The dynamical method uses perturbation theory to estimate asteroid mass based on gravitational pull from other asteroids. It has successfully estimated the masses of 24 major asteroids, but is limited by the small size of asteroids and the n-body problem. Conditions for accurate mass determination include repeated encounters with other asteroids and comparison to past motion. It took 200 years to determine the masses of 24 asteroids, with Ceres being the largest. Some asteroids have natural satellites or have been visited by spacecraft to aid in mass determination.
The dynamical method is an approach used in astrophysics to try to determine what the mass of an asteroid is from how its motion through space is affected by the gravitational pull of another asteroid passing by it. The process is also referred to as perturbation theory and has led to estimates for the masses of 24 major asteroids. Using the dynamic method to determine the mass of asteroids has been the most successful method available except for direct spacecraft flybys as of 2011, but is prone to problems due to two significant limitations. Since asteroids are generally extremely small bodies, the gravitational effects they have on each other at a distance are often so small that they cannot be measured with current technology. Second, the dynamical method only works with two bodies isolated in space that are in close proximity, since the n-body problem arises with complex celestial mechanics effects if other asteroids or planets in range simultaneously affect the motion of the two bodies directly studied.
A small group of conditions in astronomy must be present to determine the masses of asteroids by the dynamic method, where the margin of error is not more than 10% of the real mass of the object. These conditions include factors such as the measured asteroid having a repeated, one-on-one encounter with another asteroid so that more measurements can be taken, and a comparison made to the past motion of the asteroid over many years. The mass determination of the first 19 asteroids using the dynamical method since 2003 was based on historical records for the objects’ orbits from the years 1900 to 2002 to ensure the best possible accuracy in the calculations.
As of 2011, it took 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 quite 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% the mass of Earth’s Moon, however, which has made determining its mass difficult as well. Some asteroids have their own natural satellites, such as 1998 WW31 and 2001 QT297, which makes more frequent calculations of gravitational perturbations possible. The asteroids have also been visited by spacecraft such as 433 Eros and 253 Mathilde which were visited by the Near Earth Asteroid Rendezvous-Shoemaker (NEAR Shoemaker) probe in 2000, and their gravitational effect on the spacecraft was used to determine its mass.
Other large asteroids whose masses have been determined using the dynamical method include 2 Pallas and 4 Vesta, which also included perturbations caused by the planet Mars as it passed within its gravitational field in 2001. Vesta also observed a spacecraft as part of its mass calculations. Asteroids such as 45 Eugenia, 87 Sylvia, and 90 Antiope have had dynamical calculations of their mass based solely on their orbiting satellites.
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