Why is the Earth’s orbit an ellipse?

Quick Answers

The Earth’s orbit is elliptical rather than circular for a few key reasons:

• The gravitational pull between the Earth and Sun is unequal across the orbit due to variations in their distance from each other.
• The combined gravitational forces of other planets and bodies in our solar system cause perturbations in the Earth’s orbit.
• Conservation of angular momentum causes the Earth’s velocity to increase as it gets closer to the Sun and decrease as it gets farther away.

The orbit of the Earth around the Sun has fascinated astronomers, physicists, and thinkers throughout history. Unlike the circular orbits followed by the Moon around the Earth or by man-made satellites, the Earth’s orbit around the Sun follows an elliptical or oval-shaped path. This results in the Earth being closer to the Sun at some points during its orbit than at others.

The elliptical nature of Earth’s orbit was first described mathematically by Johannes Kepler in the early 17th century. Kepler studied detailed observations of the positions of planets made by his predecessor Tycho Brahe and determined that the Earth and other planets followed elliptical rather than circular paths in their motion around the Sun. This finding was an important breakthrough in astronomers’ understanding of celestial mechanics.

Kepler’s discovery raised an obvious question – why does the Earth follow an elliptical orbit rather than a circular one like other bodies in the solar system? In this article, we’ll explore the reasons behind the elliptical shape of Earth’s orbit, including the gravitational forces involved, conservation of momentum, and perturbations caused by other solar system bodies. Gaining a better understanding of the causes of Earth’s elliptical orbit provides insight into fundamental physics and our place in the solar system.

Newton’s Law of Universal Gravitation

In order to understand why the Earth’s orbit is elliptical, it’s important to first consider Newton’s law of universal gravitation. Isaac Newton published this fundamental law in the 17th century to describe the gravitational force experienced between two objects with mass.

Newton’s law of universal gravitation states that every particle in the universe attracts every other particle with a force that is proportional to the product of the two masses and inversely proportional to the square of the distance between them. This can be expressed mathematically as:

Newton’s Law of Universal Gravitation Formula

Where:

F = Gravitational force between the two objects
G = Universal gravitational constant (6.67 x 10^-11 N m²/kg²)
m₁ = Mass of first object
m₂ = Mass of second object
r = Distance between the centers of mass of the two objects

Some key implications of Newton’s law are:

• The gravitational force is directly proportional to the masses of the two interacting objects – the larger their masses, the larger the gravitational attraction.
• The gravitational force decreases with increasing distance between the objects – as the distance increases, the force drops off rapidly.
• All objects with mass exert and experience gravitational forces.

This fundamental law applies to the gravitational interaction between the Sun and Earth that governs Earth’s orbital motion. The Sun contains 99.8% of the mass of the solar system so it exerts a dominant gravitational pull on all the planets including Earth.

Variation in Gravitational Force Across Earth’s Elliptical Orbit

Now that we have reviewed Newton’s law of gravity, we can apply it to understand how the gravitational force between the Sun and Earth leads to an elliptical orbit.

As mentioned in Newton’s law, the gravitational force depends directly on the distance between two objects. For the Sun-Earth system, this distance varies greatly across different points in Earth’s orbit due to the elliptical shape. Here are some key points:

• At perihelion (the point where the Earth is closest to the Sun), the Sun-Earth distance is about 147 million km.
• At aphelion (the point where the Earth is farthest from the Sun), the Sun-Earth distance is about 152 million km.
• Therefore, the Sun-Earth distance varies by about 5 million km across Earth’s orbit.

Because gravitational force drops off with distance, this means the gravitational pull between the Sun and Earth is not constant across the elliptical orbit but is weaker at aphelion compared to perihelion. The table below shows how the gravitational force changes with distance:

Variation in Sun-Earth Gravitational Force

This difference in gravitational force at different distances leads to an elliptical rather than circular orbit. When the Earth is closer to the Sun near perihelion, the stronger gravitational force causes the Earth to accelerate in its orbit. When the Earth is farther from the Sun near aphelion, the gravitational force is weaker so the Earth’s acceleration decreases. This causes the elliptical shape rather than a circular path where acceleration would be constant.

