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.
HYPOTHESIS: If I use the Metric Measurement and become more familiar with it, then I will be able to convert other measurements and learn to use it and understand it better since other countries used the Metric Measurement.
60 What is Angle T? When there is more than 500 mils difference between the gun target line and the observer target line.
Next we have the acronym SOHCAHTOA. A way to remember it is: some old horse caught another horse tripping over apples. This method is used to find angles when given the sides of a triangle, unlike special rights. The acronym stands for sine- opposite divided by the hypotenuse, cosine- adjacent divided by the hypotenuse, and tangent- opposite divided by adjacent. This method also can only be used with right triangles. When doing a problem like this it will state which method you should use (sine, cosine, and tangent). Let’s start with sine first.
We used the same formula and procedure as before to find the radius of the star. The distance from Earth was given to us to complete the small angel formula. We then needed to convert from the au to km by the following equation.
= [(sec^2 theta sin theta + tan theta cos theta)/(sec^2 theta cos theta - tan thetasin theta)]
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...
The declination of ecliptic path fluctuates throughout each year. It has a periodic pattern. The sun’s declination in January is around -23 degrees. Then, the degree of declination starts to increase towards positive and reach 0 degree in the middle of March. It reaches the maximum declination of approximately +23 degrees in mid-June. The declination then starts to drop towards negative. It reaches 0 degree again in mid-September and finally returns to -23 degree as the time approaches to January. If this process is graphed with time at x-axis and declination at y-axis, the fluctuation within a year can be seen as a cycle of cosine function. This happens because the angle between the ecliptic and celestial equator is around 23 degrees. The Earth travels around sun on ecliptic plane, which is defined by ecliptic path. The ecliptic path has a 23.6°angle between celestial equator. Since the declination is measured from the celestial equator, the declination of the sun’s path observed from Earth should theoretically vary from -23.6° to +23.6°.
Missing Figures A Brief History of Telescopes Although telescopes have been around for several hundred years, there has been great discrepancy as to who invented them first. Here is the author's opinion. Lippershey was a Dutch spectacle marker during the early 17th century (approximately 1600).
The main purpose of this investigation is to prove the circumference formula to be correct. Through this investigation I will use different processes of math to prove this formula correct. This will show that the formula holds true in multiple settings.
this tells me that the measure of angle h, the angle of elevation, is .
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.
one and a half times to produce a shadow of 2.3 cm. The three ray
Since, according to scientific calculations, the sun still has a very long focal length, the
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.