Answer:
the most elliptical orbit is that of COMETA
Explanation:
The eccentricity of a curve in defined as the ratio between lacia to the focus, called c and the value of the axis greater than
ε = c / a
if we use Pythagoras' theorem
c = [tex]\sqrt{a^2 - b^2}[/tex]
substituting
ε = [tex]\sqrt{1 - (b/a)^2 }[/tex]
if ε = 0 we have a circumference
In the diagram presented the orbit of the comet is an ellipse a> b
ε=[tex]\sqrt{1- x} \\ x = (\frac{b}{a} )^2[/tex]
if we expand in series
ε = 1 - x/2
ε= [tex]1 - \frac{1}{2} \ (\frac{ b}{a} )^2[/tex]
if we neglect the non-linear terms
ε = 1
Earth's orbit is a small ellipse
b / a = 149 10⁶ / 151 10⁶
b / a = 0.98675
ε = [tex]\sqrt{1- 0.98675^2}[/tex]
ε = 0.16
a very small ellipse
Planet X, despite not having data, it seems that the sun is in the scepter of the orbit, so b = a
therefore both the semi-axes of the curve
e = a / b
Consequently, the most elliptical orbit is that of COMETA.
