Engineering domain: Mechanical Systems

## Task Description
You are tasked with designing a heat shield for a small spacecraft re-entering Earth’s atmosphere from low Earth orbit (LEO). The spacecraft follows a ballistic reentry trajectory. Your goal is to determine an appropriate heat shield radius (in meters) that satisfies the following performance constraints:

- The peak heat flux on the heat shield must not exceed **1000 W/cm²**
- The total heat load must not exceed **100 MJ/m²**
- The peak deceleration must not exceed **30g** (where 1g = 9.81 m/s²)

The spacecraft is spherical with the following properties:
- by experience it reaches highest heat at 40km above sea level
- Initial velocity: 7.8 km/s
- at 40km the speed is about 5500m/s and lose about half the heat
- Entry altitude: 400 km
- Flight path angle: –6 degrees
- Mass: 250 kg
- Drag coefficient: 0.47


Your output should propose a value of the heat shield radius that satisfies all three constraints.