Where can I find the following motor run(?) capacitor?

Magnetec
175863-20
005-1477-RMF
20uF 370 VAC
P10000 AFC

It is three inches long and 1 3/4 inches in diameter.

Do you have an NTE electronics distributor nearby? They have a pretty good line of AC motor capacitors...
http://www.nteinc.com/capacitor_web/pdf/motor_run.pdf

The part number you want is MRC370V20

WW Graingers has an 800 number you can call and get a direct cross if not the exact product. They will tell you what, how much, your closest distributor, or arrange for it to be shipped to you. They do the same with motors.

BTW, the phone # you want at Graingers is 1-800-323-0620 for the cross reference.

I already emailed and then called Grainger's (I should have mentioned that). Their product support was unable to help. They recommended that I go to a motor shop.

Johnstone Supply has a run capacitor, 20Mfd 370v 1¾" by 3 5/8". Part #G31-791. http://www.johnstonesupply.com