Halley's comet has an elliptical orbit with the sun at one focus. its orbit is given below approx. by r=10.21/1+0.874sin theta. in the formula r is measure in astronomical units. (one astronomical unit is the average distance from the Earth to the sun, approx. 93 million miles.) Whats the distance from Halley's comet to the sun at the shortest distance from the sun?

Question

wolf1728 · Answer

I'm an amateur astronomer (one of the zillions) and I'm somewhat familiar with the mathematics of orbits but I'll admit I've never seen an orbital formula such as:
r=10.21/1+0.874sin theta
Is that just one formula?  Is it exactly the way the problem is stated?
Don't think I'm just giving you a hard time about this.  I really want to help.

anonymous · Answer

Halley's comet has an elliptical orbit with the sun at one focus. its orbit is given approximately by r=10.21/1+0.874sin theta. in the formula r is measure in astronomical units. (one astronomical unit is the average distance from the Earth to the sun, approx. 93 million miles.) Find the distance from Halley's comet to the sun at the shortest distance from the sun?

anonymous · Answer

i changed two words

anonymous · Answer

thank you

wolf1728 · Answer

How exactly am I supposed to read that formula?
r=10.21/1+0.874sin theta
Among other things it mentions the sine of theta.  Shouldn't we be told what theta is?  10 degrees? 2 radians?

ranga · Answer

Is the formula  $\Large r = \frac{10.21}{1+0.874sin(\theta)} $?

anonymous · Answer

yes

ranga · Answer

Then the above formula is probably in polar coordinates with r measured from the focus.  r will be minimum when $sin(\theta)$ is maximum which is 1.

anonymous · Answer

I think answer is 11.68 astronomical units, 1086 million miles

anonymous · Answer

im not sure though

anonymous · Answer

i've been studying polar coordinates so that sound right Ranga

wolf1728 · Answer

no the perihelion is .586 astronomical units.

anonymous · Answer

How many millions of miles?

anonymous · Answer

543 million Miles?

wolf1728 · Answer

Wkipedia says
aphelion = 35.1 AU
perihelion = .586 AU

My calculations:
average = 17.843 AU
eccentricity = (aph -per) / (aph + per)
= 0.9671579891

1 au is about 92,900,000 miles

so .586 au = 54,439,400 miles

anonymous · Answer

thank you wolf

wolf1728 · Answer

it's okay u r welcome
:-)