How do you calculate the distance in AU(Astronomical Unit)?

Question

Okay, I am not so good at science...and I can't really get a hold of calculating the distance of planets using Astronomical Units . . .

I Know 1 AU is the earth's distance to the Sun.

But how do you calculate how far is the Earth is from Neptune or something? Please teach me in Words and Numbers and in Easy steps.

If You can please answer this question and teach me in simple steps.

The Distance of Saturn from the sun is 9.54 AU and the earth's distance to the sun is 1 AU.

- If you put a model earth 1m from the sun, how far would you put Saturn?

- If you put a model Earth 50 cm from the sun, How far would you put Saturn?

Thanks.

Answer 1

AUS are all the same length.  If 1 AU = 1 M, then 9.54 AU = 9.54 M, et cetera.

If 1 AU = 50cm (or 1/2  of a meter) then 9.54 AU = (whatever half of 9.54 meters is, I don't have a calculator.)  The multiplication in a scale model is always the same.

Answer 2

Scale everything down by 1 AU per meter gives

earth at 1 m ==> Saturn at 9.54 m

Scale everything down by 1 AU per (1/20 == 50 cm) meter gives

earth at (50 cm) 1/20 m ==> Saturn at 9.54/20 m ==> 0.477m

Answer 3

Sun to Earth = 1 au  (the official symbol is with lower case letters, no punctuation -- no, I don't know why)

Sun to Saturn = 9.54 au

Therefore Saturn is 9.54 times further away form the Sun than Earth is.

If you place Earth at 1 cm, you would place Saturn at 9.54 cm.

If you placed Earth at 7.2 inches, you would place Saturn at 9.54 times 7.2 inches.

If you placed Earth at 3 cubits, you would place Saturn at 9.54 times 3 cubits (it's an old, very old unit of length)

If you placed Earth at 50 whatevers, then Saturn would be at 9.54 times 50 whatevers (= 477 whatevers)

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The idea of using au as a distance unit is to make things simpler.  The other trick is to use 1 Earth-year as the unit of time for orbital periods.

For example, you could calculate Saturn's "year" in Saturn days, in Earth-days, in seconds, in heartbeats.  But the simplest measure is to do it in Earth-years.

Saturn's year is 29.466 Earth-years (that is how long it takes Saturn to go once around the Sun).

Later, you will see why astronomers use Earth-years and astronomical units.  One of the reasons was discovered by Kepler in the 16th century.

The square of the orbital period is like the cube of the distance.

distance in astronomical units = 9.54

9.54 cubed = 9.54 * 9.54 * 9.65 = 868.25

orbital period in Earth-years = 29.466

29.466 squared = 29.466 * 29.466 = 868.25

Astronomy tables give the distances in astronomical units.

If you are given the distance in other units, you divide by the Earth's average distance (and most of us use rounded figures)

in kilometres:

1 au = 150,000,000 km

in miles:

1 au = 93,750,000 mi

Answer 4

The AU was invented specifically to simplify questions like yours.  For the earth's distance we are just calling it 1.  Now using that scale, then Jupiter is 5.2 and Saturn 9.54, etc.  Those are the easy multiples of 1.  Now if you are building a scale, take whatever distance it is from the earth to the sun and multiply it by the AUs to those planets.

For example, if your earth is 50 cm from the sun, then Saturn will be 9.54 times that, or 477 cm.  Neptune is 30 AU.  So multiply 30 times 50 cm.  That's 1500 cm.  It's simpler than you are thinking.

Answer 5

I like this one-- toilet paper solar system

http://solar.physics.montana.edu/tslater...