How To Find Eccentricity | The Science



The Science

How to find eccentricity

Eccentricity is called a numerical characteristic of a conic section (figure resulting at the intersection of a plane and a cone). Eccentricity is not changed by the plane of motion, as well as the similarity transformations (resizing when saving the form). Figuratively speaking, the eccentricity is a characteristic form ( "flattening", in the case of an ellipse) shape, not its size.

How to find eccentricity

You will need:

- compass; - Line; - Calculator.

Instruction how to find eccentricity

Step 1:

If you set the focus and directrix of a conic section, then to find eccentricity use the definition of this class of figures. All non-degenerate conic sections (except the circle) can be constructed as follows: - select a point on the plane and the line - set a positive real number e - tick all the points for which the distance to the selected point and to direct different e times.

Step 2:

The selected point is called the focus of the conic section, straight - headmistress, and the number of e - eccentricity. Depending on the number e, there are four types of conic sections: - at e1 - hyperbole; - For e = 0 - circle (conventionally).

Step 3:

Based on the definition, in order to find the eccentricity of the conic section: - select in this figure an arbitrary point - Measure the distance from this point to the section of the focus - measure the distance from this point to the headmistress (for this, lower the directrix perpendicular and determine the point of intersection headmistress and perpendicular); - divide the distance from a point to focus on the distance from the point to the headmistress.

Step 4:

If you know the lengths of the major and minor axes of the ellipse (its "length" and "width"), then to calculate the eccentricity use the following formula: f = √ (1-a² / A²), where a, A - the length of the minor and major axes (or semi-axes), respectively.

Step 5:

If the terms of the task given radius Apsis ellipse, then to find the eccentricity, apply the following formula: e = (Ra-Rp) / (Ra + Rp), wherein Ra and Rp - radius Apsis ellipse, respectively (radius apocenter called the distance from the focus of the ellipse to the most distant point; pericenter radius is the distance from the focus of the ellipse to the least of the point).

Step 6:

If you know the distance between the foci of the ellipse and the length of its major axis, the eccentricity calculation simply divide the distance between the foci on the axis length: f = f / A, where f - the distance between the foci of the ellipse.