Φ(r) GM (r² +r²)¹/2

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The Plummer sphere is a model for some star clusters, and it has the gravitational potential as given in the provided image. M and rp are both constant.

What is the density profile ρ(r)? When the Plummer sphere is observed from a large distance along the z axis, what is its surface density, Σ(R), where R is the distance from the center?

Φ(r)
GM
(r² +r²)¹/2
Transcribed Image Text:Φ(r) GM (r² +r²)¹/2
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