Spherical velocity conservation

I am trying to create an object that accelerates around a sphere. In the object’s update function, I apply a force to it that it parallel to its forward. I also have this code to keep the object at a constant distance from the sphere and parallel to the sphere’s surface. However, no acceleration occurs because the velocity is not conserved in spherical coordinates. To fix this I tried adding the commented lines, which are supposed to first store the current local velocity, and after the position and rotation change, set it again to the previous value. However, it only produces extreme jerkiness. What is the best method?

    var hit : RaycastHit;
	var newForward : Vector3;
	if (surfaceCol.Raycast(new Ray(thisTransform.position, surface.position - thisTransform.position), hit, 100)) {
		newForward = Vector3.Cross(hit.normal, thisTransform.right);
		
	    //	var oldVel = thisTransform.InverseTransformDirection(thisBody.velocity);
		
	    thisTransform.LookAt(thisTransform.position + newForward * 50, hit.normal);
        thisTransform.position = hit.point + hit.normal * height;
        
        //  thisBody.velocity = thisTransform.TransformDirection(oldVel);
    }

do you want to do it with physics or with just movement formula?

with physics you could have 2 constant forces that apply pressure to it towarde the centre and away from the centre of the orbital sphere depending on its distance to the orbital sphere, and apply a constant force forwards and a lookat centre+90degrees. in this way you use physics to keep it in the sphere instead of using some special position formulas that cancel the physics. also it makes real orbital physical forces that you can tweak the strength of an have lots of different effects, and if you knock a thing from its orbit it moves back there physically, i did that to simulate electrons it looks great.

if you dont need physics just use sine and cosine to make sphere and make them multiply with time.time inside the cosine and sine like x=sine(time.time*time.time(accellerates exponentially) and y is with cos.

does it have a disc orbit, a spirograph orbit, or other?