The solar system can be accurately described by the following Schwarzschild metric:
$$
\mathrm{d} \tau^{2}=-\left( 1-\frac{2 G M} {r c^{2}} \right) c^{2} \mathrm{d} t^{2}+\frac{1} {1-\frac{2 G M} {r c^{2}}} \mathrm{d} r^{2}+r^{2} \left( \mathrm{d} \theta^{2}+\sin^{2} \theta\mathrm{d} \varphi^{2} \right)
$$
where $M$ is the mass of the sun, $t$ is the time coordinate, $r$ is the radial coordinate, $\theta$ is the polar angle, and $\varphi$ is the azimuthal angle. A radio wave is emitted from Earth, reflected back from a moon of Jupiter (which is treated as a point), and received on Earth. Assuming the distance from Jupiter to the Sun is $r_{2}$, and the distance from Earth to the Sun is $r_{1}$, and further, Jupiter is on the opposite side of the Sun. Let $r_{0}$ be the closest distance of the radio wave to the Sun.
Try to calculate the gravitational delay of the radio wave on its round trip, expressing it as a function of $r_{0}$ and accurate to the lowest order in $G$. Also, estimate the magnitude of this effect.
The mass of the Sun is approximately $2 \times 10^{33} \mathrm{g}$, the radius of the Sun is approximately $7 \times 10^{10} \mathrm{cm}$, the distance from the Sun to the Earth is approximately $1.5 \times 10^{13} \mathrm{cm}$, the distance from the Sun to Jupiter is approximately $8 \times 10^{13} \mathrm{cm}$, and $G \approx 6.67 \times 10^{-8} \mathrm{cm}^{3} / \mathrm{g \cdot s^{2}}$.

Options:
A. $$
T-{\frac{10} {c}} {\sqrt{r_{1}^{2}-r_{0}^{2}}}-{\frac{10} {c}} {\sqrt{r_{2}^{2}-r_{0}^{2}}}
$$
$$
\approx{\frac{20 G M} {c^{3}}} \left( 6 \operatorname{l n} 1 0+1 \right) \approx1. 5 \times1 0^{-3} \mathrm{s}
$$
B. $$
T-{\frac{9} {c}} {\sqrt{r_{1}^{2}-r_{0}^{2}}}-{\frac{9} {c}} {\sqrt{r_{2}^{2}-r_{0}^{2}}}
$$
$$
\approx{\frac{18 G M} {c^{3}}} \left( 6 \operatorname{l n} 1 0+1 \right) \approx1. 3 \times1 0^{-3} \mathrm{s}
$$
C. $$
T-{\frac{8} {c}} {\sqrt{r_{1}^{2}-r_{0}^{2}}}-{\frac{8} {c}} {\sqrt{r_{2}^{2}-r_{0}^{2}}}
$$
$$
\approx{\frac{16 G M} {c^{3}}} \left( 6 \operatorname{l n} 1 0+1 \right) \approx1. 2 \times1 0^{-3} \mathrm{s}
$$
D. $$
T-{\frac{5} {c}} {\sqrt{r_{1}^{2}-r_{0}^{2}}}-{\frac{5} {c}} {\sqrt{r_{2}^{2}-r_{0}^{2}}}
$$
$$
\approx{\frac{10 G M} {c^{3}}} \left( 6 \operatorname{l n} 1 0+1 \right) \approx7. 2 \times1 0^{-4} \mathrm{s}
$$
E. $$
T-{\frac{6} {c}} {\sqrt{r_{1}^{2}-r_{0}^{2}}}-{\frac{6} {c}} {\sqrt{r_{2}^{2}-r_{0}^{2}}}
$$
$$
\approx{\frac{12 G M} {c^{3}}} \left( 6 \operatorname{l n} 1 0+1 \right) \approx8. 7 \times1 0^{-4} \mathrm{s}
$$
F. $$
T-{\frac{3} {c}} {\sqrt{r_{1}^{2}-r_{0}^{2}}}-{\frac{3} {c}} {\sqrt{r_{2}^{2}-r_{0}^{2}}}
$$
$$
\approx{\frac{6 G M} {c^{3}}} \left( 6 \operatorname{l n} 1 0+1 \right) \approx4. 3 \times1 0^{-4} \mathrm{s}
$$
G. $$
T-{\frac{1} {c}} {\sqrt{r_{1}^{2}-r_{0}^{2}}}-{\frac{1} {c}} {\sqrt{r_{2}^{2}-r_{0}^{2}}}
$$
$$
\approx{\frac{2 G M} {c^{3}}} \left( 6 \operatorname{l n} 1 0+1 \right) \approx1. 4 \times1 0^{-4} \mathrm{s}
$$
H. $$
T-{\frac{7} {c}} {\sqrt{r_{1}^{2}-r_{0}^{2}}}-{\frac{7} {c}} {\sqrt{r_{2}^{2}-r_{0}^{2}}}
$$
$$
\approx{\frac{14 G M} {c^{3}}} \left( 6 \operatorname{l n} 1 0+1 \right) \approx1. 0 \times1 0^{-3} \mathrm{s}
$$
I. $$
T-{\frac{2} {c}} {\sqrt{r_{1}^{2}-r_{0}^{2}}}-{\frac{2} {c}} {\sqrt{r_{2}^{2}-r_{0}^{2}}}
$$
$$
\approx{\frac{4 G M} {c^{3}}} \left( 6 \operatorname{l n} 1 0+1 \right) \approx2. 9 \times1 0^{-4} \mathrm{s}
$$
J. $$
T-{\frac{4} {c}} {\sqrt{r_{1}^{2}-r_{0}^{2}}}-{\frac{4} {c}} {\sqrt{r_{2}^{2}-r_{0}^{2}}}
$$
$$
\approx{\frac{8 G M} {c^{3}}} \left( 6 \operatorname{l n} 1 0+1 \right) \approx5. 8 \times1 0^{-4} \mathrm{s}
$$
Answer: I