Question

Does the eccentricity of the orbit increase or decrease as you shorten the initial distance of the planet from the star? Why would this be the case? (Based on my data the eccentricity of orbit decreased with shorter initial distances between the planet and star. Please explain why that is. Data is shown below)

Trial	Initial distance (thousand miles)	d (thousand miles)	c (thousand miles)	T (days)	Ti2/T02	di2/d02	eccentricity
0	91500	186000	185950	365			0.02
1	75000	128045	126422	210	0.331	0.326	0.16
2	62384	96656	91582	136	0.139	0.140	0.30
3	5000	69009	62203	83	0.052	0.051	0.43

Answer 1

The eccentricity of the orbit decrease as you shorten the initial distance of the planet from the stars.

Explanation on the basis of keplers laws:-

The orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit, and greater than 1 is a hyperbola. The eccentricity defines the shape of the ellipse. Given the semi-major axis distance a and the eccentricity 0 <e< 1, then the perihelion distance is a (1-e) and the aphelion distance is a(1 + e). The orbits of most of the planets have a small eccentricity and are nearly circular so their distance from the sun doesn't vary much. The orbits of comets have a high eccentricity so their distance from the sun varies significantly over the orbit. The eccentricity defines the shape of the ellipse.Hence, The larger the distance between the foci, the larger the eccentricity of the ellipse.
The eccentricity of Earth's orbit is very small, so Earth's orbit is nearly circular. Earth's orbital eccentricity is less than 0.02. The orbit of Pluto is the most eccentric of any planet in our Solar System. Pluto's orbital eccentricity is almost 0.25. Many comets have extremely eccentric orbits.Halley's Comet, for instance, has an orbital eccentricity of almost 0.97! The Sun is not at the center of an elliptical orbit. It is a little off to one side, at a point called a "focus" of the ellipse. Because of this offset the planet moves closer to and further away from the Sun every orbit. The close point in each orbit is called perihelion. The far away point is called aphelion. If an orbit has a large eccentricity, the difference between the perihelion distance and the aphelion distance will also be large.