How far does the Earth travel around the Sun during each month of the year? After reading about the Earth's orbit and how it moves faster in January than it does in July (based on its distance from the Sun), I started to wonder...

How far does the Earth travel around the Sun during each month of the year?

What is the math behind this calculation?

Note: I'm not asking about the average monthly distance, but the unique distance traveled for each month.
By using the Approximate Solar Coordinates formulas on the U.S. Naval Observatory website, you can calculate the ecliptic longitude of the Sun (L) and the distance between the Earth and Sun (R) for any date. Then, The distance travelled between two dates is approximately s=R*(180/pi)*(L2-L1), where R is the average distance during the interval, and L2 and L1 are the ecliptic longitudes. Since the Earth's orbit is almost circular, this approach is reasonably accurate even when performing the calculation over an entire month. These are the results that I get, where the distance s is in Astronomical Units (AU, the average distance between the Earth and Sun).

Month     Distance Travelled,  days ave. daily  ave. change  accl.
Jan 2019      0.542 AU         31   .00175 AU       0 miles 0 f/ss
Feb           0.488            28   .00174 AU   - 475 miles 0.000672
Mar           0.536            31   .00173 AU  - 1300 miles 0.001840
Apr           0.514            30   .00171 AU  - 1490 miles 0.002104
May           0.527            31   .00170 AU  - 1210 miles 0.001709
Jun           0.508            30   .00169 AU   - 651 miles 0.000921
Jul           0.525            31   .00169 AU       0 miles 0
Aug           0.526            31   .00170 AU     279 miles 0.000395
Sep           0.513            30   .00171 AU    1300 miles 0.001840
Oct           0.535            31   .00173 AU    1490 miles 0.002104
Nov           0.522            30   .00174 AU    1300 miles 0.001840
Dec           0.542            31   .00175 AU     744 miles 0.001053


Of course, the variation from month to month is heavily influenced by the number of days in each month, where as the variation from January to July is due to the distance from the Sun.

As a check, I calculated the distance travelled for each day in January 2019 and totaled the distance. That result was s=0.5419 AU compared to s=0.5422 AU when using the calculation for the first and end of the month.