Documentation / @interstellar-tools/equations / accelerationOn1By2

Function: accelerationOn1By2()

function accelerationOn1By2(
  m2: number,
  r1: Vector3DTupleType,
  r2: Vector3DTupleType,
  G?: number
): Vector3DTupleType;

Defined in: gravity/acceleration-on1-by2.ts:69

Gravitational acceleration of body 1 due to body 2 (vector, m/s²).

Definitions

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

Acceleration field

$${\mathbf{a}}_{1\leftarrow 2}=\frac{{\mathbf{F}}_{1\leftarrow 2}}{m_1}=G\frac{m_2}{r^2}\hat{\mathbf{r}}$$

Units

• Inputs: masses in kg, positions in m, ($G$) in m³·kg⁻¹·s⁻².
• Output: acceleration in m/s².

INFO

• Implemented via gravitationalForce(1, m2, r1, r2, G), so the returned vector equals the force on a 1 kg test mass (i.e., the acceleration).
• Direction points from body 1 toward body 2: ($ \hat{\mathbf r} $).

Invariants (within FP tolerance)

• ||a|| = G*m2/r²
• a = ||a|| * r̂

Parameters

Parameter	Type	Default value	Description
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

Acceleration of body 1 due to body 2 (m/s²).

Examples

// Acceleration of a satellite due to Earth at ~7000 km from Earth's center
const mSat = 500; // kg (any value; a is independent of mSat)
const mEarth = 5.972e24; // kg
const rSat: [number, number, number] = [7.0e6, 0, 0]; // m
const rEarth: [number, number, number] = [0, 0, 0];

const a = accelerationOn1By2(mSat, mEarth, rSat, rEarth);
// ≈ [-8.14, 0, 0] m/s² (toward Earth)

// Derive force from acceleration (F = m1 * a)
const m1 = 1200; // kg spacecraft
const a = accelerationOn1By2(m1, mEarth, rSat, rEarth);
const F: [number, number, number] = [a[0] * m1, a[1] * m1, a[2] * m1]; // newtons

See

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