Lets assume a body with a certain mass is in a region of space that has zero $g$ (or pretty close to zero $g$).

  1. Would acceleration in a straight line produce $g$-forces?

  2. Would that mass acquire weight?

  3. Would moving at a constant speed in a tight circle produce $g$-forces?


Let's be clear what we mean by weight. Suppose you are holding an accelerometer then you are weightless if the accelerometer reads zero and your weight is non-zero if the accelerometer reads some non-zero value $a$. Your weight is then simply $ma$ where $m$ is your mass.

So for example the accelerometer in the smartphone in my pocket currently reads 1g so my weight is around 65g (my mass is around 65 kilos). If I were inside the international space station my phone accelerometer would read zero and I would be weightless (as any number of videos from the ISS will show).

Now we've established this, it should be obvious that acceleration in a straight line and the centripetal acceleration in circular motion both result in a non-zero weight.

I would guess you're really interested in whether this weight is the same whether the acceleration is due to gravity or whether it's due to a change in velocity. The answer is that yes it is the same, and indeed this is (one form of) the Einstein equivalence principle. More precisely the equivalence principle tells that acceleration and gravity are locally equivalent.

For more on this you may want to read the answers to Is it always possible to determine whether or not one is accelerating?, or search this site for more.

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  • $\begingroup$ Thankyou! You not only answered my question, but thought of a better question to ask. $\endgroup$ – Amphibio Dec 24 '15 at 0:24
  • $\begingroup$ So does this mean that mean that standing on earth, I am continually accelerating upwards with a force of 1g? If so, the only way not to be accelating - from the inertial frame of the spacetime field - would be to be in freefall towards the centre of the planet? Does that mean that the gravitational field is moving at a 'speed' of 1g towards earth.....? $\endgroup$ – Amphibio Dec 24 '15 at 0:37
  • $\begingroup$ @JoshCoppersmithHeaven: Yes. Yes. No. $\endgroup$ – John Rennie Dec 24 '15 at 0:41
  • $\begingroup$ I like the brevity. But in regards to the last part, why not? If we took away atmospheric friction, an apple and an elephant would fall at exactly the same speed towards earth. So that means the earth is bending spacetime a specific amount, and objects travel through it / are carried along it at a specific rate. Does this not mean that a certain gravitational field has a certain speed, relative to an object in zero g? $\endgroup$ – Amphibio Dec 24 '15 at 12:16
  • $\begingroup$ @JoshCoppersmithHeaven: gravitational fields aren't physical objects and don't have velocities. Have a look at this answer of mine to see why things fall in a gravitational field. $\endgroup$ – John Rennie Dec 24 '15 at 12:23

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