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Intermediate5 equations~7 hours

Rocket Science and Spaceflight

From Tsiolkovsky to orbital mechanics and cosmology.

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  1. 1

    Tsiolkovsky Rocket Equation

    Intermediate
    Δv=veln⁡m0mf\Delta v = v_e \ln\frac{m_0}{m_f}

    Change in velocity depends on exhaust velocity and the natural log of initial to final mass ratio.

    Engineering Sciences
    Rocket Science
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  2. 2

    Rocket Thrust Equation

    Advanced
    F=m˙ve+(Pe−Pa)AeF = \dot{m} v_e + (P_e - P_a) A_e

    Thrust equals mass flow times exhaust velocity plus pressure difference at nozzle exit.

    Engineering Sciences
    Propulsion
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  3. 3

    Kepler's Third Law

    Intermediate
    T2=4π2GMa3T^2 = \frac{4\pi^2}{GM} a^3

    Orbital period squared is proportional to semi-major axis cubed.

    Space Sciences
    Orbital Mechanics
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  4. 4

    Hubble's Law

    Intermediate
    v=H0dv = H_0 d

    Galaxies recede from us at speed proportional to distance—the universe is expanding.

    Space Sciences
    Cosmology
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  5. 5

    Friedmann Equation

    Research
    (a˙a)2=8πG3ρ−kc2a2+Λc23\left(\frac{\dot{a}}{a}\right)^2 = \frac{8\pi G}{3}\rho - \frac{kc^2}{a^2} + \frac{\Lambda c^2}{3}

    Expansion rate of the universe depends on matter, curvature, and dark energy density.

    Space Sciences
    Cosmology
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