How can the acceleration of a body in an ellipse always point towards a focus?

In summary, the conversation discusses the proof for the acceleration of a body moving with constant speed in an ellipse, which is always directed towards one of the focus points. The speaker suggests asking for a vector equation for the path of a particle traveling in an ellipse, and mentions the possibility of different methods for solving the problem. They also mention the importance of showing their work in order to determine the most suitable method.
  • #1
prabhat rao
15
0
prove that the acceleration of a body moving with constant speed in ellipse is always directed towards one of the focus .
I have tried but my efforts have gone in vain
 
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  • #2
Can you write me a vector equation for the path of a particle traveling in an ellipse?
 
  • #3
Hootnannty indicates our problem! I can think of several ways of doing this, some involving simple but VERY tedious mathematics (I wouldn't want to do it that way!), others involving short calculations but much deeper mathematics. If you don't show us anything of your work (you tell us you have made efforts but don't describe them), we don't know what methods you can use.
 

FAQ: How can the acceleration of a body in an ellipse always point towards a focus?

What is acceleration in an ellipse?

Acceleration in an ellipse refers to the change in velocity of an object moving along an elliptical path. It is a vector quantity that takes into account both the magnitude and direction of the change in velocity.

How is acceleration calculated in an ellipse?

Acceleration in an ellipse can be calculated using the equation a = v^2 / r, where a is the acceleration, v is the velocity, and r is the radius of the ellipse at a given point.

Is acceleration constant in an ellipse?

No, acceleration is not constant in an ellipse. This is because the direction of the velocity vector is constantly changing as the object moves along the elliptical path.

What is the relationship between acceleration and speed in an ellipse?

The relationship between acceleration and speed in an ellipse is that acceleration is directly proportional to the square of the speed. This means that as the speed increases, the acceleration also increases.

How does acceleration in an ellipse affect the motion of an object?

Acceleration in an ellipse affects the motion of an object by causing it to change direction as it moves along the elliptical path. This change in direction is due to the changing velocity vector, which is a result of the changing acceleration.

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