Why do not the sizes of Venus and Mars as viewed from Earth change during the course of the year?

Just before his death, in 1543, Nicolaus Copernicus published in his book On the Revolutions of the Celestial Spheres a Heliocentric model of the universe, that is, a model of the universe that placed the Sun rather than the Earth at the center of the universe.  This is considered a major event in the history of science, triggering the Copernican Revolution and making an important contribution to the Scientific Revolution.

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According to Copernicus' model, since the Earth circulates the Sun in an orbit outside that of Venus and inside that of Mars, the apparent size of both Venus and Mars should change appreciably during the course of the year. This is because when the Earth is around the same side of the sun as one of those planets it is relatively close to it, whereas when it is on the opposite side of the sun to one of them it is relatively distant from it. When the matter is considered quantitatively, as it can be within Copernicus's own version of his theory, the effect is a sizeable one, with a predicted change in apparent diameter by a factor of about eight in the case of Mars and about six in the case of Venus.

On the other hand, according to the Ptolemaic system (the Geocentric model) Venus and Mars should not change appreciably during the course of the year because its epicyclical motion implies only a small change in distance from the Earth.

However, when the planets are observed carefully with the naked eye, no change in size can be detected for Venus, and Mars changes in size by no more than a factor of two. This gives us strong evidence for the Geocentric model and refutes the Heliocentric model! How is this possible?

Please, explain your reasoning. You can post your attempted answers in the comment box below. Please, do not use Facebook or Twitter to give your answers.


  1. Here is my try (for example, with Mars): Maybe the relative distance from the Earth to the orbit of Mars is so high than there is no appreciable difference between the distance today and the distance when Mars is in other positions of its orbit during the year. In other words, the orbit is relatively smaller than the average distance Earth-Mars and consequently we cannot see the changes. Nevertheless, without the heliocentric model it is very difficult to explain why we don't see this planets moving in circles as the other "stars" do, so it is a good model.

    1. Good try, but I am sorry to say that that is not the case. The relative distance from the Earth to the orbit of Mars is not so high. Notice that Mars has an orbit with a semimajor axis of 1.524 astronomical units and that 1 astronomical unit is roughly the distance from Earth to the Sun.

  2. Replies
    1. Hot. A clue: it has to do with observational errors

  3. Atmosphere blurr... not enough resolution to say how much it changes.