Mathematical genius required

[Mike53]

Trying to suss this...........

Sirius is 8.11 lt yrs away
Earth is 12,742km diameter
Keeping everything in proportion
1. What would be the size of the Earth if the distance to Sirius was 970km
2. What would be the distance to Sirius if the Earth was the size of a golf ball (42.67mm)

Thanks

Mike

 

[Ian H]

1. 12742km
2. 8.11 lt yrs + 12741.9999999999km

I have a GCSE ‘B’ in maths.

 

[SFK]

Sirius is 8.11 light yrs away (=7.67E13 km).
Earth is 12,742km diameter.
Golf ball is 42.67mm diameter (= 42.67E-6 km)

Keeping everything in proportion....

1. What would be the size of the Earth if the distance to Sirius was 970km?
New Dia of Earth = Dia of Earth * (New Distance to Sirius / Distance to Sirius)
New Dia of Earth = 12,742km * (970km / 7.67E13 km)
New Dia of Earth = 161E-9 km
New Dia of Earth = 161E-6 m
New Dia of Earth = 161 μm
<<< I was expecting this to be smaller noting that diameter of human hair is 17 to 181μm


2. What would be the distance to Sirius if the Earth was the size of a golf ball?
New Distance to Sirius = Distance to Sirius * (New Dia of Earth / Dia of Earth)
New Distance to Sirius = 7.67E13 km * (42.67E-6 km / 12,742km)
New Distance to Sirius = 256,850km
<<< I was expecting a greater distance noting that the moon is 384,400km from Earth.

 

[Ian H]

This is beyond me but why would the earth be smaller if it was further away?

If I park my car at the end of the road it looks smaller but it’s really the same size.

 

[durhamplumber]

This is beyond me but why would the earth be smaller if it was further away?

If I park my car at the end of the road it looks smaller but it’s really the same size.

That is perspective,the above is about scale

 

[Ian H]

That is perspective,the above is about scale

I still don’t get it. A KM is 1000mtrs wether your measuring from a bus in London to bus in Manchester or from a golf ball in Spain to a Golf ball in Scotland.

 

[SFK]

Ian,
I saw it is a scale question, and considered the question as him wanting to make a model that he could show to his friends.

Using his Q1, in real life distance from Sirius to the Earth is 76,700,000,000,000 km and Earth has a diameter of 12,742km.

If he then made a model of Earth the size of a hair diameter (161 μm) and put it at Land's End, he would have to put his (hair sized) model of Sirius 970km away at approx John o' Groats.

In conclusion, not a great (to scale) model to make, but an interesting thought process. Similar 'to scale' issues also happen when people consider our Solar system as the Sun is so large compared to the Planets, and the distances between them are enormous.
SFK

 

[SFK]

Just to add to that model idea, if you make a model of our Solar system on a 13,919,000,000 to 1 scale so that the model of the Sun is 100mm in diameter, then the Earth is 10mm in diameter and placed 11m from the Sun. That is relatively close as Neptune has to be placed 323m away from the model of the sun.

.........Model Diameter.......Distance from Model of Sun
Sun ......... 100.0mm ................---
Mercury ...... 0.3mm .............. 4m
Venus ......... 0.8mm .............. 8m
Earth .......... 0.9mm ............ 11m
Mars ........... 0.4mm ............ 16m
Jupiter ....... 10.2mm ............ 56m
Saturn ......... 8.3mm .......... 102m
Uranus ......... 3.3mm .......... 206m
Neptune ....... 3.2mm ......... 323m
Pluto ............ 0.1mm ......... 424m
Voyager 1 ...........................910m << NASA space probe launched 05Sept1977

 

[wobs]

This is beyond me but why would the earth be smaller if it was further away?

If I park my car at the end of the road it looks smaller but it’s really the same size.

[Father Ted]This planet is close, but small. This planet is big, but far away[/Father Ted]
Or something.

 

[SFK]

Wobs
Thanks for that reminder to "Father Ted Explains perspective",
Makes me laugh every time I see that. :>

SFK

 

[Ian H]

Ah, so we are shrinking it all down.

So Earth to Sirius is 81.46 trillion km. that’s 81,460,000,000,000km

81,460,000,000,000 / 12,742 = 6,393,030,921

42.67 x 6,393,030,921 = 272,790,629,399mm or 272,790Km

So my answer to Q2 is 272,790km.

I’ll try Q1 next time I have a brew.

 

[Mike53]

Thanks Ian & SKF,

To confirm it is a scale question.

The reason for the question is, I am advised for all practical purposes rays of light from the stars (Sirius for example) are parallel when they arrive at Earth irrespective of where we are bearing in mind the diameter 12,742km.

I would have been able to calculate this myself had the figures being much smaller, I am beat by the terminology on an online calculator. Do not understand this to the power of stuff. Thanks SKF for including your calcs but I do not understand them, sorry.

I hate to challenge an answer when someone has been kind enough to assist me in my endeavour but note in this thread we have 2 different answers to Q2. 256,850km and 272,790km

Also from another source I have other answers Q1 2.1mm Q2 19,687km

Gathering quite a selection of answers.

Mike

 

[Mike53]

Hi Ian & SKF,

I note you do not agree on the distance to Sirius

76,700 trillion
81,460 trillion

Mike

 

[Ian H]

Mine was the first thing that came up on google but I don’t know if that’s correct:

 

[SFK]

Mike,
the errors in the Sirius distance come down to rounding and also different Light Year distances.

You said Sirius is 8.11 light years away
Google says Sirius is 8.61 light years away
That is a 6% error.

I then used this site to convert light years to km
https://www.google.com/search?q=convert+8.11+light+years+to+km&ie=utf-8&oe=utf-8&client=firefox-b-ab
which gives 76,727,000,000,000 km

Ian with his 81.46trillion km presumably got his number from a difference web source.
AND there will be a tiny error as Earths orbit around Sun is 149,600,000km, so we keep moving closer and further away from Sirius.

SFK