First things on the physics object

Assets/Scenes/Main.unity

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@@ -1458,6 +1571,7 @@ GameObject:
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@@ -1493,6 +1607,8 @@ MonoBehaviour:
   m_Name: 
   m_EditorClassIdentifier: '::'
   mainEngine: {fileID: 1437557825}
+  rb: {fileID: 1172921199}
+  altimeter: {fileID: 894314916}
 --- !u!54 &1172921199
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@@ -1515,11 +1631,32 @@ Rigidbody:
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   m_ImplicitCom: 1
   m_ImplicitTensor: 1
-  m_UseGravity: 1
+  m_UseGravity: 0
   m_IsKinematic: 0
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@@ -1863,3 +2000,4 @@ SceneRoots:
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Assets/Scripts/RocketPhysics.cs

@@ -1,20 +1,70 @@
+using Unity.VisualScripting;
 using UnityEngine;
 
 public class RocketPhysics : MonoBehaviour
 {
     [Header("References")]
     public MainEngine mainEngine;
+    public Rigidbody rb;
+    public Altimeter altimeter;
 
+    [Header("Data")]
+    public DoublePrecisionVector3 position;
+    public DoublePrecisionVector3 velocity;
+    public DoublePrecisionVector3 rotation;
 
     // Start is called once before the first execution of Update after the MonoBehaviour is created
     void Start()
     {
-        
+        position = new DoublePrecisionVector3(rb.position.x, rb.position.y, rb.position.z);
+        velocity = new DoublePrecisionVector3(rb.linearVelocity.x, rb.linearVelocity.y, rb.linearVelocity.z);
+        rotation = new DoublePrecisionVector3(rb.rotation.eulerAngles.x, rb.rotation.eulerAngles.y, rb.rotation.eulerAngles.z);
     }
 
     // Update is called once per frame
     void Update()
     {
-        
+        double gravityAcceleration = altimeter.gh;
+        double thrustAcceleration = mainEngine.thrust / rb.mass;
+
+        Vector3 thrustDirection = rb.rotation * Vector3.up;
+        DoublePrecisionVector3 gravityAccelerationVector = new DoublePrecisionVector3(0, -gravityAcceleration, 0);
+        DoublePrecisionVector3 thrustAccelerationVector = new DoublePrecisionVector3(
+            thrustDirection.x * thrustAcceleration,
+            thrustDirection.y * thrustAcceleration,
+            thrustDirection.z * thrustAcceleration
+        );
+        DoublePrecisionVector3 totalAcceleration = gravityAccelerationVector + thrustAccelerationVector;
+
+        velocity = velocity + totalAcceleration * Time.deltaTime;
+        position = position + velocity * Time.deltaTime;
+
+        rb.position = new Vector3((float)position.x, (float)position.y, (float)position.z);
+        rb.linearVelocity = new Vector3((float)velocity.x, (float)velocity.y, (float)velocity.z);
+        rb.rotation = Quaternion.Euler((float)rotation.x, (float)rotation.y, (float)rotation.z);
     }
 }
+
+public class DoublePrecisionVector3
+{
+    public double x;
+    public double y;
+    public double z;
+
+    public DoublePrecisionVector3(double x, double y, double z)
+    {
+        this.x = x;
+        this.y = y;
+        this.z = z;
+    }
+
+    public static DoublePrecisionVector3 operator +(DoublePrecisionVector3 a, DoublePrecisionVector3 b)
+    {
+        return new DoublePrecisionVector3(a.x + b.x, a.y + b.y, a.z + b.z);
+    }
+
+    public static DoublePrecisionVector3 operator *(DoublePrecisionVector3 a, double d)
+    {
+        return new DoublePrecisionVector3(a.x * d, a.y * d, a.z * d);
+    }
+}