Aphelion/Perihelion of Halleys comet

[zanazzi78]

Q.Halley's comet is in an elliptic orbit about the sun. The orbit eccentricity is 0.967 and the period is 76 years. Taking the mass of the sun to be $$2 \times 10^30 kg$$ abd the usual value of G, determine the max and min distances of the comet from the sun.
Now I've worked out the answers but they differ from the values I've found on the net,(my guess is the value I've used for the solar mass isn't very accurate!) so would you mind taking a second to have a look at what I've done to see if I'm correct.
A.
using...
$$a=( \frac{GM_{\odot}T^2}{4 \Pi ^2})^\frac{1}{3}$$
i got
$$a= \sqrt[3]{ \frac{ (6.67 \times 10^-11 )( 2 \times 10^30 )( 2.4 \times 10^9)^2}{4 \Pi^2}}<br /> = 2.01 \times 10^9 m$$
from
$$e= \frac{a-R_{min}}{a}$$
$$R_{min} = 6.633\times1 0^6$$
then to get R_max i used
$$R_{max} = 2a - R_{min}<br /> = (2)(2.01\times10^9) - (6.633\times 10^6)<br /> = 2.666\times 10^{16} m$$
the problem is i`ve found a value for R_min = 8.9x10^10 and R_max = 5.3x10^12 !

 

[mezarashi]

$$a= \sqrt[3]{ \frac{ (6.67 \times 10^-11 )( 2 \times 10^30 )( 2.4 \times 10^9)^2}{4 \Pi^2}}<br /> = 2.01 \times 10^9 m$$

Check that calculation again. You have a power (-11 + 30 + 18)/3, it should be in the power 12 range.

 

[zanazzi78]

I`m blind to my own ignorance, thank you for pionting out the error.

 

[swelzba9]

I am trying to figure out the speed of Halley's Comet in km/sec. at aphelion and perihelion

I am using

v² = (4Π²a³) / (P²) * ((2/r) - (1/a))

where a = mean distance from the sun (semimajor axis of the ellipse)
P= sidereal period (75 years)
r = distance of the object from the Sun at a given instant

a=16.8 A.U. c=16 A.U.

"r" at perihelion = a-c "r" at aphelion = a + c