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

the most elliptical orbit is that of COMETA

Step-by-step 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 =
`√(a^2 - b^2)`

substituting

ε =
`√(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=
`√(1- x) \\ x = ((b)/(a) )^2`

if we expand in series

ε = 1 - x/2

ε=
`1 - (1)/(2) \ (( 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 =
`√(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.