Kepler's Law vs Newton's Amendment

[scottshannon]

Hello ..I have a question which I am sure is easy to answer. It has been a long time since I had physics. In a youtube video located here:

http://www.youtube.com/watch?v=dAI8BgCudDQ&list=UU1I__Q1k7NgSZE4PByLfQEg&index=54&feature=plcp

She writes a relationship at 4 min which is

dm=d(M)/(m+M).

Could someone tell me how she gets that? Thank you in advance...

 

[Doc Al]

She writes a relationship at 4 min which is

dm=d(M)/(m+M).

That comes from the definition of center of mass. Perhaps her notation is confusing you. She uses 'dm' to represent the distance from the center of mass to the small mass m; d(M) represents the large mass M times the distance between the masses d.