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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