The separation between the centers of Andromeda and the Milky Way during the course of their merger.

Newton's law of universal gravitation

Every point mass attracts every other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between the point masses: F = G \frac{m_1 m_2}{r^2}, where:

  • F is the magnitude of the gravitational force between the two point masses,
  • G is the gravitational constant,
  • m1 is the mass of the first point mass,
  • m2 is the mass of the second point mass,
  • r is the distance between the two point masses.

Basic 3D Computer Graphics

The calculation of orthographic surface density images assumes that rays are parallel to the line of sight. The geometry of perspective for a single particle is given in the figure below. The pyramidal volume containing the system is called the frustrum. A camera C at position (xc, yc, zc) is centered on the field of view (FOV) represented by a rectangle placed at a distance d = zi − zc. A ray traced from particle P hits the FOV to create an image I position (xi, yi) with coordinates given by:

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