## Babynini one year ago Halp!

1. Babynini

Many comets have elliptical orbits with the sun at focus. in many cases the eccentricity is cose to 1 and the ellipse is very flat. halley's comet has an elliptical orbit with eccentricity e=0.967. The closest that halley's comet comes to the sun is 0.587 AU. Approximate the max distance of the comet from the sun in AU, accurate to three decimal places. Note that one astronomical unit = 1AU = (approximately) 93,000,000miles

2. Babynini

I'm not sure where to even start...

3. Babynini

@zepdrix any ideas?

4. zepdrix

Mmmm no :x I don't remember eccentricity, sec i try to read

5. rational

$e=\frac{c}{a}$

6. Babynini

yep yep. I'm not sure how to apply formulas here hah

7. Babynini

I really don't know o.0 i've been trying to manipulate it but it's not working much.

8. rational

|dw:1433488489699:dw|

9. rational

From the diagram, clearly $\large a-c = 0.587\tag{1}$ From the eccentricity formula $\large \frac{c}{a}=0.967\tag{2}$ two equations and two unknowns, we can solve them

10. Babynini

wait, where's the 0.587 related to?

11. rational

it is shortest distance from the focus(sun) to the ellipse(path of halley comet)

12. Babynini

ah, k. I see now.

13. Babynini

so now what do we do? c=0.967(a)

14. Babynini

and plug that into the previous statment? a-c=0.587 a-(0.967)* (a)=0.587

15. Babynini

(sorry those last two were meant to be on the same line)

16. rational

solve a

17. Babynini

587/33 ?

18. Babynini

so 17.788

19. rational

Yep! a=17.8

20. rational

find c also

21. Babynini

17.200

22. rational

looks good

23. rational

look at diagram, what is the maximum distance from sun to ellipse ?

24. Babynini

a ?

25. rational

|dw:1433489528413:dw|

26. rational

try again

27. Babynini

oh oh sorry, a +c

28. rational

Yes!

29. Babynini

yay! so 34.989 is the final answer? :)

30. Babynini

Well, it asks for it in AU which is 93,000,000 so multiply the answer by that?

31. rational

nope, our calculation is already in AU 34.989 AU is the final answer

32. Babynini

ah ok.

33. Babynini

Hey, really quick. Can you help me know how we solved for a? xD I just put it into my calc but idk if the prof wants me to show work on that part. Better safe than sorry.

34. Babynini

a-(0.967)(a)=0.587 a-a= 0.587/0.967

35. rational

|dw:1433489979509:dw|

36. rational

from the (2)nd equation we have $$c = 0.967a$$ plug this in (1)st equation and get $$a-0.967a=0.587$$ factor out $$a$$ on right hand side $$a(1-0.967)=0.587$$ isolate $$a$$ $$a=\dfrac{0.587}{1-0.967}$$

37. rational

use ur calculator to do that division

38. Babynini

okies!

39. Babynini

thanks, it makes more sense now :)

40. Babynini

hey I have one very last problem that i've been stuck on. Could you check it out?

41. rational

wil try, post..

42. Babynini

thanks. I'm going to put it on a new feed.

43. rational

okk