2
$\begingroup$

Are there any equations that can calculate the burnup of an asteroid depending on the angle? I want to be able to calculate the magnitude of an asteroid impact with the angle being the changeable variable

$\endgroup$
  • $\begingroup$ This is unlikely, as you never know the consistency or makeup of the asteroid. There are indicative numbers from observed data, which may be enough for you to fit an equation to... $\endgroup$ – Rory Alsop Jul 10 at 19:10
  • 1
    $\begingroup$ I am looking into the asteroid Apophis in which we know the makeup of $\endgroup$ – sebastian Jul 11 at 5:10
2
$\begingroup$

The Purdue University Impact Earth! site will calculate this for you. Clicking on the Documentation link will give you the paper of formula and approximations that are used. The equation for the breakup altitude is: $$ z_\star\approx-H\Bigl[\ln\Bigl(\frac{Y_i}{\rho_0v_i^2}\Bigr)+1.308-0.314I_f-1.303\sqrt{1-I_f}\Bigr] $$ where $H$ is the scale height of the atmosphere (taken to be 8km), $\rho_0$ is the surface atmospheric density (taken to be $1\,kg/m^3$) and $Y_i$ is the yield strength of the impactor and $I_f$ are given by: $$ \log_{10}Y_i=2.107+0.0624\sqrt{\rho_i} $$ where $\rho_i$ is the impactor density (2600 kg m$^{-3}$ for Apophis (assumed)) and: $$ I_f=4.07\frac{C_DHY_i}{\rho_iL_0v_i^2\sin\theta} $$ here $C_D$ is the drag coefficient (taken to be 2), $L_0$ is the impactor diameter (0.34 km for Apophis; Brozovic et al. 2018), $v_i$ is the impact velocity and $\theta$ is the entry angle. If $I_f<1$, this indicates the impactor breaks up above the surface.

Given the complexities involved, I would suggest you use the website itself and vary the impact angle through tha - the dominant effects are going to be the encounter velocity (see e.g. close approach data at the JPL Small Body DB Browser) and uncertainties in the size and density.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.