The Effect of Jupiter

1
The Effect of Jupiters Mass on Earths Orbit

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

Anthony White
2
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

3
How this is Accomplished

• Python Program
• Newtons Laws
• Accurate masses, velocities and distances
• Leapfrog Acceleration
• User Prompts

4
Explanation

• Theory of Gravity Established by Newton
• Take Note Seasons determined by 23.5 degree
  tilt, not distance from the sun

5
Main Equation

• Force Created (Inverse Square Law)
• Where m1 and m2 are two masses and r is the
  distance between

6
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

7
Results (Jupiter Effect)

• First, Testing the Orbit with Jupiter having zero
  mass
• Notice Immediately Falls into Circular Orbit

8
Results (Jupiter Effect)

• Next, the Orbit with Jupiter being the mass it is
  now
• Notice Extremely Similar Orbital Pattern (Near
  Circular Orbit)

9
Results (Jupiter Effect)

• Next, the Orbit with Jupiters 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.

10
Results (Jupiter Effect)

• Next, the Orbit with Jupiters mass being 500
  times greater
• Notice Greater Eccentricity still, as well as
  that ellipse itself is rotating around the sun
  (following Jupiters orbit)

11
Results (Jupiter Effect)

• Rotating Elliptical Orbit when Jupiters Mass is
  Multiplied by 500
• Notice Elliptical Shift

12
Results (Jupiter Effect)

• Earths Orbit when Jupiters Mass is Multiplied
  by 1000
• Notice Gravitational attraction from Jupiter
  great enough to pull earth out of the orbit

13
Results (Jupiter Effect)

• Earths Orbit when distance was halved
• Notice Similar Orbit created (very close to
  circular)

14
Results (Asteroid)

• Average Asteroid Properties (averaging the
  properties of about 100 Asteroids data was found
  on)
• At the same distance each time

15
Results (Asteroid)

• At average velocity and a set distance
• Notice It gets pulled into an elliptical orbit
  as well

16
Results (Asteroid)

• At half velocity and a set distance
• Notice It gets pulled into an elliptical orbit
  as well, except it is much thinner

17
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)

18
Results (Asteroid)

• At double velocity from same distance
• Notice This is above the escape velocity needed
  to escape the simple solar system

19
Conclusion (Jupiters 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

20
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