World Builders™
World Builders™
Session One  --  Astronomy
Session One  --  Astronomy


              Big Moons
                 Big Moons

Is it possible for a planet to have a moon that looks huge in the sky? 


    On the page Can You See Your Moon we found out how to tell if our moons would be visible from the planet surface. We discovered that the earth's moon, which is certainly noticeable in the sky, has only half of a degree of visibility. What does this mean?

The night sky arches over us like a great upside-down bowl.

Scientists divide this semicircle into 180 degrees. 
In the picture, I have marked these off in groups of 10 degrees each.

The moon takes up only half of one degree in the sky. See the tiny yellow dot with its rays.  That represents our moon.


Sometimes one sees pictures that artists have drawn which show huge moons.

 Could planets really have moons like these?

Let's find out.

On the page about The Roche Limit we learned that the closest that our moon can be to earth without breaking up is about 4 earth radii.

Earth's radius is 6378 km

Earth's radius * 4 = 6378 * 4 = 25,512 km.

Let's use the Can You See Your Moon formula to find out what our moon would look like at its closest to the earth.

0.068 is the Tangent of one half of Theta
To find the Tangent of Theta we multiply 0.068 by 2.   

0.068 * 2 = 0.136    This number is the Tangent of Theta

When we know Theta, we know how much of the sky is covered by the moon.

Click here for the Tangent Table.

0.136 is between 0.123 and 0.141

If the Tangent of Theta = 0.13 then the viewing angle of Theta is nearly 8 degrees! Wow! Compare!

       Scientists believe that the moon was formed about 4.6 billion years ago when our solar system was forming. They theorize that a huge asteroid about the size of Mars smashed into our world. Some of earth's material was torn away by the impact. The rubble from the impact may have formed rings of dust and rocks around the earth at first, but much of it was pulled together by gravity to form our moon. At one time both the moon and the earth were in a molten state.

     After its formation, the moon was very close to the earth, but outside the Roche Limit. At that distance it would have orbited the earth in about 90 hours, or about three and a half of our days. (Earth days were also much shorter then.) Over billions of years the moon has slowly moved farther and farther away.  It is moving away at 4 centimeters a year right now.  Right now it is about 60 earth radii away. When it is twice as far away, will we still be able to see it?



Example:

The Moon is twice as far away:

Radius of Earth's Moon = 1738 km

Radius of the Earth = 6378 km

Distance to Earth's Moon (60 earth radii) = 382,680 km

Multiply 382,680 by 2 to make it twice as far away.

Twice the distance from earth to moon =  (382,680 * 2)  = 765,360 km

_ 1738_ = 0.00227     
   
    765,360                         

This is the   Tangent of Theta 
                2 

Round to 0.002. This is the Tangent of half of the angle Theta.

Multiply 0.002 by 2  to get the Tangent of Theta.

 0.002 * 2 = 0.004

Click here for the Tangent Table.

Look for 0.004 in the yellow columns.
We see 0.003 with a viewing angle of 0.2
We see 0.005 with a viewing angle of 0.3
We don't see 0.004, but it should be between 0.003 and 0.005.
So we reason that the viewing angle is probably between 0.2 and 0.3

The viewing angle for the future far away moon will be 0.25, which is a quarter of a degree.

The viewing angle for the moon right now is 0.5 of a degree (half of a degree).


When it is twice as far away, the viewing angle will be 0.25 of a degree (a quarter of a degree).

We would still be able to see our moon sailing among the stars in the sky.


Additional Question:   If the moon moves away from the earth at a rate of 4 cm a year, how long will it take for the moon to be twice as far away from earth as it is now?


 What we know

 Using the Math

 The moon is about 382,680  kilometers away.

1000 meters = 1 kilometer.

100 centimeters = 1 meter.

 Step One: Calculate distance of moon in centimeters:

382,680 km * 1000 = 382,680,000 meters.

382,680,000 meters * 100 = 38,268,000,000 cm.

 The moon is moving away at a rate of 4 cm a year.

 Step Two: Divide distance by 4 cm a year:

38,268,000,000 / 4 = 9,567,000,000 years.

This is more than 9.5  Billion Years!

What can we figure out from this?

  • Our solar system is about 4.6 billion years old. The lifespan of our sun is about 12 billion years. Even if the earth and moon were to survive the death of the sun, (which is very, very unlikely) there would be no one here to look at the moon when it is twice as far away.

  • The moon has reached it's present distance from the earth in 4.6 Billion years. It must have been moving away from the earth more quickly earlier in its history.

  • If the moon's rate of moving away from the earth is changing, will it eventually move away more quickly or more slowly than it does now?  Maybe we need to change our calculations!   For more information, we will need to study the rate of change of the moon's drift away from earth.


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© 2000, 2003. Elizabeth Anne Viau. All rights reserved. This material may be used by individuals for instructional purposes but not sold. Please inform the author if you use it at eviau@earthlink.net.