## Earth’s Orbital Speed and Acceleration

Earth orbits the Sun in a nearly circular orbit once each year. A year is 365.24 days, or about 3.156X10^{7} seconds (= 31.56 million seconds). The average distance between the Earth and Sun is about 1.496X10^{11} meters (= 149.6 million kilometers).

Applying the above formulas for Earth’s orbital speed and centripetal acceleration gives the following result:

When speed = distance/time, and we use the results we’ve already found, then

speed = 2 (π) (1.496X10^{11})meters/3.156X10^{7}seconds. After doing the math, we find that speed = 2.978X10^{4} meters per second = 6.664X10^{4} miles per hour = 66,640 miles per hour.

When centripetal acceleration = speed squared/radius, and we use the results from our earlier calculations, the formula looks like this:

centripetal acceleration = ((2.978X10^{4} meters per second)^{2})/(1.496X10^{11} meters).

After we do the math, we find that centripetal acceleration = 0.005928 meters per second squared.

Although Earth’s orbital velocity around the Sun is fairly high, the centripetal acceleration needed to keep it in an approximately circular orbit is quite small.

## Speed and Acceleration of Solar System Orbiting the Milky Way

Ghez et al (2008, Astrophysical Journal, v. 689, p. 1044) estimate that the Sun and solar system are about 8400 parsecs (=27,000 light years = 2.6X10^{20} meters) from the center of the Milky Way galaxy.

Because it takes so long astronomers do not directly measure the time it takes for the Sun and solar system to orbit the galactic center. Instead astronomers measure the solar system’s orbital speed from the Doppler shifts of nearby galaxies. The Sun orbits the center of the Milky Way at a speed of about 220 kilometers per second (=2.2X10^{5} meters per second = 490,000 miles per hour). Applying the formulas and distance to the galactic center above gives 240 million years for the solar system’s orbital period around the center of the galaxy. Published estimates for this orbital period may range from about 200 to 250 million years because the distance to the galactic center is uncertain.

The centripetal acceleration required for the Sun and solar system to orbit the center of the galaxy is quite small: 1.9X10^{-10} meters per second squared.

We don’t feel these motions because we perceive accelerations rather than constant velocities as motion. Even though Earth’s velocities are quite high, the accelerations are too small to perceive.

## Resources:

Ghez et al. *Measuring Distance and Properties of the Milky Way’s Central Supermassive Black Hole with Stellar Orbits*. (2008). Astrophysical Journal, v. 689, p. 1044. Accessed June 6, 2012.

NASA. *Earth Fact Sheet*. (2012). Accessed June 6, 2012.

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