Solve Parallax Equation: Find Distance to Star in km & ly

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In summary, we have a parallax equation for finding the distance to a star. The equation uses the values of D (distance to star) and theta (angle) and is D=(d/2)/tan(theta/2). We are given d=300*10^6 km and theta=5*10^-5 degrees. Using these values, we can calculate the distance to the star in km and light years. However, the conversion to light years must be done carefully, as 1 light year is equal to 9.467*10^12 km. The final result for the distance to the star in light years is actually 31.98, not 27 as previously calculated. It is important to be precise when
  • #1
radius
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please can somebody help me with this parallax equation:

D=distance to star
theta=angle
using the rule D=(d/2)/tan(theta/2)
when d = 300*10tothe6
and theta = 5*10tothe-5

what is the distance to the star in km and light years?
 
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  • #2
What's the problem?

(d is in what units?)
 
  • #3
d is in km and theta is in degrees.
This is as close as i can get:
for this answer i get a result of:

343774677078406.6587981892079753

So, is this answer the number of km?

what is this answer in exponential form? ie: 34 * 10tothepower13?

1 light year is 9.467*10tothepower12, so in light years i think the distance will be:
27 light years

Please let me know if i am right
 
  • #4
D and d have the same units. Your value for D in km is correct, but you messed up the conversion to light years. Do it over, more carefully.
 

1. How is the parallax equation used to find the distance to a star?

The parallax equation is used to measure the distance to a star by calculating the angle of parallax, which is the apparent shift of the star's position when viewed from different points.

2. What is the unit of measurement for distance in the parallax equation?

The unit of measurement for distance in the parallax equation is typically kilometers (km) or light years (ly).

3. What information is needed to solve the parallax equation?

To solve the parallax equation, you need to know the baseline distance between the two viewing points, the angle of parallax, and the angle of separation between the two viewing points.

4. Can the parallax equation be used for any star?

No, the parallax equation can only be used for relatively nearby stars within a few hundred light years. For more distant stars, other methods such as spectroscopy or standard candles are used to determine their distance.

5. How accurate is the parallax equation in determining the distance to a star?

The accuracy of the parallax equation depends on the precision of the measurements of the angles of parallax and separation. With modern technology, the accuracy can be as high as a few milliarcseconds, which corresponds to a distance error of less than 1% for stars within 1000 light years.

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