TechnologyObserving FacilitiesEducation and OutreachAbout Haystack

Lesson Plans Resolution Worksheet

Resolution Worksheet

I) Objective: Become familiar with units and calculations in resolution.

 

 

II) Intro:

 

            1. Resolution can be described by the equation

 

(q) = 1.22 (l/d)

 

Where θ = resolution in radians

            d = diameter of dish or aperture

 

2. Angular distances of degrees can be subdivided into 60 minutes of arc, with each minute of arc subdivided into 60 seconds of arc so:

 

                        1 degree = 60 minutes of arc = 3600 degrees of arc

 

3. In order to calculate radians into arc seconds, use the following:

 

                        Radian = 2.06 X 105 arc seconds

 

4. Figuring out distances.  Use appropriate units

 

Using geometry, we can figure out the distance of an object, how big it is and the resolution needed to see the object.

 

This can be illustrated in the following illustration and equation

 

            N.B. Drawing of angular size of object is exaggerated


Equation: Θ (in radians) = diameter of object/distance


 

This is true for small angle q

 

III) Problems:

 

            A. Basic conversion

 

                        1. How many arc seconds in an angular size of 32 degrees?

 

                        2. How many radians in 6.3 X 106 seconds of arc?

 

                        3. The moon takes up 0.5 degrees of arc in the sky.  How many radians is this?

 

            B. Resolution:

 

1. Using a telescope with an aperture diameter of 37 meters, you wish to observe a wavelength of 3 mm.  What is the resolution of the telescope?

 

-Would you be able to resolve two objects with an angular distance of 15 arc seconds?

 

2. Using the resolution you figured out in question one, calculate the diameter of a telescope if you had to observe at 21 cm.

 

            C. Distances

 

1. The moon is 384,000 km distant from the earth and takes up an angular size of 0.5 degrees, what is the diameter of the moon?

 

2. How big (in angular size) is an object that has an angular size of two arc seconds from a distance of 1000 km?

 

3. Using the size of object in question 2, how far is the object if it takes up an angular size of 20 arc minutes?

 

D. Putting it all together

 

                        1.You have a 0.5-meter telescope, and are looking at a blue object (~400nm).   

 

                                    a. What is the resolution of your telescope

 

b. What is the maximum distance you could resolve the object, if the object has a diameter of 0.3 mm?

HOME  |  CONTACT  |  DIRECTIONS  |  WEATHER  |  INTRANET  |  SITEMAP  |  SEARCH
Astronomy

Science

Haystack Radio Telescope

Wideband VLBI

Radio Arrays (EDGES, MWA, SKA, MAPS, Deuterium)

Small Radio Telescope (SRT)

Publications

Geodesy

Haystack VLBI Updates

Science

Westford Radio Telescope

Mark 4 VLBI Correlator

VLBI Technique Development

International VLBI Service (IVS)

Publications

Atmospheric Sciences

Science

Millstone Hill Observatory

Madrigal

Array Systems

Open Source Projects

Space Science Resources

Publications

Technology

Radio Arrays (EDGES, MWA, SKA, MAPS, Deuterium)

Very Long Baseline Interferometry (VLBI)

Haystack Memo Series

Ionospheric Techniques

Open Source Projects

Observing Facilities

Haystack Radio Telescope

Westford Radio Telescope

Millstone Hill Radar

Deuterium Array

Atmospheric Optical Facility

Education and Outreach

Undergraduate Research

Research Experiences for Undergraduates (REU)

Research Experiences for Teachers (RET)

Pre-College Resources

Public Outreach Activities

About Haystack

Northeast Radio Observatory Corp. (NEROC)

Publications

News Archive

Glossary

Staff

Positions Available

Art at Haystack

History

Computing

Library

Networks

Safety Manual

Seminars

CloseSEARCH: