World Builders™                                                                       Session One  --  Astronomy
Comparing

Apparent Moon Sizes

How big is the moon?  How far away is it?

When you see a moon in the sky, what you see is affected by

• the actual size of the moon
• how far away the moon is

Just as on earth, a big object very far away looks small. A small, distant moon may look like a dot of light, like a star.

Here is a table that Dr Viau has made for you to help you to understand what we are getting at here.

We see that when the Tangent of Theta has more than 3 zeros right after the decimal, we get a dot of light in the sky. You may see the dot moving, like a planet, but you will not get exciting moon effects with this satellite.

 Earth to Distance from Sun km Distance from Earth km Diameter km Diameter Distance Tangent of Theta Viewing Angle We see Moon 384,400 3476 3476  384,400 0.009 0.5 Disk Mercury 57,910,000 91,690,000 4880 4880    91,690,000 0.00005 0.003 dot Venus 108,200,000 41,400,000 12,104 12,104 41,400,000 0.00029 approx. 0.02 bright dot Mars 227,940,000 78,340,000 6794 6794 78,340,000 0.0001 dot Jupiter 778,330,000 628,730,000 142,984 142,984 628,730,000 0.00023 approx 0.02 bright dot Saturn 1,429,400,000 1,279,800,000 120,536 120,536 1,279,800,000 0.00009 dot Uranus 2,870,990,000 2,721,390,000 51,118 51,118 2,721,390,000 0.00002 dot The Sun 149,600,000 1,390,000 1,390,000 149,600,000 .00929 approx. 0.5 Disk

We see that on earth the moon and the sun appear to be about the same size even though the sun is actually much, much bigger. However, the sun in also much farther away.  During a solar eclipse, the moon just about covers the sun, as in this picture.

How can you get the biggest possible moon in your sky?

You will need to study orbits and The Roche Limit to find out!

Here is something else to think about.

This is a diagram of our moon, which is 0.5 degrees of viewing angle across.

What happens if we make a moon that has a viewing angle only half the size of our moon?

This moon would look as if it had half the diameter of our moon.

You can see that half the diameter is not the same as half the moon!

Actually, you only get a quarter of the area (disk surface).

Your moon is going to look quite a bit smaller in the sky.

It will not give as much light.

Here I cut the viewing angle into fifths!

Look at the tiny little moons I got!

Each one has only one 25th the area of our moon.

Would these little moons look any different from bright stars?

The albedo measures how much light an object reflects.

Example: a mirror reflects nearly all the light that falls on it: the albedo of a mirror is perhaps 0.96, which is nearly one.

Example: a black sweater, which is dark and rough, reflects very little light. Its albedo might be 0.05.

The numbers that describe albedo go from 0 (no light reflected)to 1 (all light reflected).

Remember that planets and moons shine by reflected light. A planet or moon with high albedo will shine brightly, but it will not look any larger than it would if its albedo were low.

 These two moons are the same size and the same distance from a star. They both receive the same amount of light. This is a high albedo moon. This is a low albedo moon. A moon or planet with high albedo: shines brightly can be seen for a long distance A moon or planet with low albedo does not reflect much light can be seen close up but soon gets dim

Example: Venus has an albedo of 0.7 (This means it sends back about 70% of the light that falls on it.) It is the brightest planet, and easily seen in the sky. However, its viewing angle is small, and it looks like a bright dot in the sky.

Example: Our moon has an albedo of only 0.02, which is about 2% of all the light that it receives from the sun. The moon seems bright to us because we are close to it.