long traceroutes
Physical distance and network distance have an interesting relationship. Even though intra and inter-city links can be horribly slow and therefore not a good measure of physical distance, the same is not as true for international and inter-continental links.
From the UK (a.a.a.a) to Japan (z.z.z.z) via the Internet:
traceroute to z.z.z.z (z.z.z.z), 30 hops max, 40 byte packets
1 b.b.b.b (b.b.b.b) 0.710 ms 0.606 ms 0.636 ms
2 c.c.c.c (c.c.c.c) 3.065 ms 2.447 ms 2.817 ms
3 d.ukcore.bt.net (d.d.d.d) 2.810 ms 2.793 ms 2.483 ms
4 e.e.e.e (e.e.e.e) 7.235 ms 6.432 ms 7.068 ms
5 f.ukcore.bt.net (f.f.f.f) 6.449 ms 6.360 ms 6.221 ms
6 * g.eu.bt.net (g.g.g.g) 6.151 ms 5.906 ms
7 h.eu.bt.net (h.h.h.h) 88.322 ms 88.575 ms 88.227 ms
8 i.eu.bt.net (i.i.i.i) 88.652 ms 88.257 ms 88.850 ms
9 * * *
10 j.j.j.j (j.j.j.j) 164.092 ms 163.958 ms 163.862 ms
11 k.kddnet.ad.jp (k.k.k.k) 151.157 ms 150.945 ms 150.999 ms
12 l.kddnet.ad.jp (l.l.l.l) 262.545 ms 264.215 ms 262.769 ms
13 m.kddnet.ad.jp (m.m.m.m) 284.810 ms 278.666 ms 276.577 ms
14 n.kddi.ne.jp (n.n.n.n) 270.713 ms 270.666 ms 282.805 ms
15 o.kddi.ne.jp (o.o.o.o) 278.036 ms 278.105 ms 278.458 ms
16 p.kddi.ne.jp (p.p.p.p) 269.161 ms 266.220 ms 270.104 ms
17 q.kddi.ne.jp (q.q.q.q) 279.407 ms 283.477 ms 279.755 ms
18 r.r.r.r (r.r.r.r) 295.864 ms 266.645 ms 267.897 ms
19 s.s.s.s (s.s.s.s) 268.964 ms 268.345 ms 267.745 ms
20 z.jp (z.z.z.z) 265.074 ms 275.107 ms 263.744 ms
The key hops are 6 to 7 (~82ms) [UK-Europe], 8 to 10 (~76ms) [Europe-Japan] and 11 to 12 (~110ms). These represent the respective network distances of the links between UK and somewhere in Europe and between somewhere in Europe and Japan.
From the UK (a.a.a.a) to Australia (z.z.z.z) via a private link:
traceroute to z.z.z.z (z.z.z.z), 30 hops max, 40 byte packets
1 b.b.b.b (b.b.b.b) 0.522 ms 0.491 ms 0.827 ms
2 c.c.c.c (c.c.c.c) 2.811 ms 2.788 ms 2.753 ms
3 d.d.d.d (d.d.d.d) 0.567 ms 0.543 ms 0.515 ms
4 e.e.e.e (e.e.e.e) 0.467 ms 0.771 ms 0.556 ms
5 f.f.f.f (f.f.f.f) 6.864 ms 8.488 ms 11.544 ms
6 g.g.g.g (g.g.g.g) 305.581 ms 306.083 ms 306.598 ms
7 z.z (z.z.z.z) 305.507 ms 305.506 ms 305.377 ms
In this case, the important hops are 4 to 5 (~8ms) [likely intercity] and 5 to 6 (~295ms) [obviously intercontinental].
My trusty UDP packets travelled half the world and back at an amazing ~37.8% of the speed of light! That's including routing and other network type processing, variable speeds of propagation trough different mediums, etc.