# Time between farthest and closest distance from Jupiter

1. Sep 13, 2015

### Nathanael

1 Jupiter year is 11.86 Earth years.

The rate of change of the Earth-Sun-Jupiter angle is the difference between Earth and Jupiters angular speeds:
$\frac{1}{365}\big(1-\frac{1}{11.86}\big)\frac{\text{revolutions}}{\text{day}}$

The time between the closest and farthest distances between Jupiter and and Earth (assuming circular orbits) is the time it takes for the Earth-Sun-Jupiter angle to change by 180 degrees:
$0.5\frac{365}{1-\frac{1}{11.86}}\approx199.3 \text{ days}$

Observations give a time interval of about 194.5 days from the farthest distance until the closest distance.

Why this discrepancy between theory and experiment? Is the neglected eccentricity really significant enough to cause this 5 day error, or is there another reason?

2. Sep 13, 2015

### MrAnchovy

Yes. The eccentricity of Jupiter's orbit is such that it's orbital velocity varies by about 10% between aphelion and perihelion.