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Similarities
Jupiter and Earth have some well-known, basic similarities such as they both are within the same solar system, thus revolve around the sun, and both have at least one moon. Other not so widely known commonalities include their densities, orbit eccentricities, atmospheric changes, auroras and mesoscale convective systems.
Densities
Where the raw numbers of many Jupiter-to-Earth comparisons appear distant, sometimes percentages tell a different story. This is especially so when including the comparative data of other planets that are much closer to Earth in size, structure and distance from the sun. Jupiter's density is 1.326 g/cm3 and Earth's is 5.513 g/cm3. And yet according to NASA, this translates to Jupiter's density only being 0.241 times that of Earth. This is significantly similar considering that Mercury is 0.984 and Mars is 0.714 times that of Earth, both of which are much closer to Earth's size.
Orbit Eccentricities
Generally all planets and many other celestial bodies exhibit orbital eccentricities. This means that their orbits have varying degrees of elliptical paths as opposed to perfect circles. Jupiter's orbit eccentricity is 0.04838624 and Earth's is 0.01671123. NASA cites that this equates to Jupiter's being 2.895 times that of Earth. Yet compared with Mars at 5.589 and Mercury at 12.305, Jupiter's orbit eccentricity is much more similar to Earth's despite it being much larger and farther away from Earth.
Atmospheric Changes
Periodically, Earth experiences alternating patterns of wind in its stratosphere that occur near the equator. These changing stratospheric wind patterns are called quasi-biennial oscillations. Jupiter also experiences stratospheric changes in the methane hovering above its equator, which are similar to Earth's quasi-biennial oscillations. Additionally, this translates to alternating cold and warm periods in the stratosphere for both Jupiter and Earth.
Auroras
Auroras are emissions of light within a planet's atmosphere that are primarily caused by excited nitrogen or oxygen atoms. Depending on the altitude and type of atoms involved, auroras generally appear red, green or purple in color. Auroras occur on both Jupiter and Earth, with Earth's auroras also being called aurora borealis, northern lights and southern lights.
Mesoscale Convective Systems
Mesoscale convective systems are large-scale, long-lasting thunderstorm complexes that are categorized by extreme conditions including cyclones, hail and tremendous amounts of rain. These systems occur on both Jupiter and Earth, with the only difference being their heat sources. Where Earth's storms are perpetuated by heat from the Sun, Jupiter's storms are enabled by heat from the planet's core.