How to transform geocentric emphemerides into OpenGL's normalized device coordinates (NDC) [-1, 1]?

Question

Intro I want to render celestial bodies based on their real-world positions in a geocentric system using OpenGL. I pull the daily updated real-world coordinates from NASA's Horizons system via a custom Python script and write them to a CSV file. Here is an example of the CSV file that I pass as input to my C++/OpenGL program:

The figure shows that the coordinates are outside the range [1, -1]. As a result, OpenGL will not render them. I hold this positional data in a float-vector, which I then pass to the vertex buffer object:

RenderingData convert(const EphemerisParsingResult &parsing_result) {
    const size_t num_positions = parsing_result.num_parsed_rows;
    const unsigned int vector_dimension = 3;
    std::vector<float> positions(num_positions * vector_dimension);
    for (int i = 0; i < parsing_result.num_parsed_rows; ++i) {
        positions[i + 0] = static_cast<float>(parsing_result.position_x_km[i]); // x coordinate of ephemeris i
        positions[i + 1] = static_cast<float>(parsing_result.position_y_km[i]); // y coordinate of ephemeris i
        positions[i + 2] = static_cast<float>(parsing_result.position_z_km[i]); // z coordinate of ephemeris i
    }
    RenderingData renderingPacket;
    renderingPacket.positions = positions;
    return renderingPacket;
}

// ...

VertexBufferObject::VertexBufferObject(const std::vector<float> &vertices, const GLenum usage)
        : AbstractOpenGlBufferObject(GL_ARRAY_BUFFER, vertices.size(), sizeof(float) * vertices.size()),
          vertices_(vertices), usage_(usage) {
}

void VertexBufferObject::setBufferData() {
    glBufferData(GL_ARRAY_BUFFER, getUsedMemorySize(), &vertices_[0], usage_);
}

Question

How to transform such real coordinates into normalized device coordinates? I would appreciate the exact transformation matrix.