An alien civilization occupies a planet circling a brown dwarf, several light-ye

Question

An alien civilization occupies a planet circling a brown dwarf, several light-years away. The plane of the planet's orbit is perpendicular to a line from the brown dwarf to the Sun, so the planet is at nearly a fixed position relative to the Sun. The extraterrestrials have come to love broadcasts of MacGyver, on television channel 2, at carrier frequency 145 MHz. Their line of sight to us is in the plane of the Earth's orbit. Find the difference between the highest and lowest frequencies they receive due to the Earth's orbital motion around the Sun

Explanation / Answer

An alien civilization occupies a planet circling a brown dwarf, several light-years away. The plane of the planets orbit is perpendicular to a line from the brown dwarf to to the Sun, so the planet is nearly at nearly a fixed position relative to the Sun. The extraterrestrials have come to love broadcasts of MacGyver, on television channel 2, at carrier frequency 57.0 MHz. Their line of sight to us is in the plane of the earths orbit. Find the difference between the highest and lowest frequencies they receive due to the Earth's orbital motion around the Sun. straightforward doppler calculation, no different from a radar gun. Earth's average orbital velocity is 29.78 km/s. doppler ?f = –v/? = –vf/s v = velocity of source relative to listener ? = wavelength of source, relative to source f = frequency of source, relative to source ?f = v/? = vf/c = (29.78e3 m/s)(57e6 Hz) / (3e8 m/s) = 5658 Hz double that for both directions, and you have 11316 Hz edit: no, you need the speed of earth relative to the (presumed fixed) brown dwarf.

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