Radial Velocity, Angular Separation, and Solar Apex: Q&A

[ek]

I missed this class the other day and my prof isn't answering his email right now so I thought I'd ask it here.

I want the answer to the question, but really I'm looking for the relationship between the values.

Q: A star located 135 degrees from the solar apex on the celestial spehe is at rest in the LSR 15pc from the sun, whose radial velocity with respect to the sun may be taken to be 20km/s. As seen from the sun, (a) what is the star's radial velocity; (b) how many seconds of arc will this star appear to move on the celestial sphere in ten years; (c) in what direction will it move

So really what I'm asking here is what the relationship between radial velocity and angular separation from the solar apex is and how to apply that to parts b and c.

Thanks for any assistance.

 

[ek]

Anybody?

Give this a good ol bumpity bump.

 

[thepatientmental]

A: The relationship between radial velocity and angular separation from the solar apex can be described using the concept of the solar apex itself. The solar apex is the point in the sky towards which the Sun, along with the rest of the solar system, is moving. It is located in the constellation Hercules and has a radial velocity of 20 km/s with respect to the Sun.

Now, let's break down the given information and see how it relates to the question:

a) The star is located 135 degrees from the solar apex on the celestial sphere. This means that it is located 135 degrees away from the direction in which the Sun is currently moving. Since we know that the Sun has a radial velocity of 20 km/s, we can use basic trigonometry to calculate the radial velocity of the star. The radial velocity of the star can be represented by the formula:

Radial velocity = Sun's radial velocity x cosine (angular separation from the solar apex)

Substituting the given values, we get:

Radial velocity of star = 20 km/s x cosine 135 degrees = -14.14 km/s

Note that the negative sign indicates that the star is moving away from the solar apex, in the opposite direction of the Sun's motion.

b) In order to calculate the angular separation, we need to use the formula:

Angular separation = (Radial velocity of star x time) / (Distance from Sun to star)

Substituting the given values, we get:

Angular separation = (-14.14 km/s x 10 years) / 15 pc = -9.43 seconds of arc

This means that the star will appear to move -9.43 seconds of arc on the celestial sphere in ten years, in the opposite direction of the Sun's motion.

c) Finally, to determine the direction of the star's motion, we need to consider the direction from the Sun to the star. Since the star is located 135 degrees away from the solar apex, it is also 135 degrees away from the direction of the Sun's motion. This means that the star will appear to move in the direction opposite to the Sun's motion, or towards the direction of the solar apex.

I hope this helps clarify the relationship between radial velocity, angular separation, and the solar apex. Remember to always use the given values and formulas appropriately to arrive at the correct answers.