Physics s2 knowledgeacquisitionact

Universidad Autรณnoma de Nuevo Leรณn Preparatoria no. 9

Physics STAGE 2

Acquisition of Knowledge Activity Group 330 Natalia Daenna Gonzรกlez Viera

Kepler’s Laws a) How long did it take Kepler to collect the data which proved that planets described elliptical orbits around the sun?

Kepler realized that Tycho's work could settle the question one way or the other, so he went to work with Tycho in 1600. Tycho died the next year, Kepler stole the data, and worked with it for nine years.

How did he do all of these observations?

Notably, Kepler had believed in the Copernican model of the solar system, which called for circular orbits, but could not reconcile Brahe's highly precise observations with a circular fit to Mars' orbit (Mars coincidentally having the highest eccentricity of all planets except Mercury). His first law reflected this discovery.

Through Brahe’s astronomical measurements and Kepler’s own drawings of the geometrical relationship between the Sun and Mars in various parts of the planet’s orbit, Kepler discovered that planets moved faster when they were closer to the Sun. From this realization, he concluded that the orbit of Mars was elliptical, not circular. b) What did Kepler discover about the speed of the planets and their distance from the Sun? Kepler discovered that the motions of the planets could be described very accurately by some simple mathematical formulas. The closer a planet is to the Sun, the faster it travels, and Kepler found a method to connect the average distance of a planet from the Sun to the time it takes the planet to make a complete orbit around the Sun. Kepler's discoveries allowed him to figure out how much closer or farther all the planets are to the Sun than Earth is, even though he could not figure out the actual distances. c) Why did it take so long for Kepler to discover his third law?

His analysis and observations needed many years because of the time needed to understand by a precisely way the planet’s distances

and their changes over the days, months and even years. Therefore, the slower the experiment process, the more precise the data.

Johannes Kepler published his first two laws about planetary motion in 1609, having found them by analyzing the astronomical observations of Tycho Brahe. Kepler's third law was published in 1619.

Kepler’s third law shows that there is a precise mathematical relationship between a planet’s distance from the Sun and the amount of time it takes revolve around the Sun. d) Did Kepler believe that the planets were projectiles moving under the influence of the Sun? Yes, and that was reflected in Kepler’s first law: which states that the planets move in an ellipse (a squashed circle) with the Sun at one focus point, offset from the center. e) In Kepler’s imagination, what is the direction of the force on a planet?

The planets want to move in a straight line of constant velocity but the sun’s gravitational pull forces them to orbit in a curved form by changing direction of their velocity.

Law of Universal Gravitation a) The force between the Earth and the Moon depends on their masses and the distance between them. Assume that the distance increases to double, what should be the mass of the Earth so that the force between them is constant?

The mass should be four times greater to keep the force constant. b) The force between the earth and the Moon depends on their masses and the distance between them. Assume that the mass of the Earth increases four times, what should be the distance between them so that the force stays constant?

The distance has to be four times greater.

c) Imagine that there is a planet that has twice the mass of the Earth and half of its radio, what should the acceleration of that planet be?

It should be eight times greater than the Earth gravity. d) How do I change the gravity acceleration if the diameter and mass of the Earth is reduced to half?

Giving a double value to the gravitational constant. e) The Sun is larger than the Earth, why doesn’t the gravitational force of the Sun attract us to it and separate us from the Earth?

Because we are closer to Earth than to the Sun. the sun is pretty much farther from us than the earth, obviously. f) If the gravitational force exerted by the earth on the Moon suddenly cease, what type of path would the Moon take?

The moon and all the planets would separate from the orbit of the sun as like thrown for a wave.