The Effect of Jupiter’s Mass on Earth’s Orbit

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The Effect of Jupiter’s Mass on Earth’s Orbit. Also Distance/Velocity Tests to Observe When an Asteroid Falls Into Orbit. Anthony White. Purpose. First to find the dependence of Earths orbit on the mass and relative distance of Jupiter

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### The Effect of Jupiter’s Mass on Earth’s Orbit

Also Distance/Velocity Tests to Observe When an Asteroid Falls Into Orbit

Anthony White

Purpose
• First to find the dependence of Earths orbit on the mass and relative distance of Jupiter
• Second to find out what it takes to put a traveling asteroid into orbit by changing the velocity, distance and mass
How this is Accomplished
• Python Program
• Newton’s Laws
• Accurate masses, velocities and distances
• Leapfrog Acceleration
• User Prompts
Explanation
• Theory of Gravity Established by Newton
• Take Note: Seasons determined by 23.5 degree tilt, not distance from the sun
Main Equation
• Force Created (Inverse Square Law):
• Where m1 and m2 are two masses and r is the distance between
Effects of Elliptical Orbit on Earth?
• Well, not many
• Sunlight falling during the perihelion is about 7% more intense
• However, the northern hemisphere has more land, while the southern hemisphere has more water, which makes only a moderate impact on the differences between perihelion and aphelion
Results (Jupiter Effect)
• First, Testing the Orbit with Jupiter having zero mass:
• Notice: Immediately Falls into Circular Orbit
Results (Jupiter Effect)
• Next, the Orbit with Jupiter being the mass it is now:
• Notice Extremely Similar Orbital Pattern (Near Circular Orbit)
Results (Jupiter Effect)
• Next, the Orbit with Jupiter’s mass being 100 times greater:
• Notice: Height of Curve has increased due to greater eccentricity. Also notice the graph on the distance from the sun shows this elliptical effect.
Results (Jupiter Effect)
• Next, the Orbit with Jupiter’s mass being 500 times greater:
• Notice: Greater Eccentricity still, as well as that ellipse itself is rotating around the sun (following Jupiter’s orbit)
Results (Jupiter Effect)
• Rotating Elliptical Orbit when Jupiter’s Mass is Multiplied by 500
• Notice: Elliptical Shift
Results (Jupiter Effect)
• Earth’s Orbit when Jupiter’s Mass is Multiplied by 1000
• Notice: Gravitational attraction from Jupiter great enough to pull earth out of the orbit
Results (Jupiter Effect)
• Earth’s Orbit when distance was halved:
• Notice: Similar Orbit created (very close to circular)
Results (Asteroid)
• “Average” Asteroid Properties (averaging the properties of about 100 Asteroids data was found on)
• At the same distance each time:
Results (Asteroid)
• At average velocity and a set distance
• Notice: It gets pulled into an elliptical orbit as well
Results (Asteroid)
• At half velocity and a set distance
• Notice: It gets pulled into an elliptical orbit as well, except it is much thinner
Results (Asteroid)
• At quarter velocity and a set distance
• Notice: It gets pulled into an elliptical orbit that is even still tighter (also notice the ellipse is beginning to shift)
Results (Asteroid)
• At double velocity from same distance:
• Notice: This is above the escape velocity needed to escape the simple solar system
Conclusion (Jupiter’s Mass)
• As the mass of Jupiter is increased, the orbit of the Earth goes from being more circular to elliptical
• Also that elliptical rotation itself will begin to shift around the sun as it follows Jupiter
• If the mass is increased too much the Earth will eventually escape the pull from the Sun
Conclusion (Asteroid)
• As the velocity is lower, the ellipse that is created decreases more and more in width.
• It also still shifts around the sun
• If the velocity is doubled then it is above escape velocity for the attraction from the Sun, Earth and Jupiter