Question

If the major axis of an ellipse is 16 cm, what is the semimajor axis? If the eccentricity is 0.8, would this ellipse be best described as mostly circular or very elongated?

Answer 1

Answer:

Semi major axis: 8 cm.

The ellipse will be elongated.

Explanation:

Remember that the exccentricity of an elipsis is calculated by dividing the distance from the center to the foci by the distance from the center to the vertices, the closer that ratio is to one the more elongated the ellipse will be, and the closest it is to zero the most circular it will be, in this case the eccentricity is .8 so it would be very elongated.

The semi major axis is always half the major axis of the ellipse so 16/2=8, the semi major axis would be 8.

Answer 2

Answer:

elongated orbit

Explanation:

major axis, a = 16 cm

Semi major axis, = half of major axis = 16 / 2 = 8 cm

e = 0.8

the relation between the minor axis, eccentricity and the length of major axis is given by

$b^{2}=a^{2}(1-e^{2})$

where b be the length of minor axis

$b^{2}=16^{2}(1-0.8^{2})$

b = 9.6 cm

as there is big difference in the length of major axis and the minor axis, so the orbit is elongated.