Earth's core and surface. Now that is exactly same point with pole and equator, yet the result is opposite. Please tell me what I am missing.

You are not missing anything.

The mass distribution on the Earth is not radially symmetric, nor is the Earth a perfect sphere. Depending on how much mass there is between you and the centre of the Earth and the distance between you and the centre of the Earth, then gravity, and so your weight, changes. Do not think this change is that significant; We are talking about a ±0.03 of difference in g max. The mean value we usually use for g is 9.81 m s-2 in 2dp, and at the Equator g is 9.78 m s-2 in 2dp.

So if your mass is 75 kg, on average you would weigh 735,75 N but on the Equator you would weigh 733,50 N, a difference of less than 1%!

As you take precise measurements at different point on the Earth's surface, you find that the value of g varies. Not by very much, but it does vary, and that variation is measurable. Moreover, that measurement is related to the basic equation for gravitational attraction, namely:

F = G Mm/r2

Where:

F is the force between the two gravitating objects
G is Newton's Universal Gravitational Constant (magnitude approximately 6.6 × 10-11)
M is the mass of one of the gravitating objects
m is the mass of the other gravitating object
r is the distance between those objects, or, more correctly, the distance between the centres of gravity of those objects.

Now, if we let M above be the mass of the Earth, and m be the mass of another object (e.g., a human being), then the force experienced by that other object is given by mg, where g is the acceleration due to gravity. Equating the two, we find that:

g = GM/r2

Since G and M are effectively constant, this leaves r as the varying parameter. Consequently, the larger the value of r, the smaller the value of g, and vice versa.

Of course, this elementary analysis neglects a range of effects, but is sufficient to establish why g is slightly greater at the poles than at the equator.

As for the matter of gravitational attraction being slightly greater at the summit of Everest than at sea level, first of all, what is meant here, is that the attraction is greater at the summit of Everest, than it is at a location on the Earth's surface at the same latitude as Everest. This is because, in effect, Everest constitutes a third gravitating body interspersed between ourselves and the rest of the planet. For once, this is a three body problem that is solvable, because all of the bodies are fixed in place, and we don't have to take the complexities of orbital mechanics into account in order to arrive at a reasonable solution. The general three-body problem is of course insoluble, at least from the standpoint of obtaining a closed form analytical solution - one can, however, obtain excellent numerical approximations, some of which are good enough to plot spacecraft trajectories for interplanetary missions. But I digress.

Of course, any precise determination of g at a given location will have to take into account a range of other quantities, such as the various dynamical form factors for Earth, and a host of other complications that I have omitted here, in order to arrive at a complete formula for any given part of the Earth's surface.

Very well explained Calilasseia. While you are on a roll, what's the gravity on Kepler 22b assuming a radius 2.4 greater than Earth and the same material?

a question about light speed

i read somewhere that at the speed of light time stops ... if radio waves travel at the speed of light wouldn't radio waves be transmitted instantly ...

or was the story i read wrong??

I think i got it ... the answer would be no because the radio wave is the onlu thing traveling at light speed

No, it's not the answer.

The faster one goes, the more time slows down. This is known as time dilation; the speed limit is the speed of light. So, anything or anyone traveling at the speed of light experiences no time. For example, let's say that from A to B the distance is one light year. this means that you need to travel at the speed of light for one year to cover that distance.

You, start your journey at point A and a year later you arrive at point B, then a year later you return at point A. For everyone at point A, 2 years have passed, and they would have aged by 2 years. However, since you are traveling at the speed of light, for you, no time has passed, you have not aged at all.

Now, depending on the speed, time slows down according to the equations of special relativity. The faster someone goes, the less time s/he experiences.

However, take care with your frame of reference.

If you want to know more about this, you should read about the special theory of relativity. You do not even need advanced maths for it, simple algebra will do it.