Astronomical subject. [ Self explanatory.] written for my grandchildren.

Page 1 The making of a downsized model of our solar system.
Written prior to Pluto’s removal from the planets list.

                                                                                                                         Author  A McPherson

alanmcp@xtra.co.nz New Zealand
3.6.14

The object of this exercise is to reduce the scale of our solar system to it’s smallest practical size,
With a view to making a true to scale model,so we can appreciate the scale of distances involved.

In order to downsize the solar system to fabricate a model, I have chosen Jupiter,as the largest planet and have allocated to it a diameter of 110mm. From this, and the following calculations, we can ascertain the downsized diameters of the remaining planets.

I chose110mm for Jupiter as it is the smallest practical size, without losing sight of our most distant and smallest planet Pluto,which in fact will finish up a mere 1.75mm by scale.
We can now proceed, with the aid of published astronomical figures.
To do this, simply take the diameter of Jupiter and divide the diameters of the other planets into it. This will give the proportional size of the remaining planets relative to Jupiter.These figures will give how many times smaller the other planets will be when compared with our110mm diameter model of Jupiter.

Example.
Divide Jupiter by Mercury, 142.984 km divide by 4.878km = 29.31

Now divide the remainder.

Mercury ------ 4.878 km = 29.31

Venus -------- 12.109 km = 11.80

Earth --------- 12.756 km = 11.21

Mars ---------- 6.794 km = 21.04

Saturn -------- 120.536 km = 1.19

Uranus ------- 51.118 km = 2.79

Neptune ----- 49.528 km = 2.89

Pluto ---------- 2.284 km = 62.60

Now to find the actual diameters of the planets relative to our 110mm Jupiter, for our model, simply divide the resultant figures shown above into Jupiter.

Example

Mercury = 29.31 divided into 110mm = 3.75, so Mercury measures 3.75mm diameter in our model.
These answers will give you the model sizes of the planets we calculated in millimeters

Page 2 model solar system.

Jupiter model = 110mm diameter.

Mercury ---------- 110 divided by 29.31 = 3.75 mm diameter.

Venus ------------------------------ 12.109 = 9.08 mm diameter.

Earth ------------------------------ 12.756 = 9.80 mm diameter.

Mars ------------------------------ 21.04 = 5.23 mm diameter.

Saturn ----------------------------- 1.19 = 92.44 mm diameter.

Uranus ----------------------------- 2.79 = 39.42mm diameter.

Neptune --------------------------- 2.89 = 38.06mm diameter.

Pluto ------------------------------- 62.60 = 1.76mm diameter.

So our model has the largest planet Jupiter, about the size of a flushing system float, and Pluto as the smallest planet, about the size of a grain of sand.

The sun. From available figures we know that the sun is 10 times the diameter of Jupiter.
We have allocated to Jupiter a size of 110mm for our model, therefore the sun will be 10 times larger = 1.1 meters in diameter. We must know this now to calculate the downsized orbits of our model planets.To do this we again work out the proportions of the suns diameter, and divide it into the planets average distance from the sun. This gives us a figure to calculate the proportional downsizing of our planets orbit to accurately fit our model. So let’s go to our most extreme example and work out our models orbit for Pluto.

Distance from the sun to Pluto. 5.913.520.000km
Diameter of the sun. 1.400.000km

To simplify this division, cancel the 4 zeros from the ends of each number, this makes no difference to our answer.

So now we have. 591.352 km = 4224 as a ratio.
140km

This answer tells us the half orbit of Pluto will be 4224 times the diameter of our models sun.
These figures tell us the distance between the two subjects, to find the orbit the figures will need to be doubled. We also know that our model of the sun is 1100mm in diameter.
So to more maths. We now know that Pluto is 4224 times the distance away from our models sun, the sun is 1100mm so lets multiply them. But we will get an answer in millimeters which is not really practical so let’s also divide the answer by 1000 and convert it to meters. But we must not forget that this answer only gives us the distance from the sun out to Pluto one way, so to convert
This to an orbital distance we must double it.

So 1100 multiplied by 4224 then doubled = 9292.8 meters.
1000

Pluto’s orbit in our model is 9.3 kilometers!

Page 3 model solar system.

And in descending order the orbits of.

Neptune ------------- 7.067 km.

Uranus --------------- 4.511 km.

Saturn ---------------- 2.242 km.

Jupiter---------------- 1.223 km.

Mars ----------------- 358 meters.

Earth ---------------- 235 meters.

Venus -------------- 170 meters.

Mercury ------------ 91 meters.

Now that Pluto has been removed from the list of planets, we can now produce a practical accurate model of our solar system which was not practical before.
Due to Pluto’s extreme distance from earth.

A simple way to remember the position of planets is to memorize the following sentence.

My very educated mother as. just served us new potatoes.
Mercury Venus Earth Mars asteroids Jupiter Saturn Uranus Neptune Pluto

Sun and planets comparative diameters.

Sun. ==============================================-
Sun 1.1 meter.

Jupiter =====================================
Jupiter 110mm

Saturn ==============================
Saturn 91.7mm

Neptune ==============
37.9mm

Earth =====
10mm

Venus ====
9.2mm

Mars ===
5mm

Uranus =
3.9mm

Mercury =
3.8mm

Pluto =
1.75mm

FIN.