# Velocity in eliptical trajectories

• MMS
In summary, the conversation discusses finding the minimal velocity of a particle to reach a specific point, using conservation of energy. However, it is also important to consider the radial and tangential velocities during its motion, which can be calculated through conservation of momentum.
MMS
Hello everyone,

A little question bothering me concerning elliptical trajectories:
Say I have a particle at some point with some velocity (both I know - r0, v0) and I need know its minimal velocity so that it reaches some specific r*.
I can easily find this velocity considering conservation of energy.

However, where do the radial and tangential velocities during its motion come into consideration here? Is this calculation right?

Thanks in advance.

Kinetic and potential energies depend on magnitudes not directions - so the components are figures in automatically.
If you use conservation of momentum calculations instead you'll see where the components go.

## 1. What is velocity in an elliptical trajectory?

Velocity in an elliptical trajectory refers to the speed and direction at which an object moves along its elliptical path. It is a vector quantity that takes into account both the magnitude and direction of the object's motion.

## 2. How is velocity calculated in an elliptical trajectory?

The velocity in an elliptical trajectory can be calculated using the formula v = √(μ((2/r) - (1/a))), where μ is the standard gravitational parameter, r is the distance between the object and the focus of the ellipse, and a is the semi-major axis of the ellipse.

## 3. Does the velocity change in an elliptical trajectory?

Yes, the velocity in an elliptical trajectory is not constant. It varies depending on the position of the object along the elliptical path. As the object moves closer to the focus of the ellipse, its velocity increases, and as it moves away, its velocity decreases.

## 4. What factors affect the velocity in an elliptical trajectory?

The velocity in an elliptical trajectory is affected by the mass of the objects involved, the distance between them, and the shape and orientation of the ellipse. Other factors such as external forces, such as gravitational pull from other objects, can also influence the velocity.

## 5. How does velocity in an elliptical trajectory compare to that in a circular trajectory?

In a circular trajectory, the velocity remains constant, whereas in an elliptical trajectory, it varies. Additionally, the velocity in an elliptical trajectory is highest at the point of closest approach to the focus, while in a circular trajectory, it is constant throughout the entire path.

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