An inverse-square force models attraction between point masses.
Key knowledge
In Newtonian gravity, two point masses attract along their separation with force magnitude F = Gm₁m₂/r². The same exterior relation applies to non-overlapping spherically symmetric mass distributions.
Values and equations
F = Gm₁m₂/r²
F
Attractive force magnitude N
G
Newtonian gravitational constant m³ kg⁻¹ s⁻²
m₁
First mass kg
m₂
Second mass kg
r
Separation m
Conditions and scope
r is the separation of the point masses or spherical centers and is positive.
This is a Newtonian model; strong gravitational fields or relativistic precision require additional treatment.
Sources · 3
References
Sources retain their recorded scope. A source link alone does not establish verification of every statement.
OpenStax 13.1, equation 13.1 and point/spherical scope; NASA inverse-square relation.
2026-10-10 · Force law and geometry only; no measured numerical G or uncertainty is supplied.
Foundational review
2026-10-10 · Fresh primary-source inspection of the complete compact record, including every statement, equation, quantity and material condition, followed by independent AI editorial review. This check does not certify all linked lessons or every passage of every cited publication.
Sources from other places
Agreement within this scope
Newtonian point masses attract with inverse-square separation; exterior spherical distributions act as central point masses.
The spherical reduction does not extend to arbitrary nonspherical bodies or strong-field relativistic motion.
National Council of Educational Research and Training (NCERT)
An isolated Newtonian gravitational binary has relative semimajor axis a=a₁+a₂ and period T satisfying T²=4π²a³/[G(m₁+m₂)]. Thus an independently measured physical relative orbit and period determine the total mass; barycentric radii obey m₁a₁=m₂a₂.
The relative gravitational acceleration contains G times the sum of both masses.
For a spherical quasistatic Newtonian star, enclosed mass increases with shell volume and density, while the pressure gradient balances gravity due to enclosed mass. These coupled equations describe interior structure rather than a point mass held at one pressure.
Enclosed mass supplies spherical Newtonian gravity.
Matter moving inward in a gravitational field can release binding energy if energy is dissipated. For matter initially nearly at rest far from a Newtonian object of mass M and material radius R, available gravitational power scales as GMṀ/R. A radiated accretion luminosity is often parameterized L_acc=ηṀc² using an explicitly defined inflow rate and radiative efficiency. In a rotating disk, stress transports angular momentum so material can move inward; inflow and radiation need not have a universal efficiency.
The Newtonian potential supplies the bounded energy scale.
For isotropic luminosity L and a constant flux-weighted opacity per mass κ, outward radiative acceleration is κL/(4πr²c). Comparing it with Newtonian GM/r² gives L_Edd=4πGMc/κ. With fully ionized hydrogen and low-energy Thomson scattering, κ is approximately σ_T/m_p when electron mass is neglected. This conditional balance is useful for stars and accretion; it is not a universal maximum observed luminosity.
A gravity anomaly is an observed/modelled field difference relative to a stated reference and correction convention. In the spherical reference g(h)=GM/(R+h)²≈g₀(1−2h/R); reducing an elevated observation to the reference level adds 2g₀h/R at first order. A flat infinite slab of density contrastΔρ and thicknessH contributes downward acceleration 2πGΔρH on its exterior side. Removing a positive slab contribution is a distinct Bouguer correction.
The reference and slab attraction follow Newtonian gravity.
For an infinite line parallel to y at horizontal coordinate x₀ and depth b>0 with signed excess mass per lengthm_l, its downward surface anomaly is Δg=2Gm_lb/[(x−x₀)²+b²]. Integrating lines from x₁ to x₂ gives a thin strip model Δg=2GΔρH[arctan((x₂−x)/b)−arctan((x₁−x)/b)]. Greater burial broadens a fixed line-mass anomaly and lowers its peak magnitude.
Newtonian acceleration and superposition supply the forward kernel.
The stationary spherical nonrotating Jeans moment equation connects tracer density and radial velocity dispersion to enclosed mass through velocity anisotropy. Its outer-pressure boundary enters the solution. Different mass and anisotropy profiles can reproduce the same projected dispersion.
Conceptual association supported by the recorded research scope; this relation does not assert a proven derivation or mandatory prerequisite.
In a Newtonian gravitational field g, gravitational weight is W=mg. Mass and weight are different quantities: changing the local field changes weight without changing the body’s mass. A supporting scale measures a contact force, often called apparent weight; in free fall that support can vanish while gravity remains present.
This relation concerns the stated mass, gravitational weight and apparent weight claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.