Question

The orbit of the planet Pluto is and ellipse with the sun at one focus. The maximum distance between the sun and Pluto is 7,375 km, and the minimum distance is is 4,425 km. How far (in millions of km) is it across Pluto's orbit at its widest point?
a) 5,900
b) 11,425
c) 11,800
d) 5,712.65

Answer 1

what do u mean by the widest point?

Answer 2

I guess Pluto's furthest orbit form the sun. I'm not 100% sure, that's all the question says.

Answer 3

if u draw an ellipse then the point of maximum distance from one of the focus would be the farthest point on orbit

Answer 4

A little confusing. How would this be done?

Answer 5

i can help u find out the equation of the elliptical path though

Answer 6

Okay, how?

Answer 7

let it be \[{x ^{2}/a ^{2}} + y ^{2}/b ^{2} =1\]
b^2=a^2(1-e^2)
e is ur coeff of eccentricity
foci are at (ae,0) and (-ae,0)
see a general diagram of ellipse
a+ae=maximum distance from focus=7375
a-ae=min dist from focus=4425
find a , e

Answer 8

do you have a general equation, with conics

Answer 9

yes

Answer 10

even for a hyperbolic path

Answer 11

yes whats your equation with that e thingy , thats cool, for any conic

Answer 12

Does anybody know the answer? I'm not doing so well with the equation..

Answer 13

e is called ur coefficient of eccentricity
that equation is only for an elliptical path

Answer 14

This is an elliptical path though.
What is the foci?

Answer 15

(-ae,0) and (ae,0)

Answer 16

I mean what does it represent? Like a definition.

Answer 17

foci are the two points on the major axis of the ellipse

An ellipse can be drawn using two drawing pins, a length of string, and a pencil:

Push the pins into the paper at two points, which will become the ellipse's FOCI. Tie the string into a loose loop around the two pins. Pull the loop taut with the pen's tip, so as to form a triangle. Move the pen around, while keeping the string taut, and its tip will trace out an ellipse.

Answer 18

That's a very interesting way to draw an ellipse, never heard of that technique, Thank you. Now in solving this problem, what do I need to plug into your equation to come up with numbers?

Answer 19

try to visualize it
sun is at (-ae,0) one of the foci
max distance would be when pluto is at (a,0)
so,
a+ae=7375

work out for min distance in the same way

Answer 20

Would it be either
-a+ae=4,425 or a-ae=4,425?

Answer 21

a-ae would give the correct answer

Answer 22

Does a=2,950?

Answer 23

or no, ae?

Answer 24

ae would be 1475
a = 5950

Answer 25

Does e=0.248?

Answer 26

I got C. Is that correct?

Answer 27

what did u do to find the widest point??

Answer 28

I'm not sure if it's right. But i think this is a question that's easier than you would think. You want to find the widest point, so all I did was add 7,375 and 4,425 and that gives you 11,800.

Answer 29

are you sure about his