Claire Brown, communications director of the Smithsonian Air and Space Museum, was asked the same question.
“The reason that it’s not in this museum was that it was personal
property of Alan Shepherd. In other words, he took it to space, he
brought it back, it was still his personal property he donated it and
it was his. That’s the reason,” said Claire ...
From NASA-TM-X-57097 found by Tristan:
So two manned ballistic flights were done using a heat-sink, not an ablative heat shield.
I found an image of such a heat sink.
This is a replacement "heat sink" heatshield for the Mercury-Redstone
2 capsule. The original was lost after recovery of the capsule from
the ocean and this heatshield did not fly ...
Excerpt from NASA-TM-X-57097 describing the original design:
The heat shield used on Big Joe was geometrically a 74.5-inch diameter spherical segment
with a radius of curvature of 80 inches. ... The heat shield consisted of two laminates:
an outer ablation laminate, 1.075 inches thick and an inner structural laminate, 0.550 inch
thick. The ablation laminate ...
Here is a Photograph of the KSC CMS Simulators (x2) and LMS Simulator in the Flight Crew Training Building, from 1968. I toured this building in 1971 with flight crews training in both the CMS and LMS, but cannot recall if there was more than one CMS at that time.
The three Shuttle Mission Simulator training bases are, or will "soon" be, in museums. However, they are a shadow of their operational selves.
The Fixed Base is in the Stafford Museum in Oklahoma. This is the only one currently visible to the public.
(picture from Facebook SMS page)
The Motion Base, after being in durance vile at Texas A&M ...
It's an engineering test mockup.
This model incorporates an engineering model of the Descent Stage (used at MSFC, designers of the Lunar Rover, for studies and fit checks) with a fabricated Ascent stage (note the lack of detail in the hatchway area compared to some other LM images)