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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

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
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
How this is Accomplished

  • Python Program

  • Newton’s Laws

  • Accurate masses, velocities and distances

  • Leapfrog Acceleration

  • User Prompts


Explanation
Explanation

  • Theory of Gravity Established by Newton

  • Take Note: Seasons determined by 23.5 degree tilt, not distance from the sun


Main equation
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
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
Results (Jupiter Effect)

  • First, Testing the Orbit with Jupiter having zero mass:

  • Notice: Immediately Falls into Circular Orbit


Results jupiter effect1
Results (Jupiter Effect)

  • Next, the Orbit with Jupiter being the mass it is now:

  • Notice Extremely Similar Orbital Pattern (Near Circular Orbit)


Results jupiter effect2
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 effect3
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 effect4
Results (Jupiter Effect)

  • Rotating Elliptical Orbit when Jupiter’s Mass is Multiplied by 500

  • Notice: Elliptical Shift


Results jupiter effect5
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 effect6
Results (Jupiter Effect)

  • Earth’s Orbit when distance was halved:

  • Notice: Similar Orbit created (very close to circular)


Results asteroid
Results (Asteroid)

  • “Average” Asteroid Properties (averaging the properties of about 100 Asteroids data was found on)

  • At the same distance each time:


Results asteroid1
Results (Asteroid)

  • At average velocity and a set distance

  • Notice: It gets pulled into an elliptical orbit as well


Results asteroid2
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 asteroid3
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 asteroid4
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
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
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


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