Perihelion and Aphelion: Distance, Speed, Sunlight and Seasons

What is the difference between perihelion and aphelion?

The distinction matters when reading a calendar: closest to the Sun does not mean northern summer, and farthest does not mean northern winter. This guide develops a small numerical model to show what distance changes actually do, without treating a teaching graph as a calendar ephemeris or temperature forecast.

Keep distance, speed, sunlight and season separate

All places on Earth share essentially the same annual Sun-distance change at the scale of this explanation. They do not share the same seasonal daylight or solar altitude. This gives a simple diagnostic: a cause that changes in the same direction for both hemispheres cannot, by itself, explain why their main astronomical seasons are opposite.

Conversely, saying that axial tilt causes the seasons does not mean distance has no physical effect. Solar irradiance changes with distance. The useful explanation identifies both effects and avoids turning one correct statement into an absolute denial of the other.

The Sun is at a focus, not at the ellipse's centre

An ellipse has a semi-major axis a and eccentricity e. With the Sun at one focus, the nearest and farthest distances are rₚ = a(1 − e) and rₐ = a(1 + e). Their average is a. Their difference is 2ae, which is not the same as the eccentricity itself.

Many textbook orbit pictures exaggerate the oval shape so the focus and unequal distances are visible. For the example e = 0.0167 used below, the semi-minor/semi-major ratio √(1 − e²) is about 0.99986. The outline is very close to a circle, although the focus is displaced from the centre by 0.0167a.

There is no contradiction between a nearly circular outline and a measurable distance variation. Distance is measured from the focus, not from the centre. A drawing with the Sun incorrectly placed at the centre can hide the main geometry even if its ellipse is beautifully rendered.

Declare the model before using its decimals

Our original worked model fixes a = 1 and e = 0.0167. Distances are therefore expressed in units of the semi-major axis. The rounded eccentricity is close to JPL's Earth–Moon barycentre reference value in its approximate-position table. It is not a fitted orbit for a particular day, and the model does not implement JPL's time-dependent elements.

That distinction is deliberate: JPL identifies the table's Earth-related entry as the Earth–Moon barycentre and states the interval and limitations of its approximations. The examples here illustrate ellipse relationships. They do not silently substitute a rounded two-body orbit for the actual geocentre or a high-precision ephemeris.

For converting example fractions into days, we choose T = 365.25 days. It is an illustrative period, not a claim that the tropical, sidereal and anomalistic years are identical. No calendar origin is assigned, so a model day cannot be read as a dated event.

Calculate distance at any angle from perihelion

Let ν, the true anomaly, be the angle at the Sun measured from the direction of perihelion. The ellipse equation gives r/a = (1 − e²)/(1 + e cos ν). At ν = 0°, this reduces to 1 − e; at 180°, to 1 + e. The angle is a position along the orbit, not elapsed time.

Our model consequently reaches distances 0.983300 and 1.016700. The far/near distance ratio is approximately 1.033967. In other words, the far distance is about 3.40% larger than the near distance when the near distance is the denominator.

Percentages need their denominator. The separation of the extremes is 3.34% of a, but about 3.40% of the perihelion distance. Both calculations can be correct. Reporting only “a 3.4% change” without specifying the comparison makes it harder to reconcile two sources.

Apply the inverse-square law to irradiance

For a source with fixed luminosity spreading energy over a sphere, the sphere's area grows as distance squared. The received power per unit area on a surface perpendicular to the rays therefore scales as 1/r². Relative to the irradiance F₀ at distance a, F/F₀ = (a/r)².

At the model perihelion this ratio is 1.034256, and at aphelion it is 0.967418. Their ratio is approximately 1.069088: perihelion irradiance is about 6.91% greater than aphelion irradiance. This is a comparison between the two extremes, not a claim of a 6.91% increase over the reference at a.

The stated quantity is incoming irradiance before atmospheric and surface effects, for the specified orientation. It is not the temperature of a city, daily energy on a horizontal roof, or the output of a particular solar installation. Those questions need additional geometry and environmental inputs.

