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What is the difference between a circle and an ellipse?
-- the eccentricity or -- the distance between the foci or -- the ratio of the major and minor axes
When the distance between the foci of an ellipse is increased the eccentricity of the ellipse will?
When the distance between the foci of an ellipse increases, the eccentricity of the ellipse also increases. Eccentricity is a measure of how much an ellipse deviates from being circular, calculated as the ratio of the distance between the foci to the length of the major axis. As the foci move further apart, the ellipse becomes more elongated, leading to a higher eccentricity value. Therefore, an increase in the distance between the foci results in a more eccentric ellipse.
How does the eccentricity of an ellipse change as the foci get closer together?
As the foci of an ellipse move closer together, the eccentricity of the ellipse decreases. Eccentricity is a measure of how elongated the ellipse is, defined as the ratio of the distance between the foci to the length of the major axis. When the foci are closer, the ellipse becomes more circular, resulting in a lower eccentricity value, approaching zero as the foci converge to a single point.
How does the numerical value of eccentricity change as the shape of the ellipse approaches a straight line?
As the shape of an ellipse approaches a straight line, its eccentricity increases and approaches 1. Eccentricity (e) is defined as the ratio of the distance between the foci and the length of the major axis; for a circle, it is 0, and for a line, it becomes 1. Thus, as an ellipse becomes more elongated and closer to a straight line, the numerical value of its eccentricity rises from 0 to nearly 1.
What is also known as the semimajor axis?
The major axis of an ellipse is its longest diameter, a line that runs through the center and both foci, its ends being at the widest points of the shape.The semi-major axis is one half of the major axis, and thus runs from the centre, through a focus, and to the edge of the ellipse. It represents a "long radius" of the ellipse, and is the "average" distance of an orbiting planet or moon from its parent body.
How can we calculate the eccentricity e of a planet's orbit?
The eccentricity of a planet's orbit can be calculated using the formula e c/a, where c is the distance between the center of the orbit and the focus, and a is the length of the semi-major axis of the orbit.
What is the formula for eccentricity?
eccentricity = distance between foci ________________ length of major axis
A planet average distance from the sun is also What part of the orbital ellipse?
The semi-major axis.
A planet's average distance from the sun is also what part of the orbital ellipse?
The average distance from the sun to a planet is its semi-major axis, which is the longest radius of its elliptical orbit.
At what distance from the Sun would a planets orbital period be 3 million years?
A planet's orbital period is related to its distance from the Sun by Kepler's third law, which states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit. For an orbital period of 3 million years, the planet would need to be located at a distance of approximately 367 AU from the Sun.
How does the distance of planet affect its period of revolution?
The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
What is the eccentricity of an ellipse in which the distance between the foci is 2 centimeters and the length of the major axis is 5 centimeters?
The eccentricity of that ellipse is 0.4 .
A new planet in orbit about the Sun has a semi-major axis of 1.63 AU and an eccentricity of 0.0955. What is the perihelion distance of the new planet in AU?
The perihelion distance (the closest point to the Sun) can be calculated using the formula: ( r_{peri} = a(1 - e) ), where ( a ) is the semi-major axis and ( e ) is the eccentricity. For the new planet, ( a = 1.63 ) AU and ( e = 0.0955 ). Plugging in the values: [ r_{peri} = 1.63 \times (1 - 0.0955) \approx 1.63 \times 0.9045 \approx 1.47 , \text{AU}. ] Thus, the perihelion distance of the new planet is approximately 1.47 AU.
What are the angles of the planets eccentricities in relevance to the sun?
Kepler's Laws: The orbit of a planet is an ellipse with the Sun at one of the two foci. A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.Eccentricity: the eccentricity of a planet's orbit is not an angle, it is a measure of how far each focus is from the centre of the ellipse. Most of the planets' orbits have low eccentricity so that the Sun's distance from the centre is the main effect of eccentricity.The Earth's orbit has an eccentricity of 1/60 so that the Sun is 149.6/60 million kilometres from the centre, approximately 2.5 million km. That means our distance from the Sun varies from 147.1 to 151.6 million km approximately.
What is the approximate eccentricity of it elliptical orbit?
The eccentricity measures how far off the centre each focus is, as a fraction of the distance from the centre to the extremity of the major axis.
If a planet had an average distance of 10 au what would it's orbital period be?
The orbital period of a planet can be calculated using Kepler's third law: P^2 = a^3 where P is the orbital period in years and a is the semi-major axis in astronomical units. For a planet with an average distance of 10 au, its orbital period would be approximately 31.6 years.
If a planet with twice the mass of earth orbiting a star with the same mass as the sun and an orbital distance of 1AU what is the orbital period?
The orbital period of a planet can be calculated using Kepler's Third Law, which states that the square of the orbital period is directly proportional to the cube of the semi-major axis of the orbit. For a planet with twice the mass of Earth orbiting a star with the same mass as the Sun at a distance of 1AU (Earth-Sun distance), the orbital period would be the same as Earth's, which is about 365 days.
