# Is Earth an Inertial Frame?

Q:
Earth is a non inertial frame, then why newton's 1st and 3rd are appicable on earth?
- Varun (age 15)
India
A:
If one tries to treat the Earth as an inertial frame, one gets violations of Newton's laws. Here are some:

1. You get Coriolus forces causing torques on things as they go up or down. These forces have no source, hence violate Newton's laws.

2. You get precessions of Foucault pendula, again inexplicable if you treat the Earth as an inertial frame.

Notice that both these effects are due to the Earth's spin.  The effects due to the Sun's gravity drop out locally, because in general relativity a free-fall trajectory is in fact the closest thing there is to an inertial frame. However, if you try to treat a fixed position on the Erath's surface as inertial, then obviously you have to call gravity from the Earth a force. Then you'd be hard put to explain why you don't treat gravity from other objects as forces. Certainly tidal effects fit that picture. Once you do, Newton's laws themselves tell you that the Earth's orbital motion also makes it a non-inertial frame.

In many little experiments you can ignore these effects because the regions involved are too small for tidal effects to be important and the forces involved are large compared to the gravitational force from the Sun on the objects studied.

Mike W.

(published on 04/21/2013)

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