section_path: Motion
section_name: Motion
paragraph_text: Motion
  
  Being part of the Milky Way galaxy the Sun, taking along the whole Solar System, moves in an orbital fashion around the galaxy's center of mass at an average speed of 230 km/s (828,000 km/h) or 143 mi/s (514,000 mph), taking about 220–250 million Earth years to complete a revolution (a Galactic year), having done so about 20 times since the Sun's formation. The direction of the Sun's motion, the Solar apex, is roughly in the direction of the star Vega.
  
  The Sun orbits the center of the Milky Way, and it is moving in the direction of the constellation of Cygnus with a speed of more than 220 kilometers per second (490,000 miles per hour). A simple model of the motion of a star in the galaxy gives the galactic coordinates X, Y, and Z (rotating coordinates so that the center of the galaxy is always in the X direction) as: X (t) = X (0) + U (0) κ sin (κ t) + V (0) 2 B (1 − cos (κ t)) {\displaystyle X(t)=X(0)+{\frac {U(0)}{\kappa }}\sin(\kappa t)+{\frac {V(0)}{2B}}(1-\cos(\kappa t))} Y (t) = Y (0) + 2 A (X (0) + V (0) 2 B) t − Ω 0 B κ V (0) sin (κ t) + 2 Ω 0 κ 2 U (0) (1 − cos (κ t)) {\displaystyle Y(t)=Y(0)+2A\left(X(0)+{\frac {V(0)}{2B}}\right)t-{\frac {\Omega _{0}}{B\kappa }}V(0)\sin(\kappa t)+{\frac {2\Omega _{0}}{\kappa ^{2}}}U(0)(1-\cos(\kappa t))} Z (t) = W (0) ν sin (ν t) + Z (0) cos (ν t) {\displaystyle Z(t)={\frac {W(0)}{\nu }}\sin(\nu t)+Z(0)\cos(\nu t)} where U, V, and W are the respective velocities with respect to the local standard of rest, A and B are the Oort constants, Ω 0 = A − B {\displaystyle \Omega _{0}=A-B} is the angular velocity of galactic rotation for the local standard of rest, κ = − 4 Ω 0 B {\displaystyle \kappa ={\sqrt {-4\Omega _{0}B}}} is the "epicyclic frequency", and ν is the vertical oscillation frequency. For the sun, the present values of U, V, and W are estimated as (U (0), V (0), W (0)) = (10.00, 5.25, 7.17) {\displaystyle (U(0),V(0),W(0))=(10.00,5.25,7.17)} km/s, and estimates for the other constants are A = 15.5 km/s/ kpc, B = −12.2 km/s/kpc, κ = 37 km/s/kpc, and ν=74 km/s/kpc. We take X (0) and Y (0) to be zero and Z (0) is estimated to be 17 parsecs. This model implies that the Sun circulates around a point that is itself going around the galaxy. The period of the Sun's circulation around the point is 2 π / κ {\displaystyle 2\pi /\kappa }. which, using the equivalence that a parsec equals 1 km/s times 0.978 million years, comes to 166 million years, shorter than the time it takes for the point to go around the galaxy. In the (X, Y) coordinates, the Sun describes an ellipse around the point, whose length in the Y direction is 1035 parsecs and whose width in the X direction is 691 parsecs. The moving point is presently at X = V (0) 2 B = − 215 parsec {\displaystyle X={\frac {V(0)}{2B}}=-215{\text{ parsec}}} Y = 2 Ω 0 κ 2 U (0) = 405 parsec. {\displaystyle Y={\frac {2\Omega _{0}}{\kappa ^{2}}}U(0)=405{\text{ parsec}}.} The oscillation in the Z direction takes the Sun 98 parsecs above the galactic plane and the same distance below it, with a period of 83 million years, approximately 2.7 times per orbit. Although 2 π / Ω 0 {\displaystyle 2\pi /\Omega _{0}} is 222 million years, the value of Ω {\displaystyle \Omega } at the point around which the Sun circulates is Ω ≈ Ω 0 − 2 A R 0 Δ X ≈ 26.1 km/s/kpc {\displaystyle \Omega \approx \Omega _{0}-{\frac {2A}{R_{0}}}\Delta X\approx 26.1{\text{ km/s/kpc}}} corresponding to 235 million years, and this is the time that the point takes to go once around the galaxy. Other stars with the same value of X + V / (2 B) {\displaystyle X+V/(2B)} have to take the same amount of time to go around the galaxy as the Sun and thus remain in the same general vicinity as the Sun.
  
  The Sun's orbit around the Milky Way is perturbed due to the non-uniform mass distribution in Milky Way, such as that in and between the galactic spiral arms. It takes the Solar System about 225–250 million years to complete one orbit through the Milky Way (a galactic year), so it is thought to have completed 20–25 orbits during the lifetime of the Sun. The orbital speed of the Solar System about the center of the Milky Way is approximately 251 km/s (156 mi/s). At this speed, it takes around 1,190 years for the Solar System to travel a distance of 1 light-year, or 7 days to travel 1 AU.
  
  The Milky Way is moving with respect to the cosmic microwave background radiation (CMB) in the direction of the constellation Hydra with a speed of 550 km/s, but since the sun is moving with respect to the galactic center in the direction of Cygnus (galactic longitude 90°; latitude 0°) at more than 200 km/sec, the resultant velocity with respect to the CMB is about 370 km/s in the direction of Crater or Leo (galactic latitude 264°, latitude 48°). This is 132° away from Cygnus.