We’re accustomed to seeing things travel pointy-end-first (bullets, rockets, arrows, Lamborghinis) so it seems “natural” that Entry Vehicles (EV) should be most stable traveling pointy-end-first as well. Not so.
Pointy-end-first is chosen when drag coefficient is the prime design criteria. Engineers then need to add tailfins, spin, fletching or gimbaled engines to overcome the inherent instability of this choice.
For example, bullets are inherently unstable since their Center of Gravity (CG) is behind their Center of Pressure (CP). They only achieve adequate static stability due their extremely high spin rate (hundreds of thousands of RPM).
An airgun pellet (they sometimes travel supersonic) has static stability since the CG is ahead of the CP.
A sphere has static stability due to its symmetry.
A portion of a sphere has a similar shock wave to a complete sphere. As long as the CG is ahead of the center of spherical curvature, the object is statically stable.
The static stability of a spherical section is assured if the
vehicle's center of mass is upstream from the center of curvature
An EV has a similar shape to the pizza-pie section above, but rounded at both ends. The relationship between its CG and CP is similar to an airgun pellet.
If this EV is travelling pointy-end-first, the curvature which is generating the shock wave has a much shorter radius. This places the CP in front of the CG and creates static instability, just like a bullet.