Question

the diagram below represents the orbits of earth, comet temple-tuttle, and planet x, another planet in out solar system. arrows on each orbit represent the direction of movement. which objects orbit would have and eccentricity close to 1?

Answer 1

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 = $\sqrt{a^2 - b^2}$

   substituting

           ε = $\sqrt{1 - (b/a)^2 }$

if   ε = 0 we have a circumference

In the diagram presented the orbit of the comet is an ellipse a> b

          ε=$\sqrt{1- x} \\ x = (\frac{b}{a} )^2$

if we expand in series

             ε = 1 - x/2  

             ε=  $1 - \frac{1}{2} \ (\frac{ b}{a} )^2$

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 = $\sqrt{1- 0.98675^2}$

               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.