Question

1) How many AU make up a light-year?

Answer 1

Answer:..

1.One light-year = 63,240 AU

2. It’s about 93 million miles (150 million km),or

one astronomical unit (AU) = 92,955,807 miles (149,597,871 km).

Answer 2

Answer:

1) 63241 AU make a light year.

2) $1.495x10^{8}km$, 92914853miles

The astronomical unit gives a simple way to compare distance between planets and the Sun, using the distance from the Sun to Earth as an started point.

Explanation:

1) How many AU make up a light-year?

A light year is the distance that light can travel in one year

The speed of light has a value of $3x10^{8}m/s$

That can be express in units of kilometers and years:

$3x10^{8}m/s \cdot \frac{1km}{1000m}$ -- $300000km/s \cdot \frac{31536000s}{1year}$ -- $9.4608x10^{12}Km/year$

Therefore, the distance can be found by means of the equation for average velocity.

$v = \frac{x}{t}$

$x = v \cdot t$  (2)

Then, t will be equal to 1 year ($t = 1 year$)

$x = (9.4608x10^{12}Km/year)(1year)$

$x = 9.4608x10^{12}Km$

However, an astronomical unit is defined as the distance between the Earth and the Sun ($1.495x10^{8]km$).

Therefore, to know how many astronomical units make a light year:

$\frac{9.4608^{12}km}{149597870km} = 63241$

Hence, 63241 AU make a light year.

2) What is an astronomical unit (AU) in miles and kilometers? Why is it useful for understanding the distances to planets?

As in was already said, an astronomical unit has a value of $1.495x10^{8]km$

Then, it can be express in units of miles:

$1.495x10^{8}km \frac{1mile}{1609km}$ ⇒ $92914853miles$

The astronomical unit gives a simple way to compare distance between planets and the Sun, using the distance from the Sun to Earth as an started point.