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[–] 5 points 1 year ago (4 children)

Achieving Ballistic Velocity (The Tsiolkovsky Cow Equation)

The **Rocket Equation** is brutal:  

`Δv = Isp * g₀ * ln(m₀ / m_f)`  

Where:  

* `Δv` = Change in velocity needed (`11,186 m/s` for escape).  

* `Isp` = Specific impulse (`~360 s` for CH4/LOX).  

* `g₀` = Gravity (`9.81 m/s²`).  

* `m₀` = Initial mass (cow + engines + LOX + methane).  

* `m_f` = Final mass (just... cooked cow?).

**Assumptions:**  

*   Engine mass: `300 kg` (mini-Raptor).  

*   LOX mass: **5x** methane mass (rocket ratio).  

*   Methane stored: `500 kg` (we're pumping hard).  

*   `m₀ = 700 (cow) + 300 (engine) + 500 (CH₄) + 2,500 (LOX) = 4,000 kg`.  

*   `m_f = 700 kg` (cow, assuming engines/tanks detach).  

**Calculation:**  

`Δv = 360 * 9.81 * ln(4,000 / 700)`  

`= 3,531.6 * ln(5.71)`  

`= 3,531.6 * 1.74`  

`= ~6,150 m/s`.  

**Result:** **6,150 m/s < 11,186 m/s**.  

→ **Verdict:** Suborbital cow. Maximum apogee: **~1,000 km** (a very high moo).  

→ **Impact Velocity:** **~3-4 km/s** (kinetic energy = 0.5 * 700kg * (3,500m/s)^2 ≈ **4.3 gigajoules**).  

→ **Effect:** Creates a **10m wide crater**, vaporizing the cow and any nearby farmers. A true "pasture bomb."

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