I have tried using the pathfinder but I can't use it on a grouped object.
I want to make something that looks like this.
There's a darker shadow on the side. This is what I'm trying to achieve. I have already made the light side.
This case looked like it's already completed by others, but it isn't. The plausible shadow shape should have elliptical edge. That's because the shadow should in 3D cover half of the planet. The border in 3D is circle, but it's tilted projection is an ellipse.
a black circle (no stroke) which has exactly the same size as the colored planet (image 5)
The black circle is duplicated. The duplicate is recolored for clarity. It's squeezed horizontally to get an ellipse and aligned to the same midpoint as the black circle
The anchor at 9 o'clock is edited with the direct selection tool to make the left side to cover the left half of the black circle totally.
The geometric crest-like shape of the shadow is created with Pathfinder panel > Minus front
The colored planet without the shadow
The crest is rotated to the wanted angle and placed onto the planet. The placing can be tricky, but Smart Guides = ON make it to snap easily.
The crest has got reduced opacity (=38%). You can change it in the Appearance or Transparency panel. Blending mode Normal works well because the crest is black, no need to set another blending mode.
Not asked: A sharp crest type shadow works in the simple illustration above. A gradient can be more useful if one wants to present there'a a thick gas atmosphere
If there's no atmosphere, but complex surface forms like in this small rock planet, an elementary shading of a 3D model can create the light and shadow with zero effort.
(I drew these images for other cases few months ago, the 3D model was taken from this question What are some techniques for designing realistic-looking planets and moons?, it's not mine.)
Follow this process.
1- draw your circle 2- copy-paste in front twice, thus you will get 3 circles. 3-move the uppermost circle a bit outward to form the shadow figure. 4-take the two uppermost circles and apply minus front. 5- after minus front give the remaining portion same color but slight darker one.