What Is the Dynamic Method?

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  • Written By: Ray Hawk
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The dynamic method is an approach used in astrophysics to try to determine what the mass of an asteroid is by how its movement through space is affected by the gravitational pull of another asteroid that passes close by it. The process is also referred to as perturbation theory, and has led to determining estimates for the masses of 24 prominent asteroids. Using the dynamic method to determine asteroid mass has been the most successful method available except for direct spacecraft flybys as of 2011, but it is prone to problems because of two significant limitations. Since asteroids are usually extremely small bodies, the gravitational effects that they have on each other from a distance are often so small that they cannot be measured with current technology. Secondly, the dynamic method only works with two isolated bodies in space coming within close proximity, as the n-body problem arises with complex celestial mechanics effects if other asteroids or planets in range simultaneously affect the movement of the two bodies directly being studied.


A narrow group of conditions in astronomy must be present to determine asteroid masses with the dynamic method, where the allowance for error is no more than 10% of the true mass of the object. These conditions include factors such as the asteroid being measured having a repeated, one-on-one encounter with another asteroid so that multiple measurements can be taken, and a comparison made to past movement of the asteroid over many years. The determination of the mass of the first 19 asteroids by using the dynamic method as of 2003 relied upon historical records for orbits of the objects from the years 1900 to 2002 to ensure the best possible accuracy in calculations.

As of 2011, it has taken the field of celestial mechanics in astronomy 200 years to determine the mass of 24 asteroids in the Solar System. Most of these objects are fairly large by asteroid standards, such as the asteroid Ceres, which alone accounts for 30% to 40% of the entire mass of the asteroid belt itself. Ceres is only 1% of the mass of Earth's Moon, however, which made determining even its mass a difficult task. Some asteroids have their own natural satellites, such as 1998 WW31 and 2001 QT297, which makes more frequent calculations of gravitational perturbations possible. Asteroids have also been visited by spacecraft such as 433 Eros and 253 Mathilde that were visited by the Near Earth Asteroid Rendezvous-Shoemaker (NEAR Shoemaker) probe in 2000, and their gravitational effect on the craft was used to determine their mass.

Other large asteroids that have had their masses determined using the dynamic method include 2 Pallas and 4 Vesta, which also included perturbations caused by the planet Mars as they passed within range of its gravitational field in 2001. Vesta also had a spacecraft observation as part of its mass calculations. Asteroids such as 45 Eugenia, 87 Sylvia, and 90 Antiope have had dynamic method calculations done of their mass based solely upon their own orbiting satellites.


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