# Earth's orbit

The Earth in different points in its orbit. (sizes and distances not to scale)

In astronomy, the Earth's orbit is the motion of the Earth around the Sun, from an average distance of 149.59787 million kilometers (93 million miles) away. A complete orbit of the Earth around the Sun occurs every 365.256363004 days (1 sidereal year).[nb 1] This motion gives an apparent movement of the Sun with respect to the stars at a rate of about 1°/day (or a Sun or Moon diameter every 12 hours) eastward, as seen from Earth. On average it takes 24 hours—a solar day—for Earth to complete a full rotation about its axis relative to the Sun so that the Sun returns to the meridian. The orbital speed of the Earth around the Sun averages about 30 km/s (108,000 km/h, or 67,000 mph), which is fast enough to cover the planet's diameter (about 12,700 km, or 7,900 miles) in seven minutes, and the distance to the Moon of 384,000 km (239,000 miles) in four hours.[1]

Viewed from a vantage point above the north poles of both the Sun and the Earth, the Earth would appear to revolve in a counterclockwise direction about the Sun. From the same vantage point both the Earth and the Sun would appear to rotate in a counterclockwise direction about their respective axes.

## Distance covered in an orbit

Approximating Earth's orbit around the sun to be an ellipse with semimajor axis of 1 au and eccentricity of 0.0167, the distance Earth travels in one year is 940 million kilometers (584 million miles).[2]

## History of study

Main article: Heliocentrism
Heliocentric Solar System
Heliocentrism (lower panel) in comparison to the geocentric model (upper panel)

Heliocentrism is the scientific model which places the Sun at the center of the Solar System. Historically, heliocentrism is opposed to geocentrism, which placed the earth at the center. In the 16th century, Nicolaus Copernicus' De revolutionibus presented a full discussion of a heliocentric model of the universe in much the same way as Ptolemy's Almagest had presented his geocentric model in the 2nd century. This 'Copernican revolution' resolved the issue of planetary retrograde motion by arguing that such motion was only perceived and apparent.

## Influence on the Earth

Main article: Season

Because of the axial tilt of the Earth (often known as the obliquity of the ecliptic), the inclination of the Sun's trajectory in the sky (as seen by an observer on Earth's surface) varies over the course of the year. For an observer at a northern latitude, when the northern pole is tilted toward the Sun the day lasts longer and the Sun appears higher in the sky. This results in warmer average temperatures from the increase in solar radiation reaching the surface. When the northern pole is tilted away from the Sun, the reverse is true and the climate is generally cooler. Above the Arctic Circle, an extreme case is reached where there is no daylight at all for part of the year. (This is called a polar night.) This variation in the climate (because of the direction of the Earth's axial tilt) results in the seasons.

## Events in the orbit

By one astronomical convention, the four seasons are determined by flanges, the solstices—the point in the orbit of maximum axial tilt toward or away from the Sun—and the equinoxes, when the direction of the tilt and the direction to the Sun are perpendicular. In the northern hemisphere winter solstice occurs on about December 21, summer solstice is near June 21, spring equinox is around March 20 and autumnal equinox is about September 23. The axial tilt in the southern hemisphere is exactly the opposite of the direction in the northern hemisphere. Thus the seasonal effects in the south are reversed.

In modern times, Earth's perihelion occurs around January 3, and the aphelion around July 4 (for other eras, see precession and Milankovitch cycles). The changing Earth-Sun distance results in an increase of about 6.9%[3] in solar energy reaching the Earth at perihelion relative to aphelion. Since the southern hemisphere is tilted toward the Sun at about the same time that the Earth reaches the closest approach to the Sun, the southern hemisphere receives slightly more energy from the Sun than does the northern over the course of a year. However, this effect is much less significant than the total energy change due to the axial tilt, and most of the excess energy is absorbed by the higher proportion of water in the southern hemisphere.[4]

The Hill sphere (gravitational sphere of influence) of the Earth is about 1.5 Gm (or 1,500,000 kilometers) in radius.[5][nb 2] This is the maximum distance at which the Earth's gravitational influence is stronger than the more distant Sun and planets. Objects orbiting the Earth must be within this radius, otherwise they can become unbound by the gravitational perturbation of the Sun.

Orbital Characteristics
 epoch J2000.0[nb 3] aphelion 152.10 million kilometres (94.51×106 mi) 1.0167 AU[nb 4] perihelion 147.10 million kilometres (91.40×106 mi) 0.98329 AU[nb 4] semimajor axis 149.60 million kilometres (92.96×106 mi) 1.00000261 AU[6] eccentricity 0.01671123[6] inclination 7.155° to Sun's equator 1.578690°[7] to invariable plane longitude of the ascending node 348.73936°[1][nb 5] argument of periapsis 114.20783°[1][nb 6] period 365.256363004 days[8] average speed 29.78 kilometres per second (18.50 mi/s)[1] 107,200 kilometres per hour (66,600 mph)

The following diagram shows the relation between the line of solstice and the line of apsides of Earth's elliptical orbit. The orbital ellipse (with eccentricity exaggerated for effect) goes through each of the six Earth images, which are sequentially the perihelion (periapsis—nearest point to the Sun) on anywhere from 2 January to 5 January, the point of March equinox on 19, 20, or 21 March, the point of June solstice on 20 or 21 June, the aphelion (apoapsis—farthest point from the Sun) on anywhere from 3 July to 5 July, the September equinox on 22 or 23 September, and the December solstice on 21 or 22 December. Note that the diagram shows an exaggerated representation of the shape of Earth's orbit. The actual path of Earth's orbit is not as eccentric as that portrayed in the diagram.

Because of the axial tilt of the Earth in its orbit, the maximum intensity of sun rays hits the earth 23.4 degrees north of equator at the June Solstice (at the Tropic of Cancer), and the maximum intensity of sun rays hits the earth 23.4 degrees south of equator at the December Solstice (at the Tropic of Capricorn).

## Future

Mathematicians and astronomers (such as Laplace, Lagrange, Gauss, Poincaré, Kolmogorov, Vladimir Arnold, and Jürgen Moser) have searched for evidence for the stability of the planetary motions, and this quest led to many mathematical developments, and several successive 'proofs' of stability for the solar system.[9] By most predictions, Earth's orbit will be relatively stable over long periods.[10]

In 1989, Jacques Laskar's work showed that the Earth's orbit (as well as the orbits of all the inner planets) is chaotic and that an error as small as 15 metres in measuring the initial position of the Earth today would make it impossible to predict where the Earth would be in its orbit in just over 100 million years' time. Modeling the solar system is subject to the n-body problem.

The angle of the Earth's tilt is relatively stable over long periods. However, the tilt does undergo a slight, irregular motion (known as nutation) with a main period of 18.6 years. The orientation (rather than the angle) of the Earth's axis also changes over time, precessing around in a complete circle over each 25,800 year cycle; this precession is the reason for the difference between a sidereal year and a tropical year. Both of these motions are caused by the varying attraction of the Sun and Moon on the Earth's equatorial bulge. From the perspective of the Earth, the poles also migrate a few meters across the surface. This polar motion has multiple, cyclical components, which collectively are termed quasiperiodic motion. In addition to an annual component to this motion, there is a 14-month cycle called the Chandler wobble. The rotational velocity of the Earth also varies in a phenomenon known as length-of-day variation.[11]

Future geoengineering projects may preserve the habitability of Earth through the Sun's life cycle by moving the Earth to keep it constantly within the habitable zone.[12]

## Notes

1. ^ It takes 365.256363004 days of exactly 86,400 s to orbit the Sun once in the sense of returning to the same position relative to the stars. (More precisely, this is the time required for the mean longitude of the Earth with respect to the fixed equinox of J2000 to increase 360 degrees, given the rate of change of that longitude at J2000). Such an orbit relative to the stars is called a sidereal year.
2. ^ For the Earth, the Hill radius is
$\begin{smallmatrix} R_H = a\left ( \frac{m}{3M} \right )^{\frac{1}{3}} \end{smallmatrix}$,
where m is the mass of the Earth, a is an Astronomical Unit, and M is the mass of the Sun. So the radius in A.U. is about: $\begin{smallmatrix} \left ( \frac{1}{3 \cdot 332,946} \right )^{\frac{1}{3}} = 0.01 \end{smallmatrix}$.[citation needed]
3. ^ All astronomical quantities vary, both secularly and periodically. The quantities given are the values at the instant J2000.0 of the secular variation, ignoring all periodic variations.
4. ^ a b aphelion = a × (1 + e); perihelion = a × (1 – e), where a is the semi-major axis and e is the eccentricity.
5. ^ The reference lists the longitude of the ascending node as −11.26064°, which is equivalent to 348.73936° by the fact that any angle is equal to itself plus 360°.
6. ^ The reference lists the longitude of perihelion, which is the sum of the longitude of the ascending node and the argument of perihelion. That is, 114.20783° + (−11.26064°) = 102.94719°.

## References

1. ^ a b c d Williams, David R. (2004-09-01). "Earth Fact Sheet". NASA. Retrieved 2007-03-17.
2. ^ Jean Meeus, Astronomical Algorithms (Richmond, VA: Willmann-Bell, 1998) 238. The formula by Ramanujan is accurate enough.
3. ^ Aphelion is 103.4% of the distance to perihelion. Due to the inverse square law, the radiation at perihelion is about 106.9% the energy at aphelion.[citation needed]
4. ^ Williams, Jack (2005-12-20). "Earth's tilt creates seasons". USAToday. Retrieved 2007-03-17.
5. ^ Vázquez, M.; Montañés Rodríguez, P.; Palle, E. (2006). "The Earth as an Object of Astrophysical Interest in the Search for Extrasolar Planets" (PDF). Instituto de Astrofísica de Canarias. Retrieved 2007-03-21.
6. ^ a b Standish, E. Myles; Williams, James C. "Orbital Ephemerides of the Sun, Moon, and Planets" (PDF). International Astronomical Union Commission 4: (Ephemerides). Retrieved 2010-04-03. See table 8.10.2. Calculation based upon 1 AU = 149,597,870,700(3) m.
7. ^ Allen, Clabon Walter; Cox, Arthur N. (2000). Allen's Astrophysical Quantities. Springer. p. 294. ISBN 0-387-98746-0.
8. ^ The figure appears in multiple references, and is derived from the VSOP87 elements from section 5.8.3, p 675 of the following: Simon, J.L.; Bretagnon, P.; Chapront, J.; Chapront-Touzé, M.; Francou, G.; Laskar, J. (February 1994). "Numerical expressions for precession formulae and mean elements for the Moon and planets". Astronomy and Astrophysics 282 (2): 663–683. Bibcode:1994A&A...282..663S.
9. ^ Laskar, J. (2001). "Solar System: Stability". In Murdin, Paul. Encyclopedia of Astronomy and Astropvhysics. Bristol: Institute of Physics Publishing. article 2198.
10. ^ Gribbin, John (2004). Deep simplicity : bringing order to chaos and complexity (1st U.S. ed.). New York: Random House. ISBN 978-1-4000-6256-0.
11. ^ Fisher, Rick (1996-02-05). "Earth Rotation and Equatorial Coordinates". National Radio Astronomy Observatory. Retrieved 2007-03-21.
12. ^ "[1]",Moving the Earth out of harm's way.