Calculating Jet Size & True Length from Redshift & Hubble Constant

[wolfpack693]

2 part question.

1st part: I am givin the redshift of a quasar is .158 and Hubble constant of 65km/s/Mpc. I am asked to find the size of the jet(ly) as projected on the sky which has an angular measure of 15 arc secs. I've looked up ways and on any formulas that could help me but haven't found anything. Does anyone know how to get the size (formula wise).

2nd part: What is the true length in light years if it is pointed along the line of sight but off at an angle of 6 degrees?

Now this part I don't understand where to start from.

Anything helps thanks.

 

[cristo]

Welcome to PF. You need to show some work before we can help you with homework questions. What have you tried thus far?

 

[Blueshift5]

I can help you with calculating the jet size and true length from the given information. To calculate the size of the jet, we can use the formula:

Jet Size (ly) = (Redshift * Speed of Light * Distance to Quasar) / Hubble Constant

In this case, the redshift is 0.158, the speed of light is approximately 3 x 10^8 m/s, and the Hubble constant is 65 km/s/Mpc. However, we need to convert the angular measure of 15 arc secs to radians to find the distance to the quasar.

Distance to Quasar (Mpc) = 15 arc secs * (1/3600) * (1/60) * (pi/180) * (1/206265) = 0.0000026 Mpc

Now, we can plug in all the values in the formula to find the jet size:

Jet Size (ly) = (0.158 * 3 x 10^8 m/s * 0.0000026 Mpc) / 65 km/s/Mpc = 0.0000032 ly

For the second part, we need to use the formula:

True Length (ly) = Jet Size (ly) / sin(angle)

In this case, the angle is 6 degrees, so we have:

True Length (ly) = 0.0000032 ly / sin(6 degrees) = 0.0000026 ly

Therefore, the true length of the jet in light years is 0.0000026 ly. I hope this helps you with your calculations. If you have any further questions, please feel free to ask.