In a medium bowl, cream together the sugar and shortening. Beat in eggs, one at a time.
Combine the flour, baking powder, baking soda and salt, stir into the creamed mixture. Finally, stir in the milk, orange juice and orange zest. Drop by heaping spoonfuls onto an ungreased cookie sheet.
Bake for 8 to 10 minutes in the preheated oven, until the edges turn golden.