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How do scientists predict the orbit and apparent “peak” magnitude of an incoming comet such as Comet ISON (C/2012 S1) when it is far from Earth?

Matthew Schewe, Eden Prairie, Minnesota
RELATED TOPICS: COMET | COMET ISON
Orbit of Comet ISON
Using the laws of physics, scientists determined six orbital elements of the path of Comet ISON (C/2012 S1) from just a few observations. They know the comet will reach its closest distance to the Sun on November 28 and how far it will be at that point, but it’s uncertain how bright it will appear.
Astronomy: Roen Kelly

Comets are like small planets that follow orbits of all shapes and sizes around the Sun. Usually, these orbits are chaotic and highly elongated — taking the comets far from our star at their farthest points — and they can change significantly due to the gravitational influences of the major planets. To determine a comet’s orbit, we start by observing its positions with respect to the cataloged locations of background stars, and then apply the laws of physics.
 

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