Bending radio waves by Jupiter and the Moon

Adapted from IOAA 2019 (Keszthely), theory problem 2. We have restated it in our own words and kept the original data, adding the masses and radii of Jupiter and the Moon, which the original left to the data sheet. The solution was last checked on 23 October 2026.

In the eclipse of 1919 starlight passing the edge of the Sun was found to be bent by 1.75″. A ray passing a body at the distance $d$ is bent by an angle proportional to $4GM/(d{c}^2)$. Radio interferometers spread over Earth can now measure positions to 0.1 milliarcseconds. Could they detect the bending of radio waves from a quasar by (a) Jupiter and (b) the Moon? Estimate the bending in each case. Take Jupiter's mass and radius as $1.898\times {10}^{27}$ kg and $6.991\times {10}^7$ m, and the Moon's as $7.342\times {10}^{22}$ kg and $1.737\times {10}^6$ m.

Answer(a) Yes, Jupiter bends the radio waves by about 17 milliarcseconds. (b) No, the Moon bends them by only 0.026 milliarcseconds.