Tracing it automatically - forget! It needs human reasoning to get it right. Or at least 5 times sharper original bitmap image.
You can buy manual redrawing if you cannot do it for some reason. It takes about 15 minutes if a skilled vector illustrator redraws it.
The sphere can be a simple revolution in Illustrator, but it can be drawn as well without 3D effects. I see good texts and all those small auxiliary drawings more tricky than the sphere.
How to make the sphere
Be sure you have smart guides ON, snap to points ON, all other snaps OFF.
Draw a couple of circles (=ellipses, but drawn holding Shift pressed at the same time) two lines, one horizontal and one vertical. Have only strokes, no fill color!
Align all horizontally and vertically to same centerpoint
Add two lines to make the sector limits for your dθ. This all is the backbone of your drawing. Select all, group all and make a spare copy of the group (drag aside holding Alt) because the original get trashed in step 4.
Select the backbone group. Select the Shape Builder tool. Select orange fill color & no stroke color. click the areas which you are going to revolve. Ungroup the shape and delete all plain lines and curves, leave the orange pieces. If they happen to have some stroke color, remove it.
Group the orange pieces, Object > Transform > Rotate them 90 degrees
Goto Effects > 3D > Revolve. See the dialog. Every setting is essential! I have added two lights and reduced the ambience light to get a shading that I see good. Play with it. Another possiblity is to have no shading at all. We check it later. Light options are normally hided, click "More options" to see them.
NOTE: You can recall the effect dialog for tweaks by clicking the effect in the Appearance panel.
Obviously you want to see the backbone drawing and the revolved parts in the same. You have the spare copy. Take it. It must be a group, because it must be squeezed horizontally to make it fit. 3D shell is rotated 15 degrees to show the shell thickness. The backbone drawing must be scaled horizontally (Object > Transform > Scale ) to cos(15 degrees) = 96.6% to make it fit with invisible small error:
If you the image 7, where the backbone drawing is squeezed horizontally, as told, you can say "it does not fit in the left". Wrong! It's tilted 15 degrees, the stroke is behind the horizon.
I would leave orange parts totally strokeless and delete the partially hided half circle in the backbone. If you want the stroke, you can ungroup the backbone and stretch the outer circle a little:
The "No Shading" -version. It offers clear benefits, because it has only one color. That means it's much simpler than the shaded version. It can have a stroke and it can be easily recolored. The shaded version is internally made of tens of differently colored splinters. It's useless to try to edit them.
In the revolve dialog No Shading is selected. Otherwise it's the same than 6.
The shape is expanded (=the effect is fixed) and a black stroke is given. Expanding a 3D effect happens with Object > Expand Appearance. Expanded shape is often a multilevel group. This one needs 3 subsequent ungroupings until it's freely editable.
A radial gradient color has been given to two biggest surfaces. Small surfaces are not recolored here. But they can have any color because they are separate objects, if everything is ungrouped enough many times.
12 The backbone drawing is ungrouped. Unnecessary circle arcs are selected with the direct selection tool and deleted. The unnecessary vertical line is also deleted.
- The backbone drawing is sent to back and the sphere is dragged over it.
The revolved sphere, especially the shell increment is quite different than in your original drawing. Revolved version is a right projection of a 3D object. In the original you can see projection errors which make it a little easier to draw in 2D. As an illustration of a calculation principle that can be fully acceptable.
ADDENDUM: Just to see how it can be drawn in Inkscape I made the backbone group there (it's green) and tried to insert splitted ellipses to the crossig points. Inkscape has very well working snaps - It was very easy.
Drawing it in Inkscape is a good option if you are skilled in tinkering with curves, splitting and joining them. A good amount of small curve pieces must be made and joined together until you have separate, but well fitting closed shapes that can be colored like this:
The exploded view in the right shows all separate parts. In theory the paint bucket tool could create the needed closed shapes like Live Paint or Shape Builder in Illustrator. Unfortunately Inkscape's paint bucket isn't exact, it works only in screen resolution.