Solve Hubble's Law: Proxima Centauri & Sun in Milky Way

[Fabio010]

Homework Statement

Determine for the nearest star what should be it's recessional velocity if the space between the two stars is expanding according to the Hubble's law. Compare this value with the speed of the sun when it moves with Milk Way.

Homework Equations

$H_{0} = \frac {v}{D}$

$H_{0}\approx 72 km/s/Mpc$Nearest Star: Proxima Centauri

distance from sun : 4.2421ly = $1,30 pc$

The speed of the sun in Milk Way is approx. $828km/h$

The Attempt at a Solution

$v = \frac{72km}{s} * \frac {1,30 pc }{1Mpc}$

$v = 9,11 * 10^{-5}km/s = 0,33 Km/h$

if we compare with the speed of the sun in milk way, we can see that the recessional velocity between the two stars is much smaller.

my friend said that the problem is not well solved. But i do not remember his explanation.

Can u tell me if it is wrong? If yes where is the error?

 

[mfb]

Your conclusion is correct, but you underestimated the speed of the sun in our galaxy significantly.

 

[Fabio010]

Your conclusion is correct, but you underestimated the speed of the sun in our galaxy significantly.

Yes, your are right.



"Away from the central bulge or outer rim, the typical stellar orbital speed is between 210 and 240 km/s"

Instead of $828km/h$ it is $828000km/h$

Thanks for the help!