OpenGL ES (Android) scaled sphere cut by z near and far

Question

I have an OpenGL ES 1.0 textured sphere that I can rotate by panning:

As you can see, my viewport is a square of the size of the biggest side of my screen (which is what I want). The sphere has a radius of 1, so it fills the biggest side (again, that's what I want).

Now I want to be able to zoom in / out. I'm doing it by using gl.glScalef(x, y, z). It works but at some point, the sphere becomes too big and is being cut, I guess by the default z near/far planes:

Is it possible to increase these default values, or do I need to use glFrustumf?

When using glFrustumf, the sphere is no longer cut when zooming in/out, but the image is weird:

When zooming out:

Any idea on what's happening?

Here are the relevant part of the code I'm using:

@Override
public void onDrawFrame(GL10 gl) {

    if(mTextureToLoad != null) {

        mSphere.loadGLTexture(gl, mTextureToLoad);
        mTextureToLoad = null;
    }

    gl.glClearColor(0.5f, 0.5f, 0.5f, 0.0f);
    gl.glClear(GL10.GL_COLOR_BUFFER_BIT | GL10.GL_DEPTH_BUFFER_BIT);
    gl.glLoadIdentity();

    gl.glScalef(mScale, mScale, mScale);

    gl.glRotatef( (1-mRotationY) * 360, 1, 0, 0);
    gl.glRotatef( (1-mRotationX) * 360, 0, 1, 0);

    mSphere.draw(gl);
}

@Override
public void onSurfaceChanged(GL10 gl, int width, int height) {

    float side = Math.max(width, height);

    int x = (int) (width - side) / 2;
    int y = (int) (height - side) / 2;

    gl.glViewport(x, y, (int) side, (int) side);

    /*
    // When using glFrustumf:
    gl.glMatrixMode(GL10.GL_PROJECTION);
    gl.glLoadIdentity();
    gl.glFrustumf(-1, 1, -1, 1, 0.1f, 100);

    gl.glMatrixMode(GL10.GL_MODELVIEW);
    gl.glLoadIdentity();
    */
}