Mar 01, 2026
To:Euis Aisyah Lituhayu
Now let's calculate for the planet Aelonisova first.
Radius ($R$) = $2.5 \times 10^7 \text{ meter}$$V = \frac{4}{3} \times \pi \times (2.5 \times 10^7 \text{ m})^3$$V = \frac{4}{3} \times 3.14159 \times (1.5625 \times 10^{22} \text{ m}^3)$$V = \frac{4}{3} \times 3.14159 \times 1.5625 \times 10^{22} \text{ m}^3$$V = 6.54497 \times 10^{22} \text{ m}^3$
($\rho$) = $6 \text{ gram/cm}^3$
$\rho = 6000 \text{ kg/m}^3$
$M = 6000 \text{ kg/m}^3 \times 6.54497 \times 10^{22} \text{ m}^3$
$M = 3.926982 \times 10^{26} \text{ kg}$
current volume and orbital distance
$$V_{\text{ring}} = (2\pi R_{\text{ring}}) \cdot (\pi r^2)$$$$V_{\text{ring}} = 2 \cdot 3,14159 \cdot 25.000 \cdot 3,14159 \cdot (2.500)^2$$$$V_{\text{ring}} \approx 157.079,5 \cdot 19.634.937,5$$$$V_{\text{ring}} \approx \mathbf{3,087 \times 10^{12} \text{ km}^3}$$
$$V_{\text{command}} = \frac{1}{3} \cdot A \cdot h_c$$$$V_{\text{command}} = \frac{1}{3} \cdot 25.000 \cdot 6.000$$$$V_{\text{command}} = 25.000 \cdot 2.000$$$$V_{\text{command}} = \mathbf{5 \times 10^7 \text{ km}^3}$$
$$V_{\text{military}} = \frac{1}{3} \cdot A \cdot h_m$$$$V_{\text{military}} = \frac{1}{3} \cdot 25.000 \cdot 10.000$$$$V_{\text{military}} \approx \mathbf{8,33 \times 10^7 \text{ km}^3}$$
$$V_{\text{total}} = V_{\text{ring}} + V_{\text{command}} + V_{\text{military}}$$$$V_{\text{total}} = (3,087 \times 10^{12}) + (5 \times 10^7) + (8,33 \times 10^7)$$
$$V_{\text{total}} \approx \mathbf{3,087 \times 10^{12} \text{ km}^3}$$
$$m_A = \rho_A \cdot V$$$$m_A = 3,44 \text{ g/cm}^3 \cdot 3,087 \times 10^{27} \text{ cm}^3$$$$m_A = \mathbf{1,062 \times 10^{28} \text{ gram}}$$$$m_A = \mathbf{1,062 \times 10^{25} \text{ kg}}$$
$$R_A = \sqrt[3]{\frac{(6,674 \times 10^{-11}) \cdot (4,036 \times 10^{26}) \cdot (216.000)^2}{4\pi^2}}$$$$R_A = \sqrt[3]{\frac{1,255 \times 10^{27}}{39,478}}$$$$R_A = \sqrt[3]{3,179 \times 10^{25}}$$$$R_A \approx \mathbf{3,17 \times 10^8 \text{ meter}}$$
316,928,801.64 Meter
