Astrophysics, simple parallax error

[dink87522]

Homework Statement

Experiment 15.2 (note this is from a book about 5 years old, and the book has no solutions!). I am simply unsure how to calculate between parallax with 1% error and parallax with 50% error etc. Please see the scan I done of the page: http://img210.imageshack.us/my.php?image=savevx9.jpghttp://img210.imageshack.us/my.php?image=savevx9.jpg

Homework Equations

d = 1/p

The Attempt at a Solution

I've tried p=1/d = 1/30 (for ground based) although how do I then account for '50%' error etc? With this book not having solutions (or even answers!) I am just getting further confused as I know these should be very simple calculations.

 

[dink87522]

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[baba89]

Hello,

Astrophysics can be a complex and challenging subject, so it is understandable that you may have some difficulty with certain concepts. In this case, it seems like you are struggling with calculating parallax with different levels of error. Let me try to help you understand this better.

Parallax is a method used in astronomy to measure the distance to a nearby star by observing its apparent shift in position relative to more distant stars as the Earth moves around the Sun. This shift is caused by the Earth's changing perspective on the star's position. The smaller the parallax angle, the farther away the star is from Earth.

Now, let's consider the equation d = 1/p, where d is the distance to the star and p is the parallax angle. This equation assumes that the parallax angle is measured with 100% accuracy, meaning there is no error in the measurement. However, in reality, there will always be some degree of error in our measurements. This is where the concept of percentage error comes in.

Percentage error is a way to express the difference between the measured value and the actual value as a percentage. It is calculated as (measured value - actual value)/actual value * 100%. So, if we have a parallax angle of 1% error, it means that the measured value is 1% different from the actual value.

To calculate the distance with 1% error, we can use the equation d = 1/p and substitute p with the actual parallax angle plus 1% of that angle. For example, if the actual parallax angle is 30 arcseconds, the measured angle with 1% error would be 30 arcseconds + 1% of 30 arcseconds, which is 30.3 arcseconds. Then, we can plug this value into the equation to get d = 1/30.3 = 0.033 light years.

Similarly, for 50% error, we would use the equation d = 1/p and substitute p with the actual parallax angle plus 50% of that angle (30 arcseconds + 50% of 30 arcseconds = 45 arcseconds). This gives us d = 1/45 = 0.022 light years.

I hope this helps you understand how to calculate parallax with different levels of error. Remember, the key is to add the percentage error to the actual parallax angle before plugging it into the