Documentation / @interstellar-tools/equations / forceOn1By2

Function: forceOn1By2()

function forceOn1By2(
  m1: number,
  m2: number,
  r1: Vector3DTupleType,
  r2: Vector3DTupleType,
  G?: number
): Vector3DTupleType;

Defined in: gravity/force-on1-by2.ts:90

Gravitational force vector on body 1 due to body 2 (newtons, N).

Definitions

$$\mathbf{r}={\mathbf{r}}_2-{\mathbf{r}}_1,r=\Vert \mathbf{r}\Vert ,\hat{\mathbf{r}}=\frac{\mathbf{r}}{r}$$

Newton's law (vector form)

$${\mathbf{F}}_{1\leftarrow 2}=G\frac{m_1{m}_2}{r^2}\hat{\mathbf{r}}$$

Magnitude & Components

$$\Vert \mathbf{F}\Vert =G\frac{m_1{m}_2}{r^2},\mathbf{F}=⟨F_x,F_y,F_z⟩=\Vert \mathbf{F}\Vert \hat{\mathbf{r}}$$$$F_x=\Vert \mathbf{F}\Vert {\hat{r}}_x,F_y=\Vert \mathbf{F}\Vert {\hat{r}}_y,F_z=\Vert \mathbf{F}\Vert {\hat{r}}_z$$

Newton's 3rd law (context)

$${\mathbf{F}}_{1\leftarrow 2}=-{\mathbf{F}}_{2\leftarrow 1}$$

Units

• Inputs: masses in kg, positions in m, ($G$) in m³·kg⁻¹·s⁻².
• Output: force vector in newtons (N).

INFO

• The returned vector points from body 1 toward body 2 (i.e., along ($ \hat{\mathbf r} $)).
• Internally delegates to gravitationalForce(m1, m2, r1, r2, G) and returns its direction-scaled magnitude as a 3-tuple.
• For acceleration instead of force, use accelerationOn1By2 or compute ($ \mathbf a=\mathbf F/m_1 $).

Invariants (within FP tolerance)

• ||F|| = G*m1*m2/r²
• F = ||F|| * r̂

Parameters

Parameter	Type	Default value	Description
m1	number	undefined	Mass of body 1 (kg).
m2	number	undefined	Mass of body 2 (kg).
r1	Vector3DTupleType	undefined	Position of body 1 [x, y, z] in meters.
r2	Vector3DTupleType	undefined	Position of body 2 [x, y, z] in meters.
G?	number	G_SI	Gravitational constant.

Returns

Vector3DTupleType

Force on body 1 due to body 2, in newtons [Fx, Fy, Fz].

Throws

Error Propagated from gravitationalForce if inputs are invalid (non-finite/negative masses, coincident positions ($r=0$), or non-positive ($G$)).

Examples

// Earth–Sun at ~1 AU (force on Earth due to Sun)
const mEarth = 5.972e24; // kg
const mSun = 1.9885e30; // kg
const rEarth: [number, number, number] = [0, 0, 0];
const rSun: [number, number, number] = [1.495978707e11, 0, 0]; // m

const F = forceOn1By2(mEarth, mSun, rEarth, rSun); // N
const Fmag = Math.hypot(F[0], F[1], F[2]); // ≈ 3.54e22 N

// Derive acceleration from the returned force: a = F / m1
const a: [number, number, number] = [
  F[0] / mEarth,
  F[1] / mEarth,
  F[2] / mEarth
]; // m/s²

See

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