IOAA 2019, Теория — Задача 2. Deflection of radio photons in the gravitational field of solar system bodies
Theory problem sheet · 10 т.
Условие
A. Eddington and F. Dyson from Principe, and C. Davidson and A. Crommelin from Sobral, Brazil measured the deflection of light coming from stars apparently very close to the Sun during the total solar eclipse in 1919. The deflection was found to agree with the theoretically predicted value of 1.75".
A light ray (or photon) which passes the Sun at a distance is deflected by an angle
The present-day accuracy of the VLBI (Very Long Baseline Interferometry) technique in the radio wavelength range is 0.1 mas (milliarcsecond). Is it possible to detect a deflection of radio photons from a quasar by (a) Jupiter, (b) the Moon? Estimate the angle of deflection in both cases and mark "YES" or "NO" on the answer sheet.
Решение
One has to notice that in the case of the Sun , that is equals the solar radius. (1 p)
The angular deflection scales as (mass over radius) of the deflector body, so one has to consider , where b stands for Jupiter and Moon, respectively.
This means that:
a)
Jupiter
Substituting the masses and radii one gets:
The deflection of radio waves by Jupiter's gravitational field is greater than 0.1 mas, so it is observable with the VLBI network. The answer is: YES (1 p)
b)
Moon
Substituting the masses and radii one gets:
The deflection of radio waves by Moon's gravitational field is smaller than 0.1 mas, so it is not observable with the VLBI network. The answer is: NO (1 p)
Оригинал в Архива: TH-problem-final.pdf · официални решения: TH-solution-final.pdf · допълнителни данни: TH-anssheet.pdf