What shape are the orbits of the planets, and how do we measure how stretched an orbit is?
Calculate the eccentricity of an elliptical orbit using the Reference Tables equation (distance between foci divided by length of the major axis) and relate eccentricity to orbital shape and orbital velocity.
A Regents answer on orbital eccentricity: ellipses and foci, the Reference Tables formula (distance between foci over the length of the major axis), worked calculations rounded to the nearest thousandth, and how eccentricity and the Sun's off-center position affect orbital velocity and apparent solar diameter.
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What this topic is asking
Planets orbit the Sun in ellipses, not circles. The Regents wants you to calculate eccentricity with the page-1 Reference Tables equation and to relate eccentricity to the shape of an orbit and to changes in orbital velocity. This is the single most reliable calculation in the astronomy unit.
Ellipses and foci
You can draw an ellipse with two pins (the foci) and a loop of string: the more the pins are spread apart, the more flattened the ellipse. Spread them to the same point and you get a circle.
The eccentricity equation
The Reference Tables (page 1) give:
Key features the Regents tests:
- Eccentricity is unitless (the lengths cancel), so never write a unit on the answer.
- Round to the nearest thousandth (three decimal places) unless told otherwise.
- A value of 0 is a perfect circle; values approaching 1 are very flattened. The value can never reach or exceed 1 for a closed orbit.
- The smaller the distance between the foci (for a given major axis), the closer to circular the orbit.
Eccentricity and orbital velocity
Because the Sun is at one focus and not at the center, a planet's distance from the Sun changes through its orbit:
- Perihelion is the closest point to the Sun. Here the planet moves fastest, and the Sun appears largest in the sky.
- Aphelion is the farthest point. Here the planet moves slowest, and the Sun appears smallest.
This follows Kepler's second law (a planet sweeps out equal areas in equal times). Earth's orbit is nearly circular, so this effect is small but real, and the Regents asks about it.
Try this
Q1. State the formula for eccentricity and the unit of the answer. [2 points]
- Cue. Distance between foci divided by length of the major axis; the answer is unitless.
Q2. An orbit has foci 2.0 cm apart and a major axis of 10.0 cm. Calculate the eccentricity. [2 points]
- Cue. , written as .
Exam-style practice questions
Practice questions written in the style of NYSED exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
Regents (style)2 marksPart B-2. An ellipse is drawn with two foci. The distance between the foci is 3.2 cm and the length of the major axis is 8.0 cm. Calculate the eccentricity of this ellipse. Show the equation, the substitution and the answer rounded to the nearest thousandth.Show worked answer →
A 2-point calculation using the Reference Tables equation.
1 point for the correct setup and substitution, 1 point for the correct answer rounded to the nearest thousandth.
Equation (from page 1 of the Reference Tables): eccentricity = distance between foci divided by length of major axis.
Substitution: 3.2 cm / 8.0 cm.
Answer: 0.40, written to the nearest thousandth as 0.400.
Markers reward showing the equation and substitution; eccentricity is unitless because the centimeters cancel.
Regents (style)1 marksPart A. As the eccentricity of a planet's orbit increases, the shape of the orbit becomes (1) more circular (2) more elliptical (flattened) (3) a perfect circle (4) a straight line. Justify your choice.Show worked answer →
A 1-point multiple-choice question. The answer is (2).
Eccentricity measures how stretched (flattened) an ellipse is. An eccentricity of 0 is a perfect circle; as eccentricity increases towards 1 the ellipse becomes more elongated and flattened. Planetary orbits have low eccentricities (Earth's is about 0.017, almost circular). (1) and (3) describe decreasing eccentricity; (4) would need an eccentricity of essentially 1. The trap is thinking a higher eccentricity is "rounder".
Related dot points
- Explain Earth's rotation and revolution, the evidence for each, and how they produce the apparent daily motion of celestial objects at 15 degrees per hour, including the use of Polaris to find latitude.
A Regents answer on Earth's rotation and revolution: the evidence for each, the apparent daily motion of the Sun, Moon and stars at 15 degrees per hour, Foucault's pendulum and the Coriolis effect, and how the altitude of Polaris gives an observer's latitude in the Northern Hemisphere.
- Explain how the tilt of Earth's axis and its revolution change the angle and duration of insolation through the year, producing the seasons, the solstices and the equinoxes.
A Regents answer on insolation and the seasons: why the 23.5 degree axial tilt and Earth's revolution change the angle and duration of insolation, the solstices and equinoxes, the Sun's path across the sky at New York latitudes, and why summer is warm even though Earth is near aphelion.
- Describe the structure of the solar system and use the Selected Properties of the Planets table and Kepler's laws to relate a planet's distance from the Sun to its period and orbital velocity.
A Regents answer on the solar system: terrestrial versus Jovian planets, gravity as the controlling force, and Kepler's laws used with the Reference Tables Selected Properties of the Planets so that planets farther from the Sun have longer periods and slower orbital velocities.
- Describe the phases of the Moon, solar and lunar eclipses, and the tides as consequences of the motions and gravitational interactions of the Earth, Moon and Sun.
A Regents answer on the Earth-Moon-Sun system: the cause of the Moon's phases, why solar and lunar eclipses are rare, the roughly two-week phase cycle, and how the Moon's and Sun's gravity produce spring and neap tides.
- Use the Luminosity and Temperature of Stars diagram to classify stars, describe the Sun and nuclear fusion, and state the evidence for the Big Bang (red shift and cosmic background radiation).
A Regents answer on stars and cosmology: reading the Luminosity and Temperature of Stars (Hertzsprung-Russell) diagram, the Sun as a main sequence star powered by nuclear fusion, star color and temperature, and the red shift and cosmic background radiation as evidence for the Big Bang.
Sources & how we know this
- Reference Tables for Physical Setting/Earth Science (2011 edition) — New York State Education Department (2011)
- Regents Examination in Physical Setting/Earth Science — New York State Education Department (2026)