Question 8.3: Calculate the radius of the earth’s sphere of influence.

In Table A.1 we find

m_{\text {earth }}=5.974 \times 10^{24} kg
m_{\text {sun }}=1.989 \times 10^{30} kg
R_{\text {earth }}=149.6 \times 10^{6} km

Substituting this data into Equation 8.34 yields

\frac{r_{ SOI }}{R}=\left\lgroup \frac{m_{p}}{m_{s}} \right\rgroup ^{2 / 5}                (8.34)

Since the radius of the earth is 6378 km,

r_{ SOI } = 145 earth radii

Relative to the earth, its sphere of influence is very large. However, relative to the sun it is tiny, as illustrated in Figure 8.7.