How can one determine the required altitude/velocity/time from release required for a small spacecraft (1 to 10 kg) in a suborbital trajectory to ensure that it burns up as it re-enters the atmosphere?

  • $\begingroup$ By integrating the heat flux? $\endgroup$ – Deer Hunter Jun 11 '15 at 4:15

This question from Physics.SE is very relevant, I'll condense it's main features here.

The change in temperature of a body in the Earth's atmosphere is calculated using:

$$\frac{T_2}{T_1} = \left( 1+\frac{1}{2} \rho v^2 / P1 \right)^{2/7}$$

Assuming: Air temperature is $293 K$, and air density is $1.3 kg/m^3$, and pressure is $1 atm$.

Using this equation, you can plug in the required change in temperature to burn up your payload, and hence calculate the velocity required. With the velocity, you can reverse-engineer one out of infinite possible suborbital trajectories.

This particular question assumed a sphere of radius 1 meter, and asked about what speed would be required to increase it's temperature by $200º C$. Approximately, the answer was $2000 mph$ or around $900 m/s$. De-orbit speed from LEO is about 7 times that.

My (uneducated) guess is that any payload under $10 kg$ will burn up in the atmosphere if it re-enters from LEO at $7 km/s$. It depends on the material and shape of the craft, as well as the size and density, but I still don't think any debris will survive the fall.

Sources and Further Reading:

Physics.SE Question (heavily referenced)

FAA 4.1.7 on Atmospheric Re-entry.

'Re-entry Dynamics' : Dr. A. Pechev, University of Surrey.

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  • $\begingroup$ The question is about sub-orbital trajectories, not LEO $\endgroup$ – GdD Jun 11 '15 at 9:47
  • $\begingroup$ I'm reasonably sure he means a suborbital trajectory from LEO, bringing the periapse below the surface. At least, that's how I interpreted it. $\endgroup$ – Vedant Chandra Jul 8 '15 at 20:02

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