Peel, core and thinly slice the apples, toss them with the orange juice. Optionally sprinkle with cinnamon, nutmeg, cardamom.
Cream butter and sugar well; add eggs and beat well. Put the yogurt in a 2 cup measuring cup, add the baking soda and mix. Sift together the flour and baking powder. Add the yogurt and flour mixture to the butter and sugar.
Put half the batter in the pan, cover with all the apples, cover with remaining batter.
Cover with the crumb topping.
Bake for 45minutes, test with butter knife, should come out dry except for some apple juice.