Conservation of Angular Momentum

In addition to the variation in gravitational force, another factor that leads to an elliptical orbit is the law of conservation of angular momentum. Angular momentum is a quantity in physics defined as the product of an object’s mass, velocity, and distance from the axis of rotation. For a planet orbiting the Sun, angular momentum depends on the planet’s mass, orbital velocity, and the distance between the Sun and planet.

According to the law of conservation of angular momentum, the total angular momentum of a system remains constant over time when no external forces act on the system. For the Earth orbiting the Sun, this means angular momentum is conserved.

As the Earth gets closer to the Sun near perihelion, its distance to the Sun decreases. To conserve angular momentum, the Earth’s orbital velocity must therefore increase. Similarly, as the Earth gets farther from the Sun near aphelion, its distance increases so the orbital velocity decreases to keep overall angular momentum constant.

This relationship between distance and velocity is known as Kepler’s second law and results in the elliptical shape of Earth’s orbit. When nearer the Sun, the higher velocity causes the Earth to whip around quickly in its orbit. When farther from the Sun, the lower velocity causes the Earth to move more slowly. This causes the elliptical orbit shape rather than a circular path with constant velocity.

Variation in Earth’s Orbital Velocity

Perturbations from Other Bodies

Up until now, we have considered the ideal two-body case of the Sun and Earth interacting via gravity. However, in reality there are additional gravitational forces that impact the Earth’s orbit caused by other bodies in the solar system. The gravitational pulls of these other bodies lead to perturbations – small changes or deviations – in the elliptical path the Earth would follow if only the Sun’s gravity was considered.

Some of the major perturbations come from the gravitational forces of:

• Other planets, especially giant Jupiter
• The Moon orbiting the Earth
• The oblateness or bulge of the Earth itself

For example, Jupiter’s gravity can periodically either pull the Earth slightly closer to the Sun or pull it farther away. The combined gravitational tugs of Jupiter and the other planets cause the orientation of Earth’s elliptical orbit to slowly rotate or precess over time. The locations of perihelion and aphelion slowly change.

The Moon’s gravity also creates periodic variations in the Earth’s orbit, altering the orbit shape over monthly and yearly timescales. Even the Earth’s oblateness, caused by its slight equatorial bulge, perturbs the orbit enough to shift the orbital ellipse over time.

While these perturbations are small, they introduce periodic variations on top of the main elliptical orbit caused by the Sun’s gravity. Detailed gravitational simulations that include all solar system bodies are needed to precisely predict the Earth’s exact orbital path at any given time.

Evidence for Earth’s Elliptical Orbit

Detailed astronomical observations over centuries have confirmed that Earth’s orbit around the Sun does indeed follow an elliptical path rather than a circular one. Here is some of the key evidence:

• Changes in the Sun’s apparent size in the sky over a year – the Sun appears slightly larger at perihelion compared to aphelion.
• Variations in the Sun-Earth distance measured via radar and spacecraft tracking over a year.
• Slight changes in the Earth’s orbital speed measured via precision Doppler shifts of radio waves.
• Precise observations of the timing of eclipses, transits, and occultations which match predictions based on an elliptical orbit.

Modern laser ranging techniques can measure the Sun-Earth distance with an accuracy of a few centimeters, definitively showing the ~5 million km variation characteristic of an elliptical orbit. Careful astronomical observations over centuries have confirmed Kepler’s early 17th century insight into the elliptical shape of Earth’s orbit.

Conclusion

In summary, the Earth follows an elliptical rather than circular orbit due to primarily three factors:

• The gravitational force between the Sun and Earth varies across the elliptical orbit due to differences in Sun-Earth distance.
• Conservation of angular momentum causes the Earth’s orbital velocity to increase when nearer the Sun and decrease when farther away.
• Gravitational perturbations from other solar system bodies introduce variations on top of the main elliptical orbit.

Kepler’s discovery of the elliptical nature of planetary orbits was a revolutionary breakthrough in astronomy. Understanding the reasons behind the elliptical shape of Earth’s orbit provides insight into fundamental physics that governs celestial motions and our place in the solar system. Continued study and observations of tiny perturbations in the Earth’s orbit also allow astronomers to test general relativity and refine our grasp of gravity.