The mass density of a spherical galaxy varies as K r over a large distance r from its center. In that region, a small star is in a circular orbit of radius R . Then the period of revolution, T depends on R as:

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Aicharya · Accepted Answer

M = &#8747; &#961; d V M = &#8747; 0 R k r 4 &#960; r 2 d r M = 4 &#960; k &#8747; 0 R r d r M = 4 &#960; k R 2 2 = 2 &#960; k R 2 F G = G M m R 2 = m &#969; 0 2 R &#8658; &#160;&#160; G 4 &#960; k R 2 2 R 2 = &#969; 0 2 R &#160;&#160; &#8658; &#969; 0 = 2 &#960; k G R &#8757; T = 2 &#960; &#969; 0 = 2 &#960; R 2 &#960; k G = 2 &#960; R k G &#8658; T 2 &#8733; R

The mass density of a spherical galaxy varies as K r over a large distance r from its center. In that region…

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