Question

(please type it and not write down the answer) astronomy

4. The first normal star besides the Sun in which a planet was discovered is called "51 Pegasi," in the constellation Pegasus the horse. Its parallax is measured to be 0.064 arcsec. a. What is its distance from us? b. The apparent brightness is 1.79 × 10-10 J/(s·m2 ). What is the luminosity? How does that compare with that of the Sun? Look up the temperature: how does it compare to that of the Sun? As always, show each step of your calculation and keep track of units.

Answer 1

PART A:

We know,

where,

d is the distance measured in parsecs and p is the parallax measured in arcseconds. So,

PART B:

We know,

where,

F is apparent brightness,

L is luminosity and

d is the distance of the object from the observer.

Now,

Solar luminosity

So, the ratio of luminosity

Both the star and the sun are comparable in terms of the luminosity. The star is slightly more luminous than the sun.

The surface temperature of this star is 5571 K (from Wikipedia). (To calculate the surface temperature we need the radius of the star)

The formula is

where,

R is the radius of the star,

T is the temperature of the star and

is Stephan-Boltzmann Constant valued as 5.67 x 10^-8 in SI units.

The surface temperature of the sun is 5778 K (from Wikipedia).

So, in terms of the surface temperature both the stars are very close.