Thursday, October 15, 2009

Is it bigger than a bread box?

When I read about the giant rings recently discovered around Saturn, I wanted some frame of reference to help understand how big they are. So I started calculating some ratios between various measurements...

Scale: If you could walk around the earth

Suppose you made a map of the earth to the size of a city. The equatorial circumference of the Earth is 40,075 km. The length of Manhattan, or an average city like Edmonton, is about 21 km. This is a long walk for an average person, but most should be able to do it in a day.

If you laid a large map of the globe across such a city, the map scale would be 21:40075, or 1 to 1908.333 (repeating, of course). You can multiply this ratio by any map distance to find the equivalent distance on earth, or divide to do the reverse. For example, a big 1 m step taken in your city map would cover 1908 m on Earth, which is about half the length of Central Park (on your map, the park would be about the size of a tub). The distance from London to Paris is 343 km, which would be 180 m on your map. That's about the depth of the Met Museum of Art in real life.

Note: This ratio is actually only valid along the equator on the map, because the projection from sphere to plane will deform the map, but let's just pretend that the map was made in such a way that any of the distances we measure here share the same ratio.

By the way, the ratio also means that if you laid 1908 average cities side by side, they would circle the entire globe.

A map of Earth the size of a city.
Scale: 1 : 1908.3

MeasurementActual sizeSize on mapAbout as big as...
Width of a house10 m5.2 mma pea
Height of CN Tower in Toronto553.3 m0.29 mthe height of a garden gnome
Height of Mount Everest8848 m4.637 mthe height of a house. Imagine a city the size of Manhattan with nothing taller than 1-story buildings. That's how relatively "flat" the Earth is.
Average city length21 km11 ma house
Length of the equator40075 km21 kma city, of course!
Diameter of the moon3475 km1.820 mhalf the length of central park
Average distance to the moon384,403 km201 kmLong Island
Diameter of the sun1,391,000 km728.9 kmNew York to Chicago; highway driving for 7 hours
1 AU (Distance to sun)149,598,000 km78391 km6 Earths side by side
Distance to Proxima Centauri (nearest star to sun, 4.3 light-years)4.07×1013 km21,317,173,156 km142.5 AU... within the heliosheath of the solar system; 5x the distance from sun to Uranus

Scale: The solar system in a ball park...

Suppose we have a park that is 60 m (just under 200 ft) from home plate to the outfield fence, and we want to build a scale model of the solar system with the sun at home plate and Neptune orbiting around where the fence is.

Home plate is 0.4318 m across, the pitching rubber is 18.44 m away, 1st base is 27.43 m away, and the outfield grass line is 47.40 m straight ahead.

Neptune orbits at about 30 AU, or 4.48794×1012 m.
Scale: 60 : 4.48794×1012 = 1 : 74799 million

MeasurementActual sizeSize in ballpark modelAbout as big as...
Diameter of the sun1,391,000 km18.60 mma nickel
Diameter of Mercury4,879.4 km0.0652 mmthe width of a thin hair. All of the inner planets are like hairs of varying thickness.
Distance to Mercury59,839,200 km0.8 ma big step
Venus12103.6 km0.1618 mm
To Venus104,718,600 km1.4 ma short person laying down
Earth12756.2 km0.1705 mm
To Earth149,598,000 km2 mwidth of a car. If you tape a nickel to a window and stand 2 m away from it, the coin should just eclipse the sun. Try this with the moon to be safe, if you're curious. The moon looks slightly (103%) bigger than the sun, on average.
Diameter of the moon3475 km0.0465 mm
Average distance to the moon384,403 km5.14 mma pea
Mars6794 km0.0908 mm
To Mars224,397,000 km3 m
Distance to the Asteroid belt418,874,400 km5.6 ma limousine
Jupiter142,984 km1.9116 mm
To Jupiter777,909,600 km10.4 m
Saturn120,536 km1.6115 mmwidth of a grain of rice
To Saturn1,421,181,000 km19 mjust past the pitching rubber
Diameter of Saturn's main rings273,560 km3.66 mmthe width of 3 pennies
Saturn's new ring13,000,000 km173.8 mma cantaloupe. As seen from Earth (2 m from home plate), this should look twice as big as the moon or sun.
Uranus51,118 km0.6834 mmUranus is huge.
To Uranus2,932,120,800 km39.2 mhalfway between 2nd base and the outfield grass line
Neptune49,528 km0.6621 mm
To Neptune4,487,940,000 km60 mthe park, to the outfield fence
Solar system bow shock34,407,540,000 km460 ma few long city blocks
Distance to Proxima Centauri (nearest star to sun, 4.3 light-years)4.07×1013 km543 kmToronto to Montreal. If it took us a year to get from the sun to Neptune's orbit, it would take 9064 years to get to the nearest star.
Diameter of Proxima Centauri201,695 km2.70 mma spitball
Size of the galaxy9.50×1017 km12,700,705 kmSize of Saturn's newly discovered rings. 33 times the average distance to the moon and a twelfth of the distance to the sun.

In a model where the planets' orbits fit in a ball park, the galaxy fits in Saturn's "new" rings. The next time you make a model this big, have someone in another city 543 km away hold up a spitball, to represent the nearest star.

Scale: If the distance to the nearest star was the length of a house...

Length of house: 14 m
Distance to Proxima Centauri: 4.3 light-years = 4.07×1013 km
Scale: 1 : 2905733 billion

MeasurementActual sizeSize in house modelAbout as big as...
Diameter of the sun1,391,000 km0.000479 mma bacteria cell. Though not visible to the naked eye, if it was very bright and seen from across a dark house, it would be a visible, single point of light, just like a star in the sky
Distance from sun to Earth149,598,000 km0.0515 mmwidth of a thin hair
To Neptune4,487,940,000 km1.54 mmwidth of a grain of rice
To bow shock34,407,540,000 km11.8 mma marble
Distance to Proxima Centauri (4.3 light-years)4.07×1013 km14 mlength of house
Size of the galaxy9.50×1017 km327 kmDistance from Edmonton to Calgary
Distance to nearest galaxy2.37×1017 km81.4 km
Distance to Andromeda Galaxy (whose size is comparable to the Milky Way Galaxy)1.89×1019 km6512 kmRadius of Earth
Size of the visible universe4.40×1023 km151,395,348 kmDistance to the sun

References: google, wikipedia


Anonymous said...

So, I didn't read this whole blog. But I liked your BBC Office reference! Uh... unless it was a reference to the actual joke, and not the part of the show where he tells the joke. Maybe you've never even see the show and don't even know what I'm talking about. Maybe I just keep *thinking* I get all your sly pop culture references when I really don't. Anyway. Forget it.

Anonymous said...

Hey, wait, it did post my original comment after all! (I had hit the Back button so I could change "see" to "seen"... you know how anal I am about that stuff...and I thought it made me lose the comment.) Now I have two posted comments that say virtually the same thing. I hate when that happens.

Anonymous said...

Hey, wait, it left my first and last comments, but not the one in the middle! That's OK... it was just a repeat of the first comment, and therefore kind of stupid. Maybe it knew how stupid it was and was trying to do me a favor. Computers can be really benevolent sometimes.

Michael Devine said...

I like how this post has the most discussion and comments of any of the posts.

I uh :$ didn't realize I was referencing The Office. But I just looked it up. I guess I was referencing 20 Questions or What's My Line? Also... Leroy Jenkins.