Rotation and translation of the Earth opengl c++ - c++

Question

I am trying to get a sphere to rotate around another simulating the orbit of the Earth.
I am able to get the Earth to orbit around the sun; however, I can't get it to rotate around itself.
This is the code I have so far:
//sun
glMaterialAmbientAndDiffuse(GLMaterialEnums::FRONT,GLColor<GLfloat,4>(1.5f,1.0f,0.0f));
glTranslate(0.0f, 0.0f, 0.0f);
glRotate(15.0, 1.0, 0.0, 0.0);
drawEllipsoid(10.0, 1.0, 4, 4);
glPushMatrix();
//Earth
glMaterialAmbientAndDiffuse(GLMaterialEnums::FRONT,GLColor<GLfloat,4>(0.5f,10.5f,10.5f));
glRotate(orbit,Vrui::Vector(0,0,1));
glTranslate(105.0, 0.0, 0.0);
drawPlanetGrid(5, 1, 4, 4, 1);
glPopMatrix();
orbit += .1;
if (orbit > 360)
{
orbit = 0;
}
Could anyone help me move in the right direction? I also needed to know how I can get the Earth to orbit around the sun in a tilted angle.

Answer 1

Basically, you need to manage some model matrices. The sun's model matrix (if centered in (0,0,0) has just a rotational part). The earth rotating around the sun, needs a model matrix which is first rotated and then translated to be placed in the orbit of the sun. So when calculating a new frame you increase your rotation parameter, create the rotation and then apply the translation. If you want to add a moon, you need another model matrix, which is accumulated. That is, the moon needs a separate rotation and translation (like the sun) but you have to account also for the transformation of the earth. Make sure that you understand what a transformation matrix does. In that case the transformation matrix is just a coordinate transformation. So, you have your sun, earth and moon in a local frame. The model matrices achieve the transformation from local coordinate system to the world coordinate system. The view matrix transforms world coordinates to eye coordinates. And then there is only projection left for you.

Answer 2

To solve this, you need to understand the idea of co-ordinate systems and how to use them within OpenGL.
A co-ordinate system is just a set of points that share the same XYZ axes. In each system, the XYZ axes do not necessarily point in the same direction, so in one system moving in positive X could move in negative Y in other system. To convert points from one system to another you use a transformation matrix.
A scene is made up of several co-ordinate systems:-
World space
Camera space (or view space)
Object space
Model space
So, your model (the Earth, say) has a transformation from its model space to object space - this is the rotation of the earth around the vertical axis. Then it has a transformation from object space to world space - this is the translation about the sun and tilting. The final transformation is from world space to camera space.
So, you need three matrices to put your Earth model into the right place on screen. this may seem like a lot of processing, but the thing about these matrices is that they can be multiplied together to form a single object->camera space matrix.
Once you've set up the scene using the various co-ordinate systems and transformations, it should work.
You may want to work with cubes rather than spheres to start with as it's easier to follow what is happening to the vertices as they're being transformed.