Why the planet moves faster near the Sun

Kepler's second law says that the line from the Sun to a planet sweeps equal areas in equal times. Near the Sun, the shorter radius must turn through a greater angle to sweep the same area. The planet's orbital speed also increases toward perihelion.

For a two-body ellipse, the vis-viva relation gives v² = μ(2/r − 1/a), where μ is the gravitational parameter. Choose v₀ = √(μ/a), the speed of a circular orbit of radius a. Then v/v₀ = √(2a/r − 1). We can compare speeds without assigning a mass or a kilometre-per-second scale.

The model's perihelion and aphelion speed ratios are 1.016842 and 0.983437. Their ratio equals the far/near distance ratio at those two special points. That endpoint relationship should not be generalized to “v is proportional to 1/r everywhere”: away from the apsides, velocity is not wholly perpendicular to the radius.

Nine checked orbital positions

The distance, speed and irradiance columns can be checked independently. Larger distance corresponds to lower speed and lower irradiance in this fixed ellipse. However, the numerical changes are different: irradiance follows an inverse square, while speed follows the square-root expression above.

At 90°, the distance is slightly below a rather than exactly a. A right angle at the Sun does not place the planet at the end of the ellipse's minor axis measured from its centre. This is another consequence of distinguishing the focus from the centre.

The last column already hints at unequal timing. Reaching 90° takes about 24.47% of the orbit, while reaching 270° takes about 75.53%. The 0° and 360° rows share the same physical position but identify the start and end of one completed model circuit.

Read the original distance and sunlight graph

Follow the same horizontal position through both panels. At 180°, the upper curve is highest and the lower curve lowest. Near 0° and 360°, the pattern reverses. The display contains 361 calculated positions at one-degree intervals, making the inverse relationship visible.

Do not interpret the curve's steepness as how quickly the quantity changes per day. Equal horizontal intervals represent equal angles, and the elapsed time between them varies. A graph against time would require the anomaly-to-time conversion described next.

Equal angular quarters take different times

Introduce the eccentric anomaly E, an auxiliary angle for the ellipse. A convenient quadrant-preserving conversion is E = 2 atan2(√(1 − e) sin(ν/2), √(1 + e) cos(ν/2)), kept continuously from 0 to 2π for one circuit. Use radians in the following equation.

The mean anomaly is M = E − e sin E. In the ideal two-body model, elapsed fraction t/T = M/(2π). Mean anomaly advances uniformly; true anomaly does not. Mixing degrees with the radian sine term would produce a numerical error.

The arcs beside perihelion take about 89.371 model days each, while those beside aphelion take about 93.254. Their sum is 365.25. These arcs begin at perihelion-based angles, so they are not the four calendar seasons: solstices and equinoxes are defined by Earth's orientation relative to the Sun.

Why northern winter can coincide with the nearest distance

NASA's seasons explanation identifies axial tilt as the main cause of the alternating hemispheric seasons. When one hemisphere tilts toward the Sun, its daylight geometry differs from that of the hemisphere tilted away. Solar altitude and daylight duration change together over the year.

A simple local illustration isolates incidence angle. For parallel rays on a horizontal surface, the direct-beam geometric factor is sin h, where h is solar altitude above the horizon. At 30° this factor is 0.5; at 60° it is about 0.866. That example demonstrates an orientation effect; it does not include atmosphere or integrate a whole day's energy.

The Sun-distance factor still applies to both hemispheres. It modifies the available sunlight, while the tilt explains their opposite seasonal pattern. A complete climate account includes more than this geometry, so neither the orbit graph nor two noon angles should be used to predict a city's hottest day.

Read event dates and local times as separate information

January and July describe the present broad timing of Earth's apsides. They are not fixed annual timestamps. To report a specific year's event, obtain an ephemeris result, identify its time scale and convert to the requested local time zone. A civil-date label can change across zones even when the event is one instant.

A perihelion time is not local sunrise or solar noon. It concerns orbital distance; local sunrise depends on the observer's position and horizon conventions. For a local daily schedule, use the sunrise and sunset tool with the appropriate city and date.

For the related clock and calendar questions, continue with solar noon versus clock noon, the shortest day and earliest sunset, and the Sun's analemma. Each needs information beyond the nearest and farthest orbital distances.

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