Respuesta :
Answer:
r₂ = 38.42 r₁
Step-by-step explanation:
Eccentricity of Ellipse is defined as
e = c /a
Where e is eccentricity, c is distance between the center of the ellipse and the focus, and a is a semi major axis.
Eccentricity is a measure of how divorce of a circular shape is ellipse and its value goes from 0 (circular shape) up to 1 very far away of circular shape
The first Kepler´s law, establishes that planets orbit sun in an elliptical path, having a sun as one focus. But in fact, even that planets move in an ellipse path most of planets in a solar system have a very close circular orbit. Our planet Earth for instance has an eccentricity close to 0,0167, and Pluto which has a biggest one is just 0,25.
If a planet complete one orbit in only 9.5 days, that planet has traveled
2π*r₁ then 9.5 ⇒ 2π*r₁ (length of the orbit)
Earth complete one orbit in 365 days so
365 ⇒ 2*π*r₂
We have a proportion
9.5/2πr₁ = 365 /2πr₂
r₂/r₁ = 365/9.5
r₂/r₁ = 38.42
r₂ = 38.42 r₁
