{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

The Restricted thre1 - The Restricted three-body problem...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
The Restricted three-body problem Although the three-body problem is not generally soluble algorithmically, we can tell much about the behaviour in restricted situations. The usual "restricted" three-body problem assumes that the third body (the motion of which we are interested in) is small in comparison to the other bodies as in the example above, but here the two main bodies are comparable in size and we look at the motion of the third in the frame rest of the two-body system (which must be a rotating frame where the bodies rotate about their common centre of gravity). So, taking axes centred on the centre of gravity of the system, containing bodies mass m 1 and m 2 , a rotating frame in which m 1 and m 2 are fixed, we have a small body m very small compared to m 1 and m 2 and m 2 , at position distance r 1 from m 1 and r 2 from m 2 : The energy equation, given that m is at (eta, epsilon) in this frame, is given by:
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern