Is Constant Acceleration Possible in Elliptical Motion?

In summary, the acceleration of an ellipse is the rate of change of velocity in an elliptical path and can be calculated using the formula a = v^2/r. It varies at different points along the path due to changing speed and direction of the object, and can be affected by factors such as mass, shape, and external forces. The acceleration of an ellipse differs from that of a circle in that the velocity and direction constantly change in an ellipse, while it remains constant in a circle, and the direction of acceleration can change in an ellipse while it remains towards the center in a circle.
  • #1
SprucerMoose
62
0
G'day all,
I was doing some maths homework and found the acceleration of a particle moving in an ellipse to be constant. Is this correct?

I would have thought that a constant acceleration would give a circle.
 
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  • #2
That would only be correct in certain special cases (and the particle speed would not be constant). Your intuition was somewhat correct - a constant (magnitude) of acceleration perpendicular to the velocity vector of an object will lead to a circle, but a circular path isn't the only possibility with constant acceleration.
 
  • #3
Thanks
 

Related to Is Constant Acceleration Possible in Elliptical Motion?

What is the definition of acceleration of an ellipse?

The acceleration of an ellipse is the rate of change of the velocity of an object moving in an elliptical path. It is a vector quantity that indicates the direction and magnitude of the change in velocity.

How is the acceleration of an ellipse calculated?

The acceleration of an ellipse can be calculated using the formula a = v^2/r, where a is the acceleration, v is the velocity, and r is the radius of the ellipse at a specific point.

Does the acceleration of an ellipse change at different points?

Yes, the acceleration of an ellipse changes at different points along the path due to the changing direction and speed of the object. The acceleration is highest at the two focal points of the ellipse and decreases as the object moves closer to the center.

What factors can affect the acceleration of an ellipse?

The acceleration of an ellipse can be affected by the mass of the object, the shape and size of the ellipse, and any external forces acting on the object such as gravity or friction.

How does the acceleration of an ellipse differ from that of a circle?

The acceleration of an ellipse is different from that of a circle because the velocity and direction of the object constantly change in an ellipse, while in a circle the velocity remains constant. Additionally, the acceleration in a circle is always directed towards the center, while in an ellipse it can change direction depending on the position of the object.

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