Thorens TD-160 motor run capacitor

I recently got an old Thorens TD 160 turntable (Mk-I I think). The motor did not turn. I removed the motor and measured the DC resistance of the coils, and they were both open. So I found someone on eBay selling a motor and bought it. So far so good. I connected the new motor and turned it on, and it turned. The wire were arranged differently (red and blue on the inside, black on the outside)but it worked and turned the right direction.

However, I thought while I had things open I would check the capacitor. The manual that I found on line indicated that the motor-run cap should be 0.33uF. However, the capacitor in the TT is 0.15uF (400V). I am concerned that the new motor would be happier with 0.33uF.

So two questions: What would be the effect of using a capacitor of half the correct value? I know the cap is supposed to introduce a 90-degree phase shift between the two windings. If the cap is 0.15 instead of 0.33 does that imply the phase shift is only 45-degrees?

Second: Is there a way, like by measuring the DC resistance of the coils, to determine the correct capacitor value for the new motor? Since the old motor was dead I have no idea what the DCR of those coils was. I do not have access to an oscilloscope to measure the phase difference between the windings.

Any help/advice much appreciated.
If the capacitor value is not correct, there will not be 90° phase shift, and the motor will vibrate. The best way is to measure the voltage between the coils, and calculate the phase shift by using some trigonometry. Hint: the coils are connected in an L fashion, so you have to measure 3 voltages. The result should be a right angle triangle with equal legs. Right angle is more important than equal legs. Best to do it under load, i.e. when the platter is turning. I could also check the capacitor in my TD-160 Super, but here we have 230V/50Hz, and it would also take some time for me to disassemble my turntable.