Pistemassaa

Pistemassaa is a term used primarily in Finnish-language physics literature to denote a point mass—an idealized object in which all of its mass is concentrated at a single point in space, with negligible physical size. In English, the standard term is “point mass.”

Definition and mathematical model

A pistemassaa is treated as a particle with mass m and position vector r(t). The mass distribution is modeled as a Dirac delta function: ρ(x) = m δ(x − r(t)). This idealization allows the use of Newton’s laws of motion for a single body: m d^2r/dt^2 = F(r, t), where F represents external forces such as gravity or electromagnetism. In gravitational problems, the potential Φ satisfies Poisson’s equation ∇^2Φ = 4πGρ, which becomes ∇^2Φ = 4πG m δ(x − r(t)) for a point mass.

Applications and limitations

Point-mass models are foundational in introductory mechanics, celestial mechanics, and orbital dynamics, where bodies are approximated as particles to simplify calculations of trajectories and interactions. The approach is effective when the size of the body is small compared with the scales of interest and internal structure or rotation can be neglected. Limitations arise at very short distances or high-precision contexts where finite size, rotation, tidal forces, or internal mass distribution cannot be ignored.

Context and terminology

The term pistemassaa is not standard English; it is typically used to translate or adapt the concept of a point mass from Finnish sources. In English-language literature, the conventional term is “point mass.”

See also: Point mass, Dirac delta function, Newtonian mechanics, Gravitational two-body problem.