And while you're at it, read the book Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time by Dava Sobel -- it's the very, very, very fascinating story of John Harrison, and the title is not an overstatement.
Flamsteed built the map, but Harrison figured out how to find out where you were on the map -- he built some of the most amazing and important timepieces ever, for sailors to use while at sea, and several of them are on display right here.
By the way, it's £5 to go into Royal Observatory and see all the astronomical and chronological devices therein, and it's definitely worth it. Very impressive, for those of us into astronomy and clocks. My only regret is that I should've bought the guidebook.
The red-orange ball you see on the roof of the observatory, to the left of the center of the picture, is the Greenwich Time Ball. Erected in 1833, it was one of the world's first visual time signals -- at 1300 (1pm) on the dot, the ball drops from the top of the post to the bottom; sailors on the Thames would be watching for it, and they'd set their marine chronometers accordingly.
As it was after 1300 when I got to Greenwich, the ball had already dropped, obviously.
They also used to fire a cannon at the same time they dropped the ball, but they don't do that any more. Pity.
The Royal Observatory Greenwich is also the source of the Prime Meridian, longitude 0° 0' 0''.
Until the 19th century, each country tended to keep its own zero meridian. The Prime Meridian for the world was adopted in 1884, at the International Meridian Conference in Washington DC. Twenty-five countries were represented and voted to adopt the Meridian at Greenwich as the Prime Meridian for the world. It was also agreed that longitude would be measured in two directions from the Prime Meridian, 'east longitude being plus and west longitude being minus.'
Impressive, eh?
Here's a shot of me standing astride the Prime Meridian, one leg in the western hemisphere and one in the east. Ok, ok, it's not a shot of me per se, but a shot I took of my own barely-visible reflection in the window. But still.
The sign above the clock reads:
Prime Meridian Of The World
Centre of Transit Circle
Latitude 51º 28' 38'' North
Longitude 00º 00' 00''
The centre of the transit circle is pretty much where I'm standing while I'm taking this picture, so this is one of the few times in my life I knew exactly where I was at. And I mean exactly.
Oh, and I took a picture for a tourist; he gave me his camera, stood on the Prime Meridian, smiled, waved, and I snapped a few shots. I was a little wide angle on the shot, but I wanted to make sure I got in everything he might want to see, just in case. You never know what other people like, so always a good idea to include more.
Here's the Royal Naval College again. As you might have guessed, you’ve not only got incredible views looking at the town from the other side of the Thames, and incredible views of the Observatory from the bottom of the hill in Greenwich park, you've also got incredible views of London from the top of the hill, from the Observatory. I went through film like crazy.

... and again with the Royal Naval College, sort of, on the left there, although my intent was just to show the generally magnificent view.
Those four smokestacks on the right are those of the Greenwich power station, built in 1906 but no longer operating.
Another shot of the power station, but look to the right of the smokestacks, at those yellow cranes in the distance -- that's the Millenium Dome under construction!
I had a late start on the entire day, so I didn't finish at the Royal Observatory until 5pm, which was closing time for the museum. Ah, if I'd gotten up a couple hours earlier, I also could have toured the Royal College, at the bottom of the park. Darn. Oh, well, there's always next year.
So I walked downhill into Greenwich, and just wandered some more. Went to "Nautalica" shop, bought Titanic whistle for Joel (£7.95) and Uffa Fox mug for Nick (£4.95).
Debated getting Mexican food for dinner ("Cafe Sol", a "Texan-Mexican Cafe"), but thought I'd go for something local. Eating now at "Green Village Restaurant." Decent burger & soup for £6. Includes bread, I think.
Oh, I set my watch at the Greenwich clock. How's that for accuracy?