Question

Show all calculations and formulas used.

The closest star to earth is 4.253 light years away. How far is that in miles?

The fastest space probe ever designed has a speed of about 58,000 km/h. How long would it take it to cross the length of the milky way galaxy?

If the parallax angle of a star is 0.000075% then how far away is that star?

What is the relative brightness of the Sun as seen from Saturn as compared to its brightness from Earth (Saturn is 9.5 times as far from the sun as the earth is).  

What is the Schwarzschild radius of our sun?

If a galaxy is moving away from us at 2.3% of the speed of light, roughly how far away is it?

Calculate the redshift parameter, z, of a star whose blue hydrogen line at 434 nm is measured on earth to be 455 nm. (hint: the wavelength measured on earth is the wavelength of the moving observer). B) How fast is that star moving?

If the known universe contains about 10¹¹ galaxies that each contain about 10¹¹ stars then roughly what is the mass of the known universe if those stars weigh the same as the sun on average?

What percent of the universe does all those stars and galaxies make up?

Answer 1

(a) How far is that in miles?

D = 4.253 ly

convert ly into mile -

D = 2.50018 x 10¹³ miles

(b) How long would it take it to cross the length of the milky way galaxy?

we know that, t = D / v

where, v = speed of space probe = 58,000 km/h

D = distance travelled = 4.253 ly = 4.02365 x 10¹³ km

THEN, we get

t = (58,000 km/h) / (4.02365 x 10¹³ km)

t = 1.44 x 10^-9 sec

(c) Using a formula, we have

d = 1 / p = 1 / (7.5 x 10^-7 arcsec)

d = 1.33 x 10⁶ parsec

(e) The Schwarzschild radius of an object is proportional to the mass. Accordingly, the Sun has a Schwarzschild radius of approximately 3.0 km (1.9 mi), whereas Earth's is only about 9 mm (0.35 in). The observable universe's mass has a Schwarzschild radius of approximately 13.7 billion light years.