Question

Some stars are so far away that their position appear fixed as earth orbits the sun. Other stars, however, appear over time to shift their positions relative to the background of "fixed" stars. Suppose that the star shown below appears to shift through an arc of theta = 0 degrees 0 minutes and 1.5 seconds when viewed on the first day of winter and the first day of summer. If the distance from earth to the sun is about 1.5 x 10^8km, find the approximate distance from earth to the star.

Answer 1

absolutely no idea :/

Answer 2

I know how to do the actual problem, but my answer keeps ending up being .1 to large. I don't know where I'm making a mistake.

Answer 3

If u show ur eqn, i will be happy to take a look :)

Answer 4

But a difference of 0.1 is not too big right?

Answer 5

The correct answer is 4.1 x 10^13
I keep ending up with 4.2 x 10^13

Answer 6

This is the equation.
1.5 x 10^8 = 0.0004/360 (2)(pi)(r)

Answer 7

Hm...going through it now.....1.5 seconds is 0.0004167....checking the rest now...

Answer 8

I got 4.13x10^13 so it is 4.1x10^13 :)

Answer 9

Think u shorten the 1.5 second value to 0.0004 causes the difference!

Answer 10

Oh, okay. so I shouldn't round theta?

Answer 11

U rounded it too early n too much - try it again n see if u get my results ;)

Answer 12

I have no idea what I did wrong but I somehow ended up with 2.1 x 10^13....

Answer 13

Oh sorry forgot to tell u because it is only from winter to summer, it is pi(r) - u got an extra 2x in ur eqn there

Answer 14

Oh so I need to multiply 2.1 x 10^13 by 2?

Answer 15

Yes but then...it will still be 4.2 instead of 4.1 :(

Answer 16

What theat value u use in ur calc? i used 0.0004167 n got 4.1 as ans

Answer 17

I used the same theta you did.
But because 1.5 x 10^8 only applies to the first location of the earth, should I multiply that by 2 first and then solve?

Answer 18

Well try that and see if u get 4.1 as answer :)

Answer 19

I think I might be entering the information wrong. Every time I try the problem, I end up with different answers.

Answer 20

Hahahaa want to see my steps?

Answer 21

I got it! :D
But can I please see them just to double check?

Answer 22

Sure here it goes:
theta=1.5/60/60=0.0004167
1.5x10^8 = theat/360 * pi * r = 3.636x10^-6 * r
r = 4.13x10^13

Answer 23

But the equation is S=theta/360 *2*pi*r

What happened to the 2 in yours? Or am I just using the wrong equation?

Answer 24

No, u are right...twice - ur eqn is right n u also right about doing 2x for 1.5x10^8 Same result though :)

Answer 25

Okay, thank you for your help :)

Answer 26

welcome n thanx 4 the medal!