To calculate Delta-V:
\[ \Delta v = V_e \cdot \ln\left(\frac{m_i}{m_f}\right) \]
Where:
Delta-V, denoted \(\Delta v\), is a term used in aerospace to describe the change in velocity of a rocket or spacecraft. It represents the impulse per unit mass required to achieve a maneuver, such as changing orbit or landing on a planetary surface. Delta-V is critical for mission planning, as it helps determine the feasibility of maneuvers and the required propulsion capabilities.
Let's assume an exhaust velocity of 3,000 m/s, an initial mass of 10,000 kg, and a final mass of 4,000 kg.
Using the formula:
\[ \Delta v = 3{,}000 \cdot \ln\left(\frac{10{,}000}{4{,}000}\right) \approx 3{,}000 \cdot 0.916 = 2{,}748 \text{ m/s} \]
The Delta-V is approximately 2,748 m/s.
