How long should I take my dog for a walk ?

That may be enough but you should have done it the moment you got him. GS have the tendency to have hip dysplacia. Their hind quarters weaken as they grow old. It's genetic. Regular exercise is the best preventive measure. At 9 years, it's probably full blown by now. I advise you consult a vet about it.

Has your Vet put him on pain pills for the arthritis?  He needs to loose some weight to make walking easier.  Put him on a diet.  Stop feeding people food.  He probably has hip dysplasia.

What is the meaning of hip dysplasia?

Hip dysplasia is the medical term for a hip socket that doesn't fully cover the ball portion of the upper thighbone. This allows the hip joint to become partially or completely dislocated. Most people with hip dysplasia are born with the condition.Mar 20, 2020

Hip dysplasia - Symptoms and causes - Mayo Clinicwww.mayoclinic.org › symptoms-causes › syc-20350209

Almost all GSDs have it cause BYBers don't breed this severe fault out of their GSDs.

You dog is in severe pain & needs to be medicated for it, cause he is suffering from it now.

It depends on a bunch of things but in the end, it’s up to the dog. One of the things it depends on is; is the dog showing signs it’s in pain or is done but doesn’t want to stop to please you? As soon as the dog shows any pain at all you’ve gone far enough. You may have to experiment a bit. Walk a certain distance. If the dog doesn’t show any signs it’s in pain, go a little further the next day and so on until you find the optimal distance. Hopefully, you have pain medication and can give it to the dog if it’s exhibiting pain. If no ask your vet, he should give you some, it’s always good to have some on hand. https://esacare.com/best-trainers-certified-therap...

Short and often daily walks ON SOFT GROUND is better than a long lead walk and arthritus is helped by the correct amount of daily exercise,  get his obesity under control this is totally your responsibility to ensure his weight is right and get your dog to the vets to make sure there are no other underlying health issues

First of all cut his food down if he is obese as this will aggravate his arthritis even more.

Start walks gently for about 15-20 minutes and work up gradually to an hour at least, over 3-4 weeks.

I assume he had some medication for his arthritis  from the vet

If not he should have.

He should never have been allowed to get so overweight in the first place and should have been exercised daily, even if he had arthritis, as without exercise the arthritic joints will seize up making mobility worse.

Where is his arthritis? Legs, hips, elbows?

It`s essential you cut down on food and treats to help him get back to a fit state.

Although 9 is considered `old` for a GSD, most fit and healthy GSD`s live until an average age of 12 years and some a lot longer. 

My old fellow lived until almost 15 years old and I never allowed him to get overweight. He was coming on 3 - 4 hour walks when he was 9 years old and still walking on 2 hour walks at 13 years old. No signs of any arthritis either. 

yes that is good. he is oldish so u don't want to over do it.

Rule of thumb:

All dogs needs a least one hour of exercise a day no matter what their age (this can be leash walking, playing in the garden or house) unless they have a medical reason.

Exercise if better for arthritis than no exercise.

If he he tolerating it add in another 20 minutes so he gets the full hour, especially as he has weight to lose and this is not a breed you want extra weight on. If he finds 3 20 minutes walks too much. Try 4 15 minute walks. If you notice he's lagging behind more, reluctant to walk, looking back towards home or any stiffness once home then maybe 1 hour is too much at his age. 

There are other forms of exercise besides walking. Swimming is excellent and the best form for over-weight dogs with joint problems. Even a toddle around the garden helps. Extra play time instead of a walk.

This is what I did with my dog once walks became too much. I just cut time off the walk and added it to time in the garden and play indoors. If you think he's doing as much as he can, then stick with it. Maybe even cut it into 2 fifteen minute walks and then a 10 minute walk. Remember it's ok for him to sit or lie down and rest on a walk. My dog could still do an hours walk as long as she could rest every 15 minutes for 5 minutes. Just play about with it. You don't want him to hurt himself or over do it, but it's vital he gets that weight off for the betterment of his joints and his health.

Yeah 15 minutes to 30. It depends because his hips may hurt.

I had a dog and at 11 years old he only wanted to go to the stop sign and back, then no walks at all. I had to lift his hips by the fur so he could stand up on all fours to get water or go outside.

I'd serve him food too.

But I used to walk him for 45 mi utes to 2 hours even. Or ride my bike.

Since he is older and a little chubby, I'd say that's the perfect amount of time.