Satellite Orbits Around an Elliptical Earth: A Comprehensive Guide

Given the Earth's elliptical shape, do satellites orbiting the poles and equator follow an irregular but constant distance, a regular circular distance, or a pre-programmed distance dictated by scientists? The answers to these questions are complex and fascinating, involving both the shape of the Earth and the principles of orbital mechanics.

The Shape of the Earth

Firstly, it is important to clarify a common misconception: the Earth is not as elliptical as many believe. In reality, the Earth's equatorial diameter is approximately 26 miles wider than its polar diameter. This means the Earth is only mildly oblate, or ellipsoidal, and it is important to consider this when discussing satellite orbits.

When viewed from space, the Earth appears almost perfectly spherical. The equator is a circular band around the Earth, and as satellites orbit the Earth, they primarily orbit around its center of mass, which is a single point in space. For this reason, orbits can be circular without any additional efforts or special modifications. Therefore, the Earth's elliptical shape does not significantly impact the basic circular orbits that satellites follow.

Orbital Mechanics

Satellites in orbit follow paths determined by the gravitational field of the Earth. These orbits can be either circular or elliptical. A constant height orbit around the Earth is only achievable over the equator if the satellite has enough fuel to make constant orbital adjustments. In a purely spherical Earth, orbits would be either circular or elliptical, and would remain in a fixed plane.

However, the Earth is not perfectly spherical but slightly ellipsoidal due to its equatorial bulge. This effect causes the orbits to be slightly distorted. The main effects are twofold: the orbital plane rotates, and the orbit itself rotates. In a pure elliptical orbit, the satellite would complete a 360-degree rotation between one close approach and the next. However, on a real Earth orbit, the distance between close approaches is no longer exactly 360 degrees. This means that for any orbit, whether over the equator or near the poles, the satellite's orbit will naturally rotate.

Orbits Over the Equator and Poles

For an orbit over the equator, the orbital plane remains fixed. However, for any other tilt, the orbital plane will twist relative to the stars. This twisting can be beneficial for certain applications, such as the Molniya orbits used by the Soviet Union and Russia.

Molniya Orbits

Molniya orbits are highly tilted orbits used by the Soviets and Russian Federation to ensure that satellites spend a significant portion of their orbit above the northern hemisphere, providing good coverage of that region. These orbits are particularly useful for using satellite communications in regions of the northern hemisphere that have poor ground-based telecommunications infrastructure.

Orbital Examples

Here’s a comparison of orbits around a spherical Earth and an oblate spheroid Earth:

Orbit around a spherical Earth Orbit around an ellipsoid Earth

From these orbital paths, it is clear that while the Earth's elliptical shape introduces minor distortions, satellites can still maintain circular or elliptical orbits without significant modification. However, for specific applications like the Molniya orbits, the Earth's shape can be utilized to achieve optimal results.

Conclusion

In summary, while the Earth's elliptical shape introduces minor distortions to satellite orbits, these orbits can still be circular or elliptical. The primary factors determining satellite orbits are gravitational forces and the need for continuous adjustments to maintain a constant height. Molniya orbits provide a practical example of how the Earth's shape can be exploited for specific applications, demonstrating the complex and fascinating interplay between celestial mechanics and the real-world shape of our planet.