Measuring the Mass of the Galaxy

Measuring the Mass of the Galaxy

Orbital Mechanics and Gravity

  • Everything orbiting in the galaxy does so due to gravity.
  • There's a direct relationship between gravitational force and orbital speed.
  • Objects closer to the center orbit faster, while those farther away orbit slower, following Kepler's laws.
  • The weaker the gravity, the slower the orbital speed.

Keplerian Orbits

  • The orbital pattern where objects farther away orbit slower is known as Keplerian orbit.
  • Objects in the galaxy orbit around the center.
  • By measuring the speed of stars orbiting the galactic center, we can compare it to expected speeds based on Keplerian orbits.
  • If orbits were purely Keplerian, objects far from the center should orbit much slower than objects closer to the center.

Mass Distribution in the Galaxy

  • Unlike the solar system with a single massive object (the Sun) at the center, the galaxy has mass distributed throughout.
  • The amount of mass inside an orbit is critical.
  • The mass outside of an orbit cancels out and can be ignored.
  • By measuring an object's speed and position in the galaxy, we can calculate the mass inside its orbit.

Calculating Orbital Speed

  • When determining orbital speeds, we consider the mass of everything within the orbit, not just the central mass.
  • Simplifying the calculation to consider only the mass within the orbit works effectively.
  • We can measure mass inside an orbit from its velocity and position.
  • v = \sqrt{\frac{GM}{r}}, where v is the velocity, G is the gravitational constant, M is the mass enclosed within radius r.

Unexpected Observations

  • If mass tailed off with increasing radius one would expect velocity to decrease following a Keplerian decline. However, observations revealed that objects maintain a roughly constant velocity regardless of distance from the galactic center.
  • v(r) \approx constant
  • If the center moved faster than the outer edge, the galaxy would wind itself up as spirals do not wind themselves up, they maintain structural integrity over time.

Estimating Mass and the Missing Component

  • We can estimate the galaxy's mass by counting stars and other visible matter.
  • However, the observed velocities don't align with the estimated mass based on visible matter alone.
  • Most of the mass of the galaxy is unaccounted for; we cannot see it.
  • This unseen matter is called dark matter.

Dark Matter

  • Dark matter is a form of matter that we cannot see, and its nature is still being investigated.
  • Dark matter plays a critical role in the dynamics of galaxies.
  • The mass of dark matter significantly outweighs the mass of all visible matter in the galaxy.