The International Space Station (ISS), the largest artificial object in space, can be seen from Earth’s surface with the naked eye when certain criteria are met. It must be at a point in its orbital trajectory where it is above the horizon with respect to the observer, it must be illuminated by the sun, and the observer’s surface location should be dark. This is a fairly common set of conditions that occurs in the few hours after sunset and before sunrise. To determine where the ISS is currently located in its orbit around Earth, there are a number of tools available on the internet.

**ISS Tracker**

One popular tool is the ISS Tracker created by Michael Lodge-Paolini. ISS Tracker traces its roots back to a contract Lodge-Paolini received in the summer of 2006 to develop a tool that shows what astronauts aboard the ISS see when looking toward Earth. This tool, coded in JavaScript, would be used in exhibits at the Smithsonian Air & Space Museum and the Boston Museum of Science. It was then extended into a web interface to allow immediate access to ISS path tracking to anyone around the world.

To understand how the ISS Tracker plots the path of the space station, some background on orbital mechanics is necessary. All objects orbiting Earth follow a repeating path around the planet defined by the laws of physics. Orbital motion can be described with varying accuracy by different models that take into account differing levels of detail in their simulation of reality.

**Keplerian Orbits**

In the Keplerian model of orbital mechanics, named after Johann Kepler (1571-1630), six elements are needed to characterize a distinct orbit:

**Orbital inclination**– the orientation of the orbit with respect to Earth’s equator.**Right ascension of the ascending node**– the location of the ascending and descending orbit locations with respect to Earth's equatorial plane.**Argument of perigee**– the location of the low point of the orbit with respect to Earth's surface.**Eccentricity**– the shape of the orbit.**Mean motion**– the average speed of the orbit (sometimes semi-major axis is specified instead, which is half the length of the orbit ellipse, and is related to mean motion by an equation).**Mean anomaly**– the angular location of the object along its orbit.

Accompanying these six parameters, a frame of reference and epoch (specific point in time) are also required to define an orbit in the Keplerian model. This model describes an ideal orbit, but in reality various additional factors affect the orbital path an object follows.

The most common methods used to model these additional factors are known as simplified perturbation models. The additional parameters these models take into account include gravitational effects from the sun and the moon, solar radiation, and atmospheric drag. The most widely used of these models is perhaps SGP4 (Simplified general perturbations-4).

**Two-line Element Sets**

Simplified perturbation models (SGP4 in particular) became popular because they use a standard data source known as two-line element sets (TLE) to determine a satellite’s orbit over time. TLE sets are made available to the public by the North American Aerospace Defense Command (NORAD) for non-classified objects orbiting Earth. These data sets consist of two 69-character lines that contain all of the parameters necessary to calculate a satellite’s orbital position and velocity for a period of time around the TLE's “epoch” (the moment in time corresponding to the TLEs data points).

The SGP4 model accepts data from the TLE set and returns the orbit of the corresponding object. For objects in low earth orbit like the ISS, the orbital accuracy is on the order of 1 km for a period of a few days around the TLE’s epoch.

With the TLE sets and SGP4 model, the orbital path of the space station (or any other object with TLE data), can be plotted. The ISS tracker website and similar tools plot the position and velocity data obtained from SGP4 on a map interface such as Google Maps to show the exact location of the satellite at any point in time for which there is TLE data.

So the next time you get up early to see the sun rise or after you enjoy a sunset, consider checking the space station’s orbital track online to see if you have a chance to view this technological marvel with your own eyes.

**Resources**