Finding Maximum Distance from Sun

• colourpalette
In summary, to find the maximum distance from the Sun for an extreme elliptical orbit with a semi-major axis of 26, we can use the equation for eccentricity and the fact that the sun is at a focus of the ellipse. As the eccentricity increases, the distance between the foci approaches the major axis and the perihelion becomes closer to the sun. By using the equation for perihelion and aphelion, we can calculate the maximum distance from the Sun to be approximately 51.995 AU.
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Homework Statement

Find the maximum (aphelion) distance from the Sun for extreme elliptical orbit. (Semi-Major axis = 26)

Homework Equations

Eccentricity = Distance between foci/Length of major axis
Major Axis = 2 * Semi-Major Axis
Major Axis = Perihelion + Aphelion

The Attempt at a Solution

Eccentricity = Distance / (26*2) = Distance / 52
Eccentricity of an elliptical orbit is between 0 and 1, 0 being a circle.
What eccentricity should I be using for an extreme elliptical orbit?
My best guess would be right under 1 (ex: 0.99) but I'm not sure if that makes sense. (Would it be too close to the sun?)

Then once I have the distance between the foci, I would do semi-major axis - 1/2 distance between foci, in order to get the perihelion. From there I can get the aphelion.

What is the smallest possible value for perihelion?

Hm I'm not sure how to find this, it's not anywhere in my textbook and I've tried Googling this too. What can I do to find the smallest perihelion value?

Think about it for a bit. If I gave you any better hint than I did I would have given the answer away.

Remember that the sun is at a focus of the ellipse.
How does the distance between foci (and shape and position of the ellipse) change as the eccentricity becomes larger?

D H said:
Think about it for a bit. If I gave you any better hint than I did I would have given the answer away.

Hm.. The closest a comet can get without going through the sun would be r(comet)+r(sun), but that would mean it's touching the sun. It would have to be a little bigger than this? Am I on the right track?

mnova said:
Remember that the sun is at a focus of the ellipse.
How does the distance between foci (and shape and position of the ellipse) change as the eccentricity becomes larger?

As the eccentricity increases, the orbit goes from being a circle to a line, so the distance of the foci approaches the major axis of the whole orbit.. I'm not sure where to go from there.

colourpalette said:
Hm.. The closest a comet can get without going through the sun would be r(comet)+r(sun), but that would mean it's touching the sun. It would have to be a little bigger than this? Am I on the right track?
Correct. So what does this tell you about perihelion, and thus about apihelion? (Hint: You know what the semi-major axis is.)

D H said:
Correct. So what does this tell you about perihelion, and thus about apihelion? (Hint: You know what the semi-major axis is.)

This means the perihelion is r(comet) + r(sun)? And therefore the aphelion would be 2(semi-major axis) - perihelion.
Aphelion = 2(26AU * 149 598 000 km/AU) - r(comet) - r(sun)
= 7 779 096 000 km - r(comet) - 695 500 km
I don't know the r(comet) but I'm assuming it would be negligible at this point? If so I'd get *huge number* and converting it back to AU would make it 51.995 AU! Is this correct?

Correct.

Thank you!

1. What is the maximum distance from the sun in the solar system?

The maximum distance from the sun in the solar system is approximately 4.5 billion kilometers. This distance is known as the aphelion and is the farthest point in an object's orbit around the sun.

2. How is the maximum distance from the sun calculated?

The maximum distance from the sun is calculated using Kepler's third law of planetary motion, which states that the square of an object's orbital period is directly proportional to the cube of the semi-major axis of its orbit. By knowing the orbital period and semi-major axis of a planet or object, the maximum distance from the sun can be calculated.

3. Which planet has the greatest distance from the sun?

The planet with the greatest distance from the sun is Neptune, with an average distance of approximately 4.5 billion kilometers. However, due to the elliptical shape of its orbit, Neptune's maximum distance from the sun can vary. At its aphelion, Neptune can be as far as 4.55 billion kilometers from the sun.

4. Can the maximum distance from the sun change?

Yes, the maximum distance from the sun can change due to the elliptical shape of an object's orbit. The orbit of a planet or object can vary in shape and size over time, causing its maximum distance from the sun to fluctuate.

5. What factors affect the maximum distance from the sun?

Some factors that can affect the maximum distance from the sun include gravitational forces from other planets, the shape and size of an object's orbit, and external forces such as comets or meteors. These factors can cause changes in an object's orbit and therefore affect its maximum distance from the sun.

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