Download Calculating Large Distances

EARTH SCIENCE
CALCULATING LARGE DISTANCES
Introduction
In this class, we have used different units when measuring distances. Very large distances on Earth may be
measured with kilometers (km), which, as you have learned, is equal to 1000 meters. Smaller distances may
be measured in centimeters (cm), which are 1/100 of a meter or millimeters, which are 1/1000 of a meter.
However, due to the extreme distances between objects in the universe or even our own solar system,
different units of measures are required. In this handout, you will learn how to calculate distances using the
two most accepted measures, astronomical units and light-years.
Astronomical Units
Astronomical Units (abbreviated A.U.) are equal to the average distance between the sun and earth. This
distance is equal to 149,600,000 km. To calculate the distance in AU for any planet in our solar system,
divide the distance of the planet from the sun by 149,600,000 km. For example, Mercury is 57,910,000 km
for the sun on average.
57,910,000 km / 149,600,000 = 0.39 AU
Complete the table that follows:
PLANET
DISTANCE (KM)
DISTANCE (AU)
Mercury
57,910,000
0.39
Venus
108,200,000
Earth
149,600,000
Mars
227,940,000
Jupiter
778,330,000
Saturn
1,429,400,000
Uranus
2,870,990,000
Neptune
4,504,000,000
1.00
Although one AU is a long distance (the distance around the Earth 11,730 times!), it is still only useful to
measure objects that are nearby in our universe. For instance, the nearest star to Earth, Proxima Centauri,
is over 250,000 AU, still quite a large number. To measure interstellar distances, another unit of measure is
required.
Light-Year
A light-year is the distance that light travels in one year. Since the speed of light is approximately
300,000,000 m/s, this is a very large distance. To help you imagine this length, let us convert the speed of
light to km/s and compare this to the AU.
First, 300,000,000 m/s x 1 km/1,000 m = 300,000 km/s.
Next, 300,000 km/s x 60 s/minute x 60 minutes/hour x 24 hours/day x 365 days/year =
9.5 x 1012 km.
Finally, 9.5 x 1012 km x 1AU/1.5 x 1011 km = 63.3 AU
So, there are over 63 AU in one light-year. That means the closest star, Proxima Centauri, is just over 4
light-years from Earth. Another way of looking at this, is that the Earth is only 8 light-minutes from the sun
(meaning it only takes 8 minutes for the sun’s light to strike Earth).
To determine how long it takes the sun to reach the other planets, multiply the distance to the sun in AU by
8 minutes. For example, Mercury is 0.39 AU from the sun:
0.39 AU x 8 min/1 AU = 3.12 minutes.
Complete the table that follows. You calculated the distance previously.
PLANET
DISTANCE (AU)
TIME (MIN)
Mercury
0.39
3.12
1.00
8.00
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Extension
Convert the following distance from light-years (l-y) to AU using the conversion factor of one l-y = 63 AU.
1.
100,000 l-y (the diameter of the Milky Way galaxy)
2. 28,000 l-y (the distance of our solar system to the center of our galaxy)