As my science fair topic, I chose to test the accuracy of using parallax to measure distance. I chose this topic because it relates to two of my favorite topics: mathematics and astronomy. Parallax uses a mathematical formula and is most commonly used to measure the distance between celestial bodies. From my research on parallax, I found how to measure it, and how to use the parallax formula to measure distances.
Parallax is defined as “any alteration in the relative apparent positions of objects produced by a shift in the position of the observer” (Columbia Electronic Encyclopedia 1). Parallax is commonly used to measure distances between celestial bodies, such as planets and stars. Parallax is measured using angles that are much smaller than a degree. Arcminutes are one sixtieth of a degree and arcseconds are one sixtieth of an arminute. One example of the infinitesimal size of an arcsecond could be the width of a dime from a point of view two kilometers away (“Cool Cosmos”). These units of measurement are used in the parallax formula, or the formula used to calculate distance when given an object’s parallax measurement. The distance given from the parallax formula is in parsecs, which are 3.26 light years or 3.18x10^13 kilometers (“PARALLAX”). The parallax formula can be written as “distance = 1/parallax” (“PARALLAX”).
The parallax formula is derived using trigonometric functions in relation to right triangles and parallax angles. “The Six Trigonometric Functions and Reciprocals” says the six basic trigonometric functions are sine, cosecant, cosine, secant, tangent, and cotangent. In a right triangle, the sine of an angle is the opposite side from the angle divided by the hypotenuse of the triangle. Cosecant is its reciprocal. The cosine of an angle is the side adjacent to the angle divided by the hypotenuse. Secant is its reciprocal. The tangent of an angle is the side opposite of the angle divided by the side adjacent to the angle. Cotangent is its reciprocal (“The Six Trigonometric Functions and Reciprocals”).
“Deriving the Parallax Formula” shows that one way of deriving the parallax formula is to set up a right triangle consisting of Earth, the Sun, and one other star as vertices. The side going from Earth to the Sun can be labeled as “a” and the side from the Sun to the other star can be labeled as “d.” The angle between the other star and Earth can be labeled as “p.
Possible sources of error in this experiment include the inaccuracy of measurements, as correct measurements are vital for the experiment.
60 What is Angle T? When there is more than 500 mils difference between the gun target line and the observer target line.
Trigonometric ratios are something you would hope to never use, but this term I was forced to find the height of a given eucalyptus tree. No instructions were given for this task other than the fact that I was not allowed physically measure the tree itself. The tools I was given were a large protractor and a measuring tape. I immediately sat down and thought why we were given the specific tools. I soon came up with a theory knowing that If I can find an angle that lines up with the top of the tree (θ) and the adjacent side (length
Introduction: The purpose of this experiment was to find how changing the angle and velocity would affect the distance the object went, height the object went, and time the object was in the air. Before this lab I could not tell how the angle and velocity would change the results. I needed to figure out what angle and what velocity made the object go farther or make it stay in the air longer. I also found mass will affect the height and distance. I used the site Galileo and Einstein to figure out these factors. (Fowler, M)
Finally, length contraction is apparent whenever an object is in motion. For instance, an observer on the Earth would measure the length of the rocket to be shorter when it is moving at its high speed as compared to its length at rest.
All the issues, raised by the author, are due to the fact, that the author decided not to use α', but α as an angle, that is equal to π/2, in order to define transverse Doppler effect. It is obvious, that α is the angle b...
More than 50 years after the publication of Astronomiae Pars Optica, another man was carrying on Kepler’s work in the field of optics....
When a curious observer looks to the cosmos, he/she travels back in time hundreds, thousands, millions, even billions of years. The photons from the mysterious stars he/she is looking at have traveled through time at 186,000 miles per second, until his/her eyes caught them. Light is the one particle that sheds luminosity over everything, and is the only way of seeing the elusive and magnificent nature of the universe. But to understand light is too understand its speed—a speed so great that nothing with mass can ever reach it.
Later after Copernicus came Johannes Kepler and Galileo Galilei, who confirmed some of Copernicus’ observations. Kepler provided concise evidence of planetary motion regarding their path around the s...
Euclidean distance was proposed by Greek mathematician Euclid of Alexandria. In mathematics, the Euclidean distance or Euclidean metric is the distance between two points, which is shown as a length of a line segment and is given by the Pythagorean theorem. The formula of Euclidean distance is a squ...
There are many different types of triangles. Obtuse and acute triangles are the two different types of oblique triangles, triangles in which are not right triangles because they do not have a 90 degree angle.A special right triangle is a right triangle with some regular features that make calculations on the triangle easier, or for which simple formulas exist. Knowing the relationships of angles or ratios of sides of special right triangles allows one
Trigonometry and vector in math to deal with progress through water/air currents. In daily life basic trigonometry is need for Carpenter. Job deals with any type of the pattern to know about trigonometric functions keep listening job at the basics are below:
In this assessment of the projectile motion of an object, I found that it can be applied to many useful situations in our daily lives. There are many different equations and theorems to apply to an object in motion to either find the path of motion, the displacement, velocity, acceleration, and time of the object in the air.
Astronomy is a natural science focusing on the study of celestial objects such as moons, stars, planets, nebulae and galaxies. Astronomy is considered to be one of the oldest natural sciences; early civilizations throughout history such as the Babylonians, Egyptians and Greeks performed methodical observations of the sky. The Babylonians had different astronomical records regarding the position of the moon, sun and stars, on the other hand the Egyptians used astronomy to know the time and afterwards they developed a calendar based on the solar year. The following paper will focus on the ancient Greek astronomy, interestingly the origin of the word astronomy is Greek it comes from two words; astron meaning "star" and nemien refers to "to name". This paper will explain and highlight the methods used, famous figures and the achievements attained during the ancient Greek astronomy era.