Relative speed of rocket depends on mass and impulse¶

The Tsiolkovsky formula determines the speed that an aircraft develops under the influence of the thrust of a rocket engine, unchanged in direction, in the absence of all other forces. For a rocket flying at a speed close to the speed of light, the generalized Tsiolkovsky formula is valid, in which the speed of light is present.

Notation:

\(c\) (c) is speed_of_light.

speed¶: Final speed of the rocket

Symbol:: v
Latex:: \(v\)
Dimension:: velocity

effective_exhaust_speed¶: Effective exhaust speed of the rocket engine.

Symbol:: v_e
Latex:: \(v_\text{e}\)
Dimension:: velocity

initial_mass¶: Initial mass of the rocket

Symbol:: m_0
Latex:: \(m_{0}\)
Dimension:: mass

final_mass¶: Final mass of the rocket

Symbol:: m_1
Latex:: \(m_{1}\)
Dimension:: mass

law¶

m_1 / m_0 = ((1 - v / c) / (1 + v / c))^(c / (2 * v_e))

Latex:: \[\frac{m_{1}}{m_{0}} = \left(\frac{1 - \frac{v}{c}}{1 + \frac{v}{c}}\right)^{\frac{c}{2 v_\text{e}}}\]