Calculate Tangential & Normal Acceleration of Particle in Elliptical Orbit

[brasilr9]

A particle is moving in a elliptical orbit with uniform speed. How can I tell whether there are tangential and normal acceleration or not on the particle? (At A B and C )


thanks for help!

 

[siddharth]

You can show your work for a start.

 

[brasilr9]

I think I figure it out.
Since it's speed is constant, there's is no change in tangential velocity, hence tangential acceleration remain zero.

 

[Hootenanny]

Since it's speed is constant, there's is no change in tangential velocity, hence tangential acceleration remain zero.

That's correct. Now what about the normal acceleration?

 

[Hootenanny]

Is it? The direction of $$e_\phi$$ continously changes with $\phi$. So, even if the speed is the same, the direction of velocity changes, doesn't it? So how can the tangential acceleration (ie, acceleration along $$e_\phi$$) be the same?

Ahh yes, I suppose constant magnitude would be an accurate term. Just re-reading through the question (and without looking at the picture obviously), I can't see the point. There is always going be tangental acceleration, and there also must always be normal acceleration, although this will change.

 

[siddharth]

What I posted first wasn't exactly correct

What I mean is, if
$$\vec{r} = r \vec{e_r}$$

then according to the OP's question,
$$|\frac{d\vec{r}}{dt}|$$ will be constant. So, for an ellipse, this doesn't mean that $$\frac{d^2\vec{r}}{dt^2}$$ along $$e_\phi$$ will be 0.

In fact, for a circular orbit, since $$\frac{dr}{dt} =0$$, the tangential acceleration will be 0.