This is an accompanion app to the paper "Optimal Path for Orbital Debris", A. Bongers and J. L. Torres.

DISE-2024 is an Integrated Assessment Model (IAM) for the economy and the space environment. The model is solved for a centralized economy where the social planner maximizes social welfare, fully internalizing the social cost of orbital debris. The maximization problem is the following:

$\max_{{c}_t} \sum_{t=0}^T \left(\frac{1}{1+\rho}\right)^t \left(\frac{\hat{c}_t^{1-\sigma}-1}{1-\sigma}\right)N_t$

subject to:

$c_t+i_t+h_t=y_t$

$y_t=a_t k_t ^{\alpha_1}s_t^{\alpha_2}(N_t)^{1-\alpha_1-\alpha_2}$

$k_{t+1}=(1-\delta_k) k_t+ i_t$

$s_{t+1}=(1-\delta_s) s_t + q_t h_t-x_t$

$D_{i,t}= W_t + Z_t + F_{i,t} \ \ \ $for$ \ \ \ i=1,2,3$

$W_{t+1}=(1-\delta_w-\varepsilon_w) W_t- \theta(D_{2,t}+S_t)W_t+\chi\delta_sS_t$

$Z_{t+1}=(1-\delta_z-\varepsilon_z) Z_t- \theta(D_{2,t}+S_t)Z_t+\varphi L_t$

$F_{1,t+1}=(1-\delta_f) F_{1,t}+\omega L_t + \gamma_s X_t+ \phi_w \varepsilon_w W_t +\phi_z \varepsilon_z Z_t+\gamma_w\theta (D_{2,t}+S_t)W_t + \gamma_z\theta (D_{2,t}+S_t)Z_t$

$X_t=(1-v_t)\theta D_{2,t}S_t$

$S_t=\mu s_t$

$L_t=\frac{\mu}{\eta}q_th_t$

$a_{t+1}=a_t exp(g_{a,0}exp(-\delta_a t))$

$q_{t+1}=q_t exp(g_{q,0}exp(-\delta_q t))$

$N_{t+1}=N_t \left(\frac{N^*}{N_t}\right)^\varsigma$

$F_{2,t}=(1+\Gamma)F_{1,t}$

Alternative migitagion policies can be simulated by setting to zero the following parameters:

• No Intervention: Baseline values for the space operational parameters.
• Mandatory de-orbiting of derelict satellites: $\chi=0$.
• Reusable launch vehicles or mandatory de-orbiting of rocket bodies: $\varphi=0$.
• Mandatory de-orbiting policy: $\chi=\varphi=0$.
• Debris-free launch systems: $\omega=\varphi=0$.
• No breakups: $\varepsilon_w=\varepsilon_z=0$.
• No collision: $v_t=1$.
• ESA zero debris: $\chi = \varphi = \omega = 0$, $v_t=1$.