Satellites Orbital Velocity Height Escape

Reference data and engineering information about satellites orbital velocity height escape for piping systems applications.

Overview

Engineering reference data for Satellites Orbital Velocity Height Escape in piping systems.

$A_1 v_1 = A_2 v_2$

Mass conservation in pipe flow.

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Darcy-Weisbach equation.

$A = \frac{\pi D^2}{4}$

Cross-sectional area of a pipe.

The theoretical maximum orbital velocity occurs at Earth's surface:

$v_{s,max} = \sqrt{g \cdot r_p} = \sqrt{9.81 \times 6.37 \times 10^6} = 7{,}905 \text{ m/s} \approx 7.9 \text{ km/s}$

The minimum velocity needed to escape Earth's gravitational field:

$v_{s,escape} = \sqrt{2 \cdot g \cdot r_p} = \sqrt{2 \times 9.81 \times 6.37 \times 10^6} = 11{,}179 \text{ m/s} \approx 11.2 \text{ km/s}$

A geostationary satellite orbits with a period of 24 hours ( $T = 86{,}400 \text{ s}$ ). Using the orbit height formula:

$h_s = r_p \left[\left(\frac{g \cdot t_s^2}{4 \pi^2 r_p}\right)^{1/3} - 1\right]$

$h_s = 6.37 \times 10^6 \left[\left(\frac{9.81 \times 86400^2}{4 \pi^2 \times 6.37 \times 10^6}\right)^{1/3} - 1\right] = 35{,}968 \text{ km}$

Orbital velocity is inversely proportional to the square root of orbital radius:

Lower orbits → higher velocity required
Higher orbits → lower velocity required
At sea level, orbital velocity equals the maximum value ( $7.9 \text{ km/s}$ )
Escape velocity is always $\sqrt{2}$ times the orbital velocity at the same altitude