Why do we treat earth and why does it work as an inertial frame

[1MileCrash]

Earth is clearly not an inertial frame, its in orbit and not following a single direction of movement.

Why then do we treat it as one?

Are there any slight differences in the laws of motion in a true inertial frame in contrast with those on earth?

 

[Mentz114]

Orbiting the sun would not make the frame non-inertial, because an orbit is a geodesic. It's the fact that we are not on a geodesic that disqualifies the 'dirt' frame.

You'll prpbably recall seeing video of people floating about in the sapce-stations, as if they were in the 'vomit comet'.

See

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

Excuse me, where's that bucket ?

 

[Passionflower]

Earth is clearly not an inertial frame, its in orbit and not following a single direction of movement.

Why then do we treat it as one?

The Earth travels more or less inertially, since its rotation, mass and volume has a negligible effect on its orbit. The change in direction is due to spacetime curvature.

 

[ghwellsjr]

We treat the Earth as an inertial frame in our thought experiments to make them simpler and because we are examining some feature of Special Relativity where we want to ignore the motions and gravitational effects of the earth.

There are slight differences in a true inertial frame compared to those on Earth but they are so slight that we can ignore them most of the time, especially when limiting the discussion to Special Relativity.

Just think about the notion of a twin traveling at half the speed of light for 1 year. We are just pretending. Except for tiny particles traveling in circles, we cannot accelerate anything to anywhere near the speed of light and we cannot do it for any length of time. It's all pretend. But we are always pretending when explaining concept in physics. If we say two twins are located in the same place, we don't really mean that, we just mean for purposes of our discussion, we will treat them as if they were in the same place because the very small difference that we would have to take into account to be perfectly accurate and precise would make the problem so cumbersome that we would lose sight of the relevant feature that we were trying to examine.

 

[D H]

Why then do we treat it as one?

Because in some circumstances we can do so without losing much accuracy. Third body effects are rather small perturbations. Even the Earth's rotation rate can be ignored in lots of settings. Suppose you are using a barometer to measure the height of a building by measuring the time it takes the barometer to fall from the top of the building to the ground. This is a crude measurement; does it really matter that you are ignoring that the Earth is not an inertial frame?

 

[pervect]

Earth is clearly not an inertial frame, its in orbit and not following a single direction of movement.

Why then do we treat it as one?

Are there any slight differences in the laws of motion in a true inertial frame in contrast with those on earth?

As others have mentioned, if you actually work out the effects of the Earth orbiting, they are small. You basically have a rotation rate of once/year (dwarfed by the fact that the Earth's natural rotation is greater than that, once per day), plus the small tidal effects from the sun.


For some discussion of the later see http://hyperphysics.phy-astr.gsu.edu/hbase/tide.html

 

[D H]

You basically have a rotation rate of once/year

In Newtonian mechanics this is not a rotating frame. It is an accelerating but non-rotating frame that happens to be following a curved path. There is a tiny effect here in general relativity, de Sitter precession. For the Earth's motion about the Sun, this is *tiny*.

plus the small tidal effects from the sun.

That is what I meant when I said "third body effect": Third body acceleration = tidal gravity. The term "third body effect" is used in the aerospace community and by some astronomers because "tidal gravity" has a completely different meaning in their world. The Sun and the Moon raise tides on the Earth. Those tides change the shape of the Earth and that in turn results in some very tiny perturbations on a satellite's orbit.