Binary mass function: Difference between revisions

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== Introduction ==

[[File:orbit2.gif|160px|frame|Two bodies orbiting a common center of mass, indicated by the red plus. The larger body has a higher mass, and therefore a smaller orbit and a lower orbital velocity than its lower-mass companion.]]

The binary mass function follows from [[Kepler's third law]] when the radial velocity of one (observed) binary component is introduced.<ref name="karttunen">{{cite book |editor1-last=Karttunen |editor1-first=Hannu |editor2-last=Kröger |editor2-first=Pekka |editor3-last=Oja |editor3-first=Heikki |editor4-last=Poutanen |editor4-first=Markku |editor5-last=Donner |editor5-first=Karl J. |title=Fundamental Astronomy |publisher=[[Springer Verlag]] |date=2007 |orig-year=1st pub. 1987 |pages=221–227 |chapter=Chapter 9: Binary Stars and Stellar Masses |chapterurl=https://books.google.com/books?id=DjeVdb0sLEAC&pg=PA221&lpg=PA221&source=bl&ots=2i8ingw47Y&sig=UdSRdIXyZn-Ao6MiVeWNJ36GD7I&hl=en&sa=X&ved=0ahUKEwi2hrGIop7MAhXrnYMKHfWyDD0Q6AEIUzAJ#v=onepage&q&f=false |isbn=978-3-540-34143-7 |lastauthoramp=y}}</ref>

Kepler's third law describes the motion of two bodies orbiting a common [[center of mass]]. It relates the orbital period (the time it takes to complete one full orbit) with the distance between the two bodies (the orbital separation), and the sum of their masses. For a given orbital separation, a higher total system mass implies higher [[Orbital speed|orbital velocities]]. On the other hand, for a given system mass, a longer orbital period implies a larger separation and lower orbital velocities.