Calculating Orbital Speed Using Conservation of Angular Momentum

[lc99]

Homework Statement

The dwarf planet Pluto orbits very ellipticaly... Pluto's nearest (perihelion) and farthest (apihelion) distances from the Sun are 30 AU and 50 AU, respectively. (One AU or Astronomical Unit=the mean distance from the center of the Earth to Astronomical Unit = the mean distance from the center of the Earth to the center of the Sun). If it orbital speed at apihelion is 4 km/s, how fast is the pluto moving when at perihelion.

Homework Equations

a) between 1km/s and 3km//s
b) between 7km/s and 9km/s
c) between 5km/s ad 7km/s
d)b/w 5-7 km/s
e) b/w 3-5km/s

The Attempt at a Solution

My answer is D) 5-7 km/s

I followed the conservation of angular momentum IW = IW

L at aphelion is = IW = MR^2W = MR^2(V/R) = MRV = 4*50*4=600
L at periphelion = IW = MRV = 4*30*v

set L at aphelion = L at periphelion and i solved for v, so v of periphelion is about 6.66, so the answer is D)

 

[haruspex]

about 6.66, so the answer is D)

Yes, but I think you meant 4*50*4=800.

 

[lc99]

Yes, but I think you meant 4*50*4=800.

Opps. Sorry about that. Thanks!