b
Let \(d\) is the maximum distance, upto it the objects From \(\Delta \mathrm{AOC}\)

\(O C^{2}=A C^{2}+A O^{2}\)

\((h+R)^{2}=d^{2}+R^{2}\)

\(d^{2}=(h+R)^{2}-R^{2}\)

\(d=\sqrt{(h+R)^{2}-R^{2}}\)

\(d=\sqrt{h^{2}+2 h R}\)

\(d=\sqrt{500^{2}+2 \times 6.4 \times 10^{6}}=80 \mathrm{km}\)