> restart: 
> g1 := 2*Pi*r+1=2*t+(2*Pi-2*a)*r;
                    g1 := 2 Pi r + 1 = 2 t + (2 Pi - 2 a) r

> a := arcsin(t/(r+h));
                                            t
                              a := arcsin(-----)
                                          r + h

> g1;
                                    /                  t   \
                 2 Pi r + 1 = 2 t + |2 Pi - 2 arcsin(-----)| r
                                    \                r + h /

> t := ((r+h)^2-r^2)^(1/2);
                                         2    2 1/2
                            t := ((r + h)  - r )

> g1;                      
                                      /                        2    2 1/2 \
                         2    2 1/2   |                ((r + h)  - r )    |
  2 Pi r + 1 = 2 ((r + h)  - r )    + |2 Pi - 2 arcsin(------------------)| r
                                      \                      r + h        /

> r := 6370*10^3;
                                 r := 6370000

> g1;            
                                  2                  1/2
12740000 Pi + 1 = 2 ((6370000 + h)  - 40576900000000)    + 12740000 Pi

                                     2                  1/2
                       ((6370000 + h)  - 40576900000000)
     - 12740000 arcsin(------------------------------------)
                                   6370000 + h

> fsolve(g1,h);            
bytes used=5013420, alloc=2096768, time=1.47
                                  121.4543680

>