Let (R, m) be a 2-dimensional regular local ring with algebraically closed residue field R/m. Let K be the quotient field of R and $upsilon$ be a prime divisor of R, i.e., a valuation of K which is birationally dominating R and residually transcendental over R. Zariski showed that there are finitely many simple $upsilon$-ideals $m;=;P_0;{supset};P_1;{supset};{cdots};{supset};P_t;=;P$ and all the other $upsilon$-ideals are uniquely factored into a product of those simple ones [17]. Lipman further showed that the predecessor of the smallest simple $upsilon$-ideal P is either simple or the product of two simple $upsilon$-ideals. The simple integrally closed ideal P is said to be free for the former and satellite for the later. In this paper we describe the sequence of simple $upsilon$-ideals when P is satellite of order 3 in terms of the invariant $b_{upsilon};=;|upsilon(x);-;upsilon(y)|$, where $upsilon$ is the prime divisor associated to P and m = (x, y). Denote $b_{upsilon}$ by b and let b = 3k + 1 for k = 0, 1, 2. Let $n_i$ be the number of nonmaximal simple $upsilon$-ideals of order i for i = 1, 2, 3. We show that the numbers $n_{upsilon}$ = ($n_1$, $n_2$, $n_3$) = (${lceil}frac{b+1}{3}{ ceil}$, 1, 1) and that the rank of P is ${lceil}frac{b+7}{3}{ ceil}$ = k + 3. We then describe all the $upsilon$-ideals from m to P as products of those simple $upsilon$-ideals. In particular, we find the conductor ideal and the $upsilon$-predecessor of the given ideal P in cases of b = 1, 2 and for b = 3k + 1, 3k + 2, 3k for $k;{geq};1$. We also find the value semigroup $upsilon(R)$ of a satellite simple valuation ideal P of order 3 in terms of $b_{upsilon}$.