Superluminal jets. Fig. (a) shows the path by a knot in a jet ofionized gas that has been expelled from a galaxy. The knot travelsat constant velocity at angle ? from the direction of Earth. Theknot occasionally emits a burst of light, which is eventuallydetected on Earth. Two bursts are indicated in Fig . (a), separatedby time t as measured in a stationary frame near the bursts. Thebursts are shown in Fig. (a) as if they were photographed on thesame piece of film, first when light from burst 1 arrived on Earthand then later when light from burst 2 arrived. The apparentdistance Dapp traveled by the knot between the two bursts is thedistance across an Earth-observer's view of the knot's path. Theapparent time Tapp between the bursts is the difference in thearrival times of the light from them. The apparent speed of theknot is then Vapp = Dapp/Tapp.
(a) What are Dapp and Tapp? (Use the following as necessary: t, v,?, and c for the speed of light.)
Dapp =
Tapp =
(b) Evaluate Vapp for v = 0.963c and ? = 28°. When superluminal(faster than light) jets were first observed, they seem to defyspecial relativity-at least the correct geometry (Fig (b)) wasunderstood.
Superluminal jets. Fig. (a) shows the path by a knot in a jet ofionized gas that has been expelled from a galaxy. The knot travelsat constant velocity at angle ? from the direction of Earth. Theknot occasionally emits a burst of light, which is eventuallydetected on Earth. Two bursts are indicated in Fig . (a), separatedby time t as measured in a stationary frame near the bursts. Thebursts are shown in Fig. (a) as if they were photographed on thesame piece of film, first when light from burst 1 arrived on Earthand then later when light from burst 2 arrived. The apparentdistance Dapp traveled by the knot between the two bursts is thedistance across an Earth-observer's view of the knot's path. Theapparent time Tapp between the bursts is the difference in thearrival times of the light from them. The apparent speed of theknot is then Vapp = Dapp/Tapp.
(a) What are Dapp and Tapp? (Use the following as necessary: t, v,?, and c for the speed of light.)
Dapp =
Tapp =
(b) Evaluate Vapp for v = 0.963c and ? = 28°. When superluminal(faster than light) jets were first observed, they seem to defyspecial relativity-at least the correct geometry (Fig (b)) wasunderstood.
