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## PowerPoint Slideshow about ' The Effect of Jupiter’s Mass on Earth’s Orbit' - galia

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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

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