TERRA

Terra's descending orbit crosses the equator at 10:30 am local time during each orbit (hence the original designation "EOS/AM-1").

According to NASA's press kit (pdf, 236 KiB) clouds typically form over tropical land in the afternoon as the surface warms, creating updrafts; hence, Terra's morning view provides clearer images of the Earth's lands.

This graph shows the actual equatorial crossing LMT and the difference between the geographic longitude of the Sun and of the satellite.
LMT is calculated as: LMT = UTC + lon / 15, where lon is the geographic longitude of the satellite when it crosses the equator.

Here's the mean orbital inclination and the mean radius vector.
The graph shows that every 2 or 3 reboosts there is also an inclination change burn.

According to the document June 2014 Terra Status (pdf, 565 KiB), based on predicted fuel usage, Terra can continue to perform propulsive maneuvers (to maintain the orbit) to support the science requirements into 2020. LMT will drift from 10:30 am to 10:15 am.