1st ATTEMPT I converted .8\" to radians = 3.8785*10^-6 I used p=r/d for the para

Question

1st ATTEMPT

I converted .8" to radians = 3.8785*10^-6

I used p=r/d for the parallax formula and got 6/3.8785*10^-6 to get d=1546989 AU = 24.46 light years but this was wrong

2nd ATTEMPT

d=4838709 AU or 76.5 light year was also incorrect

used .8/3600*pi/180 = 1.24*10^-6 radians

An alien astronomer on a distant exoplanet wants to use parallax to measure the distance to our Sun Their planet has an orbit radius of 6.0 AU. They observe our Sun shifting by a parallax angle of 0.8" wher measured from opposite sides of their orbit. How far is their exoplanet system from the Sun? Incorrect. The alien is measuring parallax from each side of the orbit. If parallax-baseline / distance what is the alien's baseline in terms of orbit radius? Number 1546989.8 AU Number 24.46 light- years

Explanation / Answer

Its good to see that you tried it yourself first.

In your first attempt, the conversion to radians is correct.

the actual parallax formula is tan(parallax angle)=(diameter of the orbit)/distance

note that the parallax angle is measured from the two opposite ends of the orbit of the alien planet.

so diameter of orbit = 2* radius=2*6 AU=12AU

0.8'' in radian is 3.87858*10^-6 radian

using the above mentioned formula

distance=12AU/tan(3.87858*10^-6)=3093915.815 AU

or, distance = 48.92 light year.

the mistake you were doing is not taking diameter but radius of the alien planet's orbit.

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