How do you think astronomers can determine the gravitational force between two celestial objects without measuring it directly?

Knowing the mass and radius of the Earth and the distance of the Earth from the sun, we can calculate the mass of the sun (right), again by using the law of universal gravitation. The gravitational attraction between the Earth and the sun is G times the sun's mass times the Earth's mass, divided by the distance between the Earth and the sun squared. This attraction must be equal to the centripetal force needed to keep the earth in its (almost circular) orbit around the sun. The centripetal force is the Earth's mass times the square of its speed divided by its distance from the sun. By astronomically determining the distance to the sun, we can calculate the earth's speed around the sun and hence the sun's mass.