Fredericksburg & Gordonsville (standard gauge) graded during the Civil War, built after the Civil War from Fredericksburg to Parker. The line lasted a few years but was sold in foreclosure to the Fredericksburg Orange & Charlottesville, which in turn failed in 1874. The existing line was then converted to narrow gauge (3 feet) and extended from Parker to Orange in 1878, and renamed the Potomac Fredericksburg & Piedmont (PF&P).
The PF&P ran until after WW I, when it was sold in foreclosure in 1925 and then became the Orange & Frederick RR. In 1926 the line was standard gauged and named the Virginia Central, apparently unrelated to an earlier line that was also called the Virginia Central. It had planned to head east from Fredericksburg in 1930, but the line was never built. The main stem of the Virginia Central was abandoned in 1938, except for short segments at either end. The Fredericksburg stub lasted until 1973; the Orange stub (serving a building materials company) probably lasted into the 1980s.
The line roughly parallels Virginia route 20 from Orange to Verdiersville. In the Rhoadsville area, it appears the right of way ran across what are now the front yards of homes. East of Verdiersville, the right of way parallels route 621 as far as Parker. Continuing further east the right of way cuts through the Fredericksburg-Spotsylvania National Military Park, and then joined the RF&P on the south side of Fredericksburg.
Thanks to Mike Palmer for contributing information about this route.