d4t_formulas/assets/formulas/gravity.d4rt

[
  // Free fall distance (vertical)
  {
    "name": "Free Fall Distance",
    "description": r"""
Calculates vertical displacement under constant gravity

$$h = \frac{1}{2}gt^2$$

Where:
- $g$: Gravitational acceleration $9.81\ \mathrm{m/s^2}$ on Earth
- $t$: Time in free fall (seconds)

![Free Fall Diagram](https://altcalculator.com/wp-content/uploads/2023/08/Free-Fall.png)""",
    "input": [
      {"name": "t", "unit": "second"},  // Time in seconds
      {"name": "g", "unit": "meters per second"}  // Gravitational acceleration
    ],
    "output": {"name": "h", "unit": "meter"},  // Height in meters
    "d4rtCode": "h = 0.5 * g * pow(t, 2);",
    "tags": ["physics", "kinematics"]
  },

  // Newton's Law of Universal Gravitation
  {
    "name": "Gravitational Force",
    "description": r'''
Newton's law of universal gravitation

\(F = G\frac{m_1m_2}{r^2}\)

Where:
- $G$: Gravitational constant $6.674\times 10^{-11}\ \mathrm{N\cdot m^2/kg^2}$
- $m_1, m_2$: Masses of two objects
- $r$: Distance between centers of masses

![Gravitation](https://upload.wikimedia.org/wikipedia/commons/thumb/3/33/NewtonsLawOfUniversalGravitation.svg/1200px-NewtonsLawOfUniversalGravitation.svg.png)''',
    "input": [
      {"name": "m1", "unit": "kilogram"},  // Mass 1
      {"name": "m2", "unit": "kilogram"},  // Mass 2
      {"name": "r", "unit": "meter"}     // Distance between masses
    ],
    "output": {"name": "F", "unit": "newton"},  // Force in newtons
    "d4rtCode": "F = (6.67430e-11 * m1 * m2) / pow(r, 2);",
    "tags": ["physics", "astronomy", "gravity"]
  },

]