# Elliptical Orbit

#### brasilr9

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

thanks for help!

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#### siddharth

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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

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brasilr9 said:
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

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siddharth said:
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

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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.

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