- #1
Calculate Tangential & Normal Acceleration of Particle in Elliptical Orbit
- Thread starter brasilr9
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- Elliptical orbit Orbit
In summary, when a particle is moving in an elliptical orbit with uniform speed, there will be no tangential acceleration due to the constant speed. However, there will always be normal acceleration as the direction of velocity continuously changes with the angle. For a circular orbit, the tangential acceleration will also be zero due to the constant rate of change of radius.
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siddharth
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You can show your work for a start.
- #3
brasilr9
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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.
Since it's speed is constant, there's is no change in tangential velocity, hence tangential acceleration remain zero.
- #4
Hootenanny
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brasilr9 said:
That's correct.
Now what about the normal acceleration?- #5
Hootenanny
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siddharth said:
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.
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siddharth
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What I posted first wasn't exactly correct
What I mean is, if
[tex] \vec{r} = r \vec{e_r} [/tex]
then according to the OP's question,
[tex] |\frac{d\vec{r}}{dt}| [/tex] will be constant. So, for an ellipse, this doesn't mean that [tex] \frac{d^2\vec{r}}{dt^2} [/tex] along [tex] e_\phi [/tex] will be 0.
In fact, for a circular orbit, since [tex] \frac{dr}{dt} =0 [/tex], the tangential acceleration will be 0.
What I mean is, if
[tex] \vec{r} = r \vec{e_r} [/tex]
then according to the OP's question,
[tex] |\frac{d\vec{r}}{dt}| [/tex] will be constant. So, for an ellipse, this doesn't mean that [tex] \frac{d^2\vec{r}}{dt^2} [/tex] along [tex] e_\phi [/tex] will be 0.
In fact, for a circular orbit, since [tex] \frac{dr}{dt} =0 [/tex], the tangential acceleration will be 0.
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FAQ: Calculate Tangential & Normal Acceleration of Particle in Elliptical Orbit
What is tangential acceleration in an elliptical orbit?
Tangential acceleration in an elliptical orbit is the acceleration of a particle along the tangent of its orbit. It is caused by the change in the particle's speed as it moves along its orbit.
How is tangential acceleration calculated in an elliptical orbit?
Tangential acceleration in an elliptical orbit can be calculated using the formula: at = (v²) / r, where v is the speed of the particle and r is the distance from the particle to the center of the orbit.
What is normal acceleration in an elliptical orbit?
Normal acceleration in an elliptical orbit is the acceleration of a particle towards the center of its orbit. It is caused by the change in the particle's direction as it moves along its orbit.
How is normal acceleration calculated in an elliptical orbit?
Normal acceleration in an elliptical orbit can be calculated using the formula: an = (v²) / r, where v is the speed of the particle and r is the distance from the particle to the center of the orbit. The direction of normal acceleration is always towards the center of the orbit.
How are tangential and normal accelerations related in an elliptical orbit?
In an elliptical orbit, tangential and normal accelerations are always perpendicular to each other. This means that they act at right angles to each other and do not affect each other's magnitude. The combination of these two accelerations results in the particle moving in a curved path along its elliptical orbit.