Telescopes >> Eyes

Before the early 1600s, scientists' interest in the stars could only go so far because they were bound by the limits of their eyesight.  The invention of the telescope provided important advances in the field of observational astronomy for many reasons, but two stand out above the rest.

1. Telescopes can collect more light than the naked eye and can thus see a more magnified image.
2. The telescope has the ability to focus on one specific portion of the field of view with a higher resolution than the human eye.

The human eye is incredible, but its size severely limits the amount of light and information it can take in.  Telescopes give humans a way to have 3-feet-wide eyes  without attracting too much unwanted attention on the street.  That 3-feet-wide eye can collect a lot of light which translates into a better, closer-appearing image.  Light enters the telescope through the primary mirror (for reflector telescopes) or the objective lens (refractors) and gets focused to an eyepiece at the end of the scope.  (More complex telescopes have more reflection steps between the first lens/ mirror and the eyepiece.)

Telescopes also put the human eye to shame when it comes to focusing on a particular point in the field of vision without letting the image get really blurry.  When human eyes look at the night sky and try to focus on a single object, the image often gets blurry because of excess light coming from other stars.  Telescopes can "squint" more effectively than the human eye can, finding the perfect balance between letting enough light in and keeping enough out.

In summation, telescopes are just better than the naked eye at producing clear, magnified images of celestial objects.  They collect more information, focus it more effectively, and can even collect information outside of the visual spectrum.  As great as the human eye is at observing things in our immediate environment, it really can't hold a candle to the telescope.

Scale of the Earth and Moon

The objective of this lab activity was to find the mass and radius of both the Earth and the moon and the distance from one's center to the other.  We were given a rock, a scale, a measuring cup half-full of water, and the following information:

• Boston and Los Angeles are 3000 miles apart from each other.
• Boston is 3 hours ahead of (or 21 hours behind) Los Angeles.
• There are about 6 kilometers in every 10 miles.  
• The Kepler Equation

With the knowledge of the distance between Boston and LA and the number of hours in a day, the first step was to set up this proportion:

$\frac{5000}{C\oplus = 2\pi R\oplus ^2} = \frac{3}{24}$

We rearranged the equation to solve for the radius of the Earth, which we found to be 6.7 x 10^8 cm.  We determined that any error would be due to rounding values during our calculations because a calculator was not listed among our tools.

The next step was to find the density of the rock by finding its mass using the scale and its volume based on how much water it displaced in the measuring cup.  Assuming that the density of the rock (2 grams per cubic cm) was comparable to the density of the Earth, we found the Earth's volume using its radius and multiplied it by the rock's density to find the mass.  We found Earth's mass to be 2.8 x 10^27 grams.  Error in this step would be due to the false assumption that the density of a rock found near the surface of the Earth is equal to the Earth's density.  We also continued to round in our calculations.  

We used Kepler's equation describing the relationship between the orbital period of an object, the mass of the object it orbits, and the distance between their centers to find the distance from the Earth to the moon.  Using a period of 28 days, converted to seconds, we found the distance to be 4 x 10^10 cm.  Error was once again attributed to rounding in our calculations. 

To find the radius of the moon, we used the hint that the thumb, when held at arm's length, takes up about 1 degree in the field of view and that the moon looks to be about half the size of a thumb.  We set up the following proportions:
 $\frac{.5}{360}=\frac{2 R_{moon}}{C_{orbit} = 2\pi a_{moon}}$
When we solved for R, we found that the radius of the moon is 1.7 x 10^8 cm.  We attributed any error in our answer to rounding in our calculation.

We found the mass of the moon by first assuming that the density of the moon is equal to that of the Earth, 2 grams per cubic cm.  Because we had already found the radius of the moon, we were able to use the following equation to find the volume of the moon: V = 4*pi*R^3 / 3
Rearranging the d = mV equation to solve for mass, we found that the mass of the moon is 6.4 x 10^25 grams.  Any error in our answer was attributed to the assumption that the moon's density was equal to that of the Earth and the rounding we did in our calculations.  

The first three problems were solved in collaboration with Dennis Lee, Delfina, and Vincent.  

Introduction

My name is Moiya McTier.  I'm a sophomore living in Mather House with a joint concentration in Astrophysics and Folklore & Mythology.  That unusual combination stems from a life-long interest in sci-fi shows and fantasy books.  When I came to Harvard, I wasn't as open-minded as I am now, and was convinced that I had to choose one or the other.  It wasn't until this past summer that I realized that I didn't feel like letting other people's doubts keep me from pursuing something I would genuinely be interested in, so I decided to go for it. Now I can proudly say that I'm the second person with that joint concentration in the history of the college.

Besides the fact that Astro 16 is required for all astrophysics concentrators, I'm taking this class because it sounds interesting! It will provide me with a basic knowledge of things like how stars form and how they come together with planets to form our Solar system, which I wouldn't have the opportunity to learn in another class, or fully understand on my own.  Taking this class will also give me further experience to draw from in any internships I (hopefully) get for this summer.

Obviously, I want to gain a firm understanding of the material covered in this course.  But, more than that, I want to polish my problem-solving and group-work skills.  Both will come in handy in any research position I may hold in the future.  I'm also just excited to take a class with this format! It will be a welcome and educational change to get away from the lecture format and take a hands-on approach to learning this material.