Trip to Jupiter
Characters:
Theme: Real numbers (Applications of real numbers)
Competencies
Competence in Linguistic Communication
Mathematical competence in science, technology and engineering
Personal, social and learning to learn competence
Competence in cultural awareness and expressions
Subjects and year by Educational System
Spain > Mathematics > 4th(A) ESO > Number sense
Spain > Mathematics > 4th(A) ESO > Socio-affective sense
Spain > Mathematics > 4th(B) ESO > Number sense
Spain > Mathematics > 4th(B) ESO > Socio-affective sense
Enunciation
Maria Cunitz, famous astronomer of the 17th century, wrote a book on astronomy named “Urania propitia” and, on it, she spread Kepler's theories, revised and simplified his astronomical tables.
Kepler's laws were stated by Johannes Kepler to mathematically describe the motion of the planets in their orbits around the Sun. The Second Law says: "The radius vector that joins the planet and the Sun sweeps equal areas in equal times", that is, when the planet is further away from the Sun its speed is less than when it is closer to the Sun.
We propose a problem about speeds and planets. Read it and then answer the questions:
• A space rocket is heading towards Jupiter at a constant speed that is 15 times greater than the speed of sound. If the speed of sound is 344.2 m/s and the distance from Earth to Jupiter is 778.3 million km, calculate how long it will take the rocket to reach the planet Jupiter. Express the result in the most appropriate unit of time (the real numbers that appear will be expressed with two decimals).
Observations and context
• It is studied in mathematics. For students of applied mathematics, they can be helped by remembering the speed formula:
$$v = \frac{e}{t} \rightarrow t = \frac{e}{v}$$
• Make the students see the importance of using the most appropriate units. In this case it is important for the result in hours to be transformed into years, months, etc., as it will make the time needed to arrive more understandable.
• Due to her great knowledge and her later contributions to science and culture, she was known as the "Silesian Pallas" (Pallas was the god of wisdom in Greek mythology). Apart from showing certain gifts for painting, music and poetry, she learned mathematics, medicine and history. She was also fluent in numerous languages.
• Since ancient times there were women like Maria who were passionate about astronomy and mathematics, such as Enheduanna (c. 2285–c. 2250 BC), considered the first astronomer in history, Aglaonice of Thessaly (c. 500–c. 400 BC), Hypatia of Alexandria (c. 370–c. 416 AC), Fatima de Madrid (c. 900–c. 1100 AC) and Ana Comneno (1083–1153).
• Contemporaries of hers were renowned astronomers and mathematicians such as Sophia Brahe (1556–1643), Elisabeth Hevelius (1647–1693) and Elena Lucrezia Cornaro Piscopia (1646–1684), philosopher and mathematician; and many others dedicated to other sciences such as Margaret Cavendish (1623–1673), prolific writer on natural philosophy (now physics); Martine Bertereau (1590–1642), specialist in mining engineering and mineralogist; or Marie Meurdrac (1610–1680), alchemist and chemist.
Description
Solving a problem of operations with real numbers, choosing the most appropriate notation, approximation and units.