Documentation / @interstellar-tools/types / ForceResultInterface

Interface: ForceResultInterface

Defined in: physics.ts:50

Result of a Newtonian gravitational force computation between two point masses.

Units: SI (newtons for force). vector and direction point from body 1 toward body 2.

Relevant equations (invariants & definitions)

$$\mathbf{F}=⟨F_x,F_y,F_z⟩,\parallel \mathbf{F}\parallel =\sqrt{F_x^2+F_y^2+F_z^2}$$$$\hat{\mathbf{r}}=\frac{{\mathbf{r}}_2-{\mathbf{r}}_1}{\parallel {\mathbf{r}}_2-{\mathbf{r}}_1\parallel },\parallel \hat{\mathbf{r}}\parallel =1$$$$\mathbf{F}=\parallel \mathbf{F}\parallel \hat{\mathbf{r}}$$

And, for context (how the magnitude is obtained in Newtonian gravity):

$$\parallel \mathbf{F}\parallel =G\frac{m_1{m}_2}{\parallel {\mathbf{r}}_2-{\mathbf{r}}_1{\parallel }^2}$$

Mappings to fields

• vector ↔ ($ \mathbf F $)
• magnitude ↔ ($ |\mathbf F| $)
• direction ↔ ($ \hat{\mathbf r} $)

Example

const res: ForceResultInterface = gravitationalForce(m1, m2, r1, r2);
// Invariant checks:
const [Fx, Fy, Fz] = res.vector;
const magFromVec = Math.hypot(Fx, Fy, Fz);
console.assert(Math.abs(magFromVec - res.magnitude) / res.magnitude < 1e-9);

See

https://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation

Properties

direction

readonly direction: Vector3DTupleType;

Defined in: physics.ts:56

Unit direction from body 1 to body 2 (dimensionless).

---

magnitude

readonly magnitude: number;

Defined in: physics.ts:54

Scalar magnitude of the force (N).

---

vector

readonly vector: Vector3DTupleType;

Defined in: physics.ts:52

Force vector on body 1 due to body 2 (N).