According a CNET News, Longhorn will run on older systems.
"Although Microsoft is recommending that computers be pretty modern to fully run the next version of Windows, Longhorn will probably also run on a good number of older machines."
"The bad news is that Longhorn is going to look and run quite differently on those older systems. Computers with a 3GHz processor and 512MB of memory, for example, will get all of the bells and whistles including fancy graphics and the ability to handle multiple video streams. According to its early testing, Microsoft says that older PCs--probably those with as little as 128MB of memory--will be able to run Longhorn, but the OS may not look like it does on a newer, more powerful machine."
There are at least four different levels of graphics for the new Windows. Two of them--Aero and Aero Glass--will have new composited graphics, The top-of-the-line interface, code-named "Aero Glass," will have transparency and other advanced three-dimensional shading features but will demand a high-end video card with at least 64MB of video memory. The midlevel "Aero" interface will offer most of the improved graphics abilities and will require just 32MB of video memory. Both Aero and Aero Glass will also require DirectX 9.0 support, AGP 4X for external graphics cards and a Longhorn graphics driver.
For those systems that lack such a powerful graphics card, Microsoft will offer a "classic" interface, designed to replicate Windows 2000, the mainstay of today's corporate desktops.
Have a look at the link provided for more information.