Please solve the following questions. This is not an assignment, it will not be graded, and you do not need to submit your solutions to anyone. The questions are simply intended to help you practice for the exam.

These questions will not appear in the exam itself. Students who don't genuinely attempt to solve the questions on their own, and only memorize the solutions, will have a very hard time in the actual exam!

These questions are not multiple-choice, to encourage you to think of the answers on your own, but the questions in the actual exam will be multiple-choice.

If you need any clarifications for these questions, you can ask for them on the course Teams channel.

Question 1 Show/hide solution

What are the differences and similarities between Copernicus's model and Ptolemy's model?

Solution: Copernicus's model was heliocentric, with the Sun at the center. Ptolemy's model was geocentric, with the Earth at the center. However, other than that, both models had epicycles, circular orbits, movement at constant speed along the orbit, and celestial spheres.

Question 2 Show/hide solution

What did Copernicus's model get right? What did it not get right?

Solution: It correctly put the Sun at the center of the solar system. However, the planets were still moving on epicycles in circular orbits around the Sun, which is incorrect - they actually move along ellipses and without epicycles. In addition, we now know that the speed of the planet varies along its orbit (per Kepler's laws) and that there is not actual "celestial sphere", the planets move in empty space.

Question 3 Show/hide solution

Why do we not feel the Earth move?

Solution: Because it is moving at a constant speed (except for negligible variations). We only feel movement when the speed changes, that is, when there is acceleration.

Question 4 Show/hide solution

Does a planet move faster or slower in its orbit if it's closer to the Sun?

Solution: Faster, according to Kepler's 2nd law.

Question 5 Show/hide solution

What is an example of a prediction that scientists can use to determine experimentally whether Copernicus's model or Ptolemy's model is more accurate?

Solution: The phases of Venus are predicted correctly by Copernicus's model, but not by Ptolemy's.

Question 6 Show/hide solution

If I push an object in empty space with no friction and no other objects to collide with, what will its motion be like?

Solution: It will keep moving at constant speed forever, since there will be no forces (like friction or air resistance) to slow it down or speed it up.

Question 7 Show/hide solution

I drop a 1 kg ball and a 2 kg ball to the ground. What does Aristotle predict about the speed in which each of the ball falls? What does Galileo predict? Which one of them is right?

Solution: Aristotle will predict that the heavier ball falls faster. Galileo predicts that both balls fall at the same speed. Galileo is right, as can be demonstrated experimentally.

Question 8 Show/hide solution

Why did the Catholic Church oppose Copernicus's heliocentric model?

Solution: The Church claimed that the Earth is the center of the universe, as in Ptolemy's model, based on the Bible. The heliocentric model claimed that the Earth is just one out of several planets orbiting the Sun, so it's no longer the center of the universe. Copernicus's model challenged the authority of the Church, and if people knew that the Church is wrong about astronomy, they might start questioning the Church's teachings about other topics as well. (Religions often rely on the ignorance of their believers to maintain power; this was true in Galileo's time, and remains just as true today.)

Question 9 Show/hide solution

What were telescopes used for before Galileo started using them for astronomical observations?

Solution: For observing far away things on Earth, for example for military purposes.

Question 10 Show/hide solution

What are the two reasons that Galileo's discovery of the moons of Jupiter strengthen the heliocentric model?

Solution: This discovery showed that there are celestial objects that revolve around other planets, not the Earth. This weakened the geocentric claim that all celestial objects revolve around the Earth. It also proved that the Earth can be moving without "losing" the Moon, since if Jupiter can do that, then the Earth also can.

Question 11 Show/hide solution

What does the heliocentric model say about humanity's role in the universe?

Solution: It shows that (despite what some of us would like to believe) we are not the center of the universe, we are just one form of life living on one planet out of trillions, and there could be other forms of life on other planets.

Question 12 Show/hide solution

What data did Tycho Brahe collect?

Solution: The positions of the Sun, Moon, planets, and stars over many years.

Question 13 Show/hide solution

What did Kepler discover about the shape of the orbits of the planets that was different from Ptolemy's and even Copernicus's models?

Solution: That the orbits were ellipses, not circles, and there were no epicycles.

Question 14 Show/hide solution

How do the foci of an ellipse compare to the center of a circle?

Solution: In a circle, the distance from the center to any point on the circle is always the same, equal to the radius of the circle. But in an ellipse, it's the SUM of distances from the two foci to any point on the ellipse that is always the same.

Question 15 Show/hide solution

What is the difference between the major axis and the semi-major axis of an ellipse?

Solution: The major axis is the widest diameter of the ellipse. It is analogous to the diameter of a circle. The semi-major axis is half the major axis (semi = half). It is analogous to the radius of a circle.

Question 16 Show/hide solution

A circle is a special case of an ellipse with a specific eccentricity. What is its eccentricity?

Solution: Zero.

Question 17 Show/hide solution

According to Kepler's first law, where is the Sun located in relation to a planet's orbit?

Solution: At one of the two foci of the ellipse.

Question 18 Show/hide solution

In simple terms, what does Kepler's second law say?

Solution: A planet moves faster in its orbit when it is closer to the Sun.

Question 19 Show/hide solution

A planet is moving at constant speed along its entire orbit. What can you say about the shape of this planet's orbit?

Solution: It's a perfect circle, so it's always the same distance from the Sun, hence it moves at constant speed according to Kepler's second law.

Question 20 Show/hide solution

What is the orbital period of the Earth?

Solution: By definition, this is exactly 1 year.

Question 21 Show/hide solution

According to Kepler's third law, is the orbital period of Jupiter longer or shorter than that of Earth?

Solution: The orbital period is larger if the semimajor axis is larger. Since Jupiter is farther away from the Sun compared to the Earth, its orbital period must be larger. Indeed, the orbital period of Jupiter is around 12 years.

Question 22 Show/hide solution

"Kepler's laws explain the fundamental forces of nature responsible for movement in the solar system." True or false?

Solution: False. Kepler's laws are just a set of observations; Newton's laws describe the actual underlying forces responsible for the motion. Indeed, Kepler's laws can be mathematically derived from Newton's laws, but not the other way around.

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