Specific relative angular momentum | Wikipedia audio article

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00:01:34 1 Definition
00:03:11 2 Proof that the specific relative angular momentum is constant under ideal conditions
00:03:26 2.1 Prerequisites
00:06:47 2.2 Proof
00:10:43 3 Kepler's laws of planetary motion
00:11:02 3.1 First law
00:16:11 3.2 Second law
00:17:57 3.3 Third law
00:19:45 4 See also






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SUMMARY

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See also: Classical central-force problemIn celestial mechanics the specific relative angular momentum






h
→





{\displaystyle {\vec {h}}}
plays a pivotal role in the analysis of the two-body problem. One can show that it is a constant vector for a given orbit under ideal conditions. This essentially proves Kepler's second law.
It's called specific angular momentum because it's not the actual angular momentum






L
→





{\displaystyle {\vec {L}}}
, but the angular momentum per mass. Thus, the word "specific" in this term is short for "mass-specific" or divided-by-mass:







h
→



=




L
→


m




{\displaystyle {\vec {h}}={\frac {\vec {L}}{m}}}
Thus the SI unit is: m2·s−1.



m


{\displaystyle m}
denotes the reduced mass





1
m


=


1

m

1




+


1

m

2






{\displaystyle {\frac {1}{m}}={\frac {1}{m_{1}}}+{\frac {1}{m_{2}}}}
.

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