Can anyone help me with parallax?

[starfire]

Hi,

Can anyone help me to show my students how to figure out distance to stars using parallax? I understand the base of the triangle is the distance from the Earth to the Earth during opposite seasons, but how is the angle figured out so that the opposite side can be determined?

Also, all the diagrams I've seen have always shown the Sun, the Earth at two opposite seasons, and a star located at a point out from, but between the two Earth locations. This would mean that the star is being observed during the daytime. That can't be, as stars are not normally visible during the daytime.

Any help at all would be appreciated. If possible email me at starfire@wt.net

Thanks,

Alan

[PhysBrain]

With traditional ground based telescopes, the method of parallax can be used for objects that are within 200 parsecs (~652 light years). This limitation is due primarily to the inability of our instruments to resolve angular displacements below 0.005 arc seconds. Atmospheric distortion also interferes with the measurement, although, I imagine that space based telescopes, active/adaptive optical telescopes (correct for atmospheric distortion), and large baseline telescopes (multiple telescopes linked together) will be able to improve upon this.

The parsec angle is traditionally measured by determining the angular separation between the object being observed and a much further object (one that should not show any observable parallax) at two different times of the year. The difference in the measured angular separation is the parallax angle (p). If the baseline distance (b) is known, then the distance (d) to the object can be computed by d = b/p (if p is in radians).

The diameter of the Earth's orbit (2 AU) is the largest possible baseline that can be established for Earth based observations. This particular baseline works well for illustration purposes, but I agree that, in practice, it would be difficult to make at least one of the observations (unless you were fortunate enough to be able to make the observations right at sunset/sunrise). It just so happens, though, that the definition of a parsec is the distance to an object which has a measured parallax of 1 arc second when observed from a baseline of 1 AU (1 parsec = 206265 AU). This would mean that you can make 2 observations 2 months apart (1/6 of an orbit) and have a baseline of 1 AU. This would enable easier observations, but you should also remember that longer baselines provide more accurate results.

Good luck with your students.

[SEDShead]

Wow! What a fantastic answer. Succinct, but detailed enough. Thanks PhysBrain!