Grand Rapids to Jackson
This abandoned railway line was first built by the Grand River Valley Railroad in the late 1860s, despite the line charter which was conceived in 1846. As built this segment was cabable of 60 mph passenger service and 40 mph frieght operations. The GRV was actually a subsidiary of the Michigan Central Railroad, itself under control of the New York Central; the MC formally merged the GRV in 1916.
The line survived through the Penn Central merger, finally abandoned by Conrail in 1976. At that time, the rails had deteriorated to the point of having a 10 MPH limit imposed; sadly, Conrail crews had difficulty even maintaining that speed due to the condition of the tracks.
The western segment of the line between Grand Rapids and Vermontville was operated for a time after Conrail's abandonment by the Kent-Barry-Eaton Connecting Railway; this segment was abandoned in 1983. The last vestige of the line exists at Charlotte and eastward, and is operated by the Charlotte Southern Railroad, which operates both freight and a "murder mystery" style dinner train along its 5 miles.
The bridge pictured above over the thornapple has been recovered. The rail bed has been opened to public non motorized access from Vermontville to Gregs Crossing west of Nashville. I have the same pictures you have but of the new bridge and trail.
I have photos of bridges over the Grand River in two other locations; one, about 2 miles northwest of Rives Junction, and the other in the village of Onondaga. Also, I believe the point of interest for your pictured bridge is in the wrong location on the map. Shouldn't it be further west, where the line crossed the Thornapple River east of Vermontville at Shaytown Hwy?
If you go to YOUTUBE you can pull up a cab ride on an RDC run throught Middleville to Hastings. Doesn't last very long but its worth the trip!