Telescope Resolving
Ability
Joe Roberts
joe@rocketroberts.com
Telescope Resolving Ability
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We will cover the basics of an optical
telescope's ability to resolve detail on a subject
An often asked question: “Can Hubble see the
Flag on the Moon?”
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Answer: not a chance, and we'll show why not!
Dawes Limit
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The ability of an optical telescope to resolve
detail is governed by the Dawes Limit:
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Resolution (in arc seconds) = 4.56/diameter of the
telescope mirror/lens (in inches)

1 degree = 60 arc minutes; 1 arc minute = 60 arc
seconds, therefore 1 degree = 3600 arc seconds
Example 1:
Telescope Mirror Diameter
= 6 inches
Resolving ability =
4.56/6 = .76 arc seconds
Example 2:
Hubble Telescope Mirror Diameter
= 94.5 inches
Resolving ability =
4.56/94.5 =
0.048254 arc seconds
Can we see the Flag on the Moon?
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First we need to make some basic assumptions
about how big the flag is
We then do some basic geometry to determine
how big (in arc seconds) the flag would look at
the distance of the Moon
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We will assume that we want to just barely be able
to make out the stripes on the flag
Once we figure this out we apply the Dawes
Limit equation to find out what size telescope is
required!
American Flag Dimensions
B
A
A=1.0
B=1.9 A
Stripes are 1/13 of A
Flag on the Moon: Assume it is 3 feet wide; therefore stripes are:
36 inches x [(1/1.9) x (1/13)] = ~ 1.46 inches tall
We'll round this up to 1.5 inches for our calculations...
So, we need a telescope that can just resolve something about
1.5 inches wide on the Moon. So how do we figure this out?
Basic geometry is all that is required!
Earth - Moon Geometry
(Sketch not to scale!!)
Moon
b
Earth
a = diameter of the Moon = 2160 miles
b = mean distance from Earth to Moon = 239,000 miles
For our diagram: tan(A) = (a/2)/b
tan(A) = (2160/2)/239,000 = 0.004519
Therefore angle A = 0.259 degrees
The TOTAL diameter of the Moon (as seen from Earth) is:
2 x 0.259 = ~
.518 degrees
a
Angle A
Earth – Flag on Moon Geometry
A
Earth
Part of
One Flag
Stripe
b
a = height of a flag stripe (1.5 inches for our assumptions)
a in miles = 1.5 inches / (5280x12) inches/mile = 2.3674e-5 miles
b = mean distance from Earth to Moon = 239,000 miles
For our diagram: tan(A) = (a/2)/b
tan(A) = (2.3674e-5/2)/239,000 = 4.9528e-11
Therefore angle A = 2.838e-9 degrees
The TOTAL width of the flag stripe (as seen from Earth) is:
2 x 2.838e-9 = 5.675e-9
degrees
a
(Sketch not to scale!!)
Apply Dawes Limit Equation
From previous slide The TOTAL width of the flag stripe (as seen from Earth) is:
2 x 2.838e-9 = 5.675e-9
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degrees
There are 3600 arc seconds per degree; therefore
5.675e-9 degrees = 2.043e-5 arc seconds
Dawes Limit: Resolution (in arc seconds) =
4.56/diameter of the telescope mirror/lens (in
inches)
2.043e-5 = 4.56/x; therefore x = 223183 inches =
~ 3.52 miles
Therefore it is not even close to possible to see the Flag on
the Moon from Earth with telescopes available today!
So what can Hubble see on the Moon?
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Hubble is in orbit ~ 375 miles above Earth, so
basically it is no closer to the Moon than we are
right now
Hubble's ability to resolve was determined to be
0.048254 arc seconds
Using geometrical methods previously used it can
be shown that 0.048254 arc seconds is equal to an
object about 295 feet wide at the distance of the
Moon
This is the smallest object that could just barely be
discerned!
What could Hubble see if it was pointed at
the Earth?
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Using geometrical methods previously shown it
can be calculated that 0.048254 arc seconds is
equal to an object about 5.56 inches wide at the
distance of 375 miles
Basically Hubble could just make out the size and
shape of a car license plate (assuming it was
laying flat on the ground)
Reading the plate would be out of the question!