Calculating the Distance and Parallax of a Star: A Practical Guide

[fatima_a]

A star exhibits a parallax of 0.250 arcseconds when measured from Earth.
a) What is its distance (pc)?

I know this uses the formula d=1/p, so i can solve this very easily

b) What would its parallax be if measured from Venus’s orbit (arcseconds)? (Look up
the one parameter you need to solve this using the relevant equation.)

I don't know what to do here at all though, I can't look up it's distance from Venus because its an arbitrary star...so what do i do? Can someone guide me to the right direction??

Thanks

 

[Bandersnatch]

What is the base of the triangle used to measured parallax of distant stars?

(by the way, you should post these kind of questions in the homework section)

 

[HallsofIvy]

Do you know what parallax means? Imagine lines drawn from this "arbitrary star" to opposite ends of Venus' orbit (on the line through the sun perpendicular to the line to the star). That gives you an isosceles triangle with one angle (the one at the star) known and one side (the distance across Venus' orbit). You can use the "cosine law" to find the lengths of the two other sides (the distance from Venus to the star).

"I know this uses the formula d=1/p".

There's your problem- you know formulas but you don't know the reasoning behind the formulas so you don't know how to change them when the situation changes!

 

[Simon Bridge]

Just to be clear here - do you know how the equation d=1/p is derived?
i.e. Do you know the relationship between parallax measurements and triangulation?

[edit]HallofIvy beat me to it.

 

[pmacias]

for your question. To calculate the parallax of the star from Venus's orbit, we can use the same formula as before, d=1/p, but instead of using the distance from Earth, we use the distance from Venus to the star. This distance can be calculated using the distance from Earth to Venus (which is known) and the distance from Earth to the star (which we can calculate using the parallax measurement from Earth).

So, the equation would be:

parallax from Venus's orbit = 1 / (distance from Venus to star / distance from Earth to Venus)

To calculate the distance from Earth to Venus, we can use the formula R = AU * (1 / tan(0.250 arcseconds)), where R is the distance from Earth to Venus and AU is the astronomical unit (149.6 million kilometers). This will give us the distance in kilometers. Then, we can use this distance to calculate the distance from Venus to the star using the same formula, d=1/p, where d is the distance from Venus to the star and p is the parallax measurement from Venus's orbit.

I hope this helps guide you in the right direction. Let me know if you have any further questions.