A couple of questions

Red_CCF

I was reading stuff on fictitious forces and encountered a section that said that gravity was a fictitious force. I read a couple of websites but still didn't find a clear enough explanation on why this is true?

Also, if gravity is a fictitious force, then doesn't that mean that so long as we're under its influence we are in an non-inertial frame of reference? Then how is it possible that we achieve an inertial frame of reference on earth if we're always accelerating?

Thanks.

Fernsanz

Think of an elevator. If you weight yourself while the elevator is going upwards your aparent weight will be higher, i.e., it is equivalent to some kind of force pulling you downwards yet that force does not really exist, it is virtual. The same is true for gravity according to general relativity: the earth is moving along the time-space structure which is equivalent to a virtual forced called gravity.

You are right, the earth is not a inertial frame of reference. However, when the acceleration of earth is negligible compared to the ones involed in your experiment you can approximate it for a inertial frame of reference.

I don't know if this is the deep of explanation you were looking for or you need something deeper.

Regards.

Red_CCF

Thanks for the response

I was wondering how this negligible is defined.

I've also been looking at some books which gave me more confusion. In a textbook they explain that it is because of the orbit around the sun that earth is not an inertial frame of reference however they argue that because this centripetal acceleration is much less than gravity, earth is essentially an inertial frame. I believe that they assume gravity was not a fictitious force, can someone clarify what they're trying to say?

Jivesh

You can say that for most of the experiments done, they have a comparatively short duration as compared to the period of revolution of the earth (this time period links to the centripetal acceleration). Now, for the duration of the experiment, the earth is almost moving along a straight line, with extremely small change in the tangential velocity component of the earth. Hence, for these durations, which are extremely small compared to the rotation of the earth around the sun, we can consider the earth as an inertial reference frame. But when we are talking about the gravity of the earth, then also we need to acknowledge the fact the experiments that are conducted are also within the accelerating frame of the earth. So, all the apparatus that we have in an experiment are at rest w.r.t. us and hence we can safely apply the laws of physics to these experiments, as would be done in an inertial frames, those experiments are done in a frame at rest w.r.t. us.

Red_CCF

Okay so basically, because everything (experiment and say me as the frame of reference) is under the influence of the same acceleration due to gravity, essentially its effect can be neglected?

Fernsanz

No. What Jivesh means is that there are two different concepts involved. On one hand is the non-inertial frame nature of the earth because it is rotating around Sun. On the other is gravity which has nothing to do with the rotation but that came up in you OP question.

The earth is non-inertial in general, but as Jivesh has explained, during most experiments lifetime it can be considered inertial. So, when you consider the earth as an inertial frame the gravity is another force like any other.

A third concept is where de gravity comes form, which again has nothing to do with two previous concepts. Here is where my answer about space-time and gravity as virtual force fits.

Red_CCF

I'm still a bit confused about the gravity part of my question and I guess I didn't understand your explanations clearly. So can one argue that a still object on earth (perhaps a standing person) is a non-inertial frame based on the fact that he/she is under the influence of gravity (ignoring the fact that it's rotating around the Sun)? Why or why not?

For a circular motion, doesn't any infinitesimal change in velocity over an infinitesimal time have the same (or in a oval trajectory similar) centripetal acceleration? I thought that centripetal acceleration is constant for any change in velocity or am I mistaken?


Thanks.