How far away is the moon?

[heresmo]

Watching Apollo 13 on telly (ITV1). Conversation - flight to Houston and response - is instantaneous. So, puzzle for Sunday to keep brains alert:

How far away is the moon; what is the speed for radio waves; how would one compensate for distance actually travelled?

Please ring 09........ with your answer. Calls cost £100 per minute from landlines...etc

Mo

[Lady Elanore]

Not sure if you are asking in jest or not Mo. But I think the moon is about 250,000 miles away and radio waves travel at the speed of light which is around 186,000 miles per second. Although I'm sure someone will be along shortly to give you the interwebs exact figures

[Taztastic]

Aristarchus around 270 BC derived the Moon's distance from the duration of a lunar eclipse.

It was commonly accepted in those days that the Earth was a sphere (although its size was only calculated a few years later, by Eratosthenes ). Astronomers also believed that the Earth was the center of the universe, and that Sun, Moon, planets and stars all orbited around it. It was only natural, then, that Aristarchus assumed that the Moon moved in a large circle around Earth.

Let R be the radius of that circle and T the time it takes the Moon to go around once, about one month. In that time the Moon covers a distance of 2 πR, where π~ 3.1415926... ,

An eclipse of the Moon occurs when the Moon passes through the shadow of the Earth, on the opposite side from the Sun (therefore, it must be a full Moon). If r is the radius of the Earth, the shadow's width is close to 2r. Let t be the time it takes the mid-point of the Moon to cross the center of the shadow, about 3 hours (in eclipses of the longest duration, when the Moon crosses the center of the shadow).

If the Moon moves around Earth at a constant speed--and it takes time T to cover 2π R ~ 6.28R, and time t to cover 2r--then

6.28 R / 2 r = T/t

From this we can obtained

R/r ~ 60

which fits the average distance of the Moon accepted today, 60 Earth radii.

So to answer the delay question, radius of earth approx 6380Km ans radio waves travel approx 300,000Km/s a delay of around 1.2 secs I would have thought.

I now have a headache and need beer.

HTH

Taz:rofl:

[Lady Elanore]

But surely Mo’s asking about the delay to the moon and back. 250/186 x 2 (roughly speaking) = a bit over 2.5 secs

[Lady Elanore]

Aristarchus around 270 BC derived the Moon's distance from the duration of a lunar eclipse.

It was commonly accepted in those days that the Earth was a sphere (although its size was only calculated a few years later, by Eratosthenes ). Astronomers also believed that the Earth was the center of the universe, and that Sun, Moon, planets and stars all orbited around it. It was only natural, then, that Aristarchus assumed that the Moon moved in a large circle around Earth.

Let R be the radius of that circle and T the time it takes the Moon to go around once, about one month. In that time the Moon covers a distance of 2 πR, where π~ 3.1415926... ,

An eclipse of the Moon occurs when the Moon passes through the shadow of the Earth, on the opposite side from the Sun (therefore, it must be a full Moon). If r is the radius of the Earth, the shadow's width is close to 2r. Let t be the time it takes the mid-point of the Moon to cross the center of the shadow, about 3 hours (in eclipses of the longest duration, when the Moon crosses the center of the shadow).

If the Moon moves around Earth at a constant speed--and it takes time T to cover 2π R ~ 6.28R, and time t to cover 2r--then

6.28 R / 2 r = T/t

From this we can obtained

R/r ~ 60

which fits the average distance of the Moon accepted today, 60 Earth radii.

So to answer the delay question, radius of earth approx 6380Km ans radio waves travel approx 300,000Km/s a delay of around 1.2 secs I would have thought.

I now have a headache and need beer.

HTH

Taz:rofl:

Bugger, you edited this as I was posting a reply

[Taztastic]

HaHa I cocked up my figures and quickly realised what I had done.......

Think we both should have a beer to celebrate:cheers:

Taz

[cheezemonkhai]

The moon is close to us

We Like The Moon - the Spongmonkeys try and cash in on the kittens' success - By Joel Veitch rathergood.com, song by Joel and Alex Veitch

[Lady Elanore]

[Lady Elanore]

The moon is close to us

We Like The Moon - the Spongmonkeys try and cash in on the kittens' success - By Joel Veitch rathergood.com, song by Joel and Alex Veitch

[Taztastic]

:orb_xmas_

hic!

[Taztastic]

The moon is close to us

We Like The Moon - the Spongmonkeys try and cash in on the kittens' success - By Joel Veitch rathergood.com, song by Joel and Alex Veitch

just seen this and I think my beer is faulty:P

[Lady Elanore]

:orb_xmas_

hic!

[Taztastic]

:orb_party cheers

[Lady Elanore]

[Taztastic]

:orb_coffe

[ric04vrs]

but how far is the moon away:confused:

[devonutopia]

238,857 on average.

[SteVRs]

We looked this up last week cos a guy at work has an old Toyota that's done 260,000 miles - we wondered if it had been to the moon and back.

[Lady Elanore]

I remember it roughly as 250,000 miles as the Earth is roughly 25,000 miles in circumference. There and back is 500K so to the moon and back is 20 times around the world.

[heresmo]

Hello again. For some reason, I had 67,000 miles sitting in my head, so I did a quick Google and it brought up the following, which might be very interesting to anyone with an expanding waistline as seemingly they are conforming to earthly influence: Quote:

The circumference of the earth at the equator is 24,901.55 miles (40,075.16 kilometers).

But, if you measure the earth through the poles the circumference is a bit shorter - 24,859.82 miles (40,008 km). This the earth is a tad wider than it is tall, giving it a slight bulge at the equator. This shape is known as an ellipsoid or more properly, geoid (earth-like).

From here: What is the circumference of the earth?

Not sure where I got 67,000 miles from yet...

Best

Mo

[heresmo]

Just found it: The earth travels at 67,000 miles an hour:

Many dream of traveling in space and viewing the wonders of the universe. In reality all of us are space travelers. Our spaceship is the planet Earth, traveling at the speed of 108,000 kilometers (67,000 miles) an hour.

From here: Earth Introduction

Knew I'd remembered it for some reason...

That's quite fast isn't it? I wonder thus if hovercrafts aren't the best thing for the future, since all you'd have to do would be to rise up and wait for the earth to move? Sounds like a plan to me :rubchin:

Mo