Lecture6

Lecture6 -...

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: Lecture
6:
Gravita.on
&
Circular
 Mo.on
 Ph
1a

 October
15,
2010
 The
Solar
System
 Kepler’s
Third
Law
 •  Square
of
the
orbital
period
is
propor.onal
to
 the
cube
of
the
semi‐major
axis
of
the
orbit
 •  •  •  Newton:
 2π Angular
velocity:
 ω = T Required
force:
|F | = mω2 R = m mR mR m |F | ∝ 2 ∝ 3 = 2 T R R T 2 ∝ R3 2π T 2 R Newton’s
Law
of
Gravita.on
 F21 M1 M2 = −G 3 r21 r21 r1 M1 r21 = r2 − r1 M2 r2 G = 6.67 × 10−11 N m2 /kg2 The
N‐body
problem
 •  The
equa.ons:
 d2 ri mi 2 dt i, j = −Gmi = 1...N j =i mj r 3 ij |rij | •  A
simple
numerical
scheme:
 vi (t + ∆t) = ri (t + ∆t) = vi (t) − ∆t G j =i mj 3 rij rij ri (t) + vi (t)∆t Globular
clusters:
N
=
few
x
105
 N
=
1010
 ...
View Full Document

Ask a homework question - tutors are online