How Big is Big?

Summary

In this homework, you will learn the types of objects in the Universe, develop an idea of the sizes of objects and the typical distances between them. You will also recall how to express very large numbers using powers of ten notation. A scientific calculator will help you.

Background and Theory

Suppose someone asks you how far it is from Seattle to Vancouver, B.C. You might reply "Oh, about three hours." Obviously, what you mean is that a car traveling at about 50 mph can drive the distance in three hours. So the distance is "three car hours".

We can launch rockets that travel at about 25,000 mph, or 40,000 km/hr. Such rockets can orbit the Earth in just over an hour. The circumference of the Earth is "one spaceship-hour". Similarly, the Moon is about 1/2 a spaceship-day away.

Questions:
1. The names of various objects are listed in the first column of the table below. Please describe the sizes of these objects using "standard" Earth units (kilometers), and spaceship travel time. The sizes of the objects can be found by browsing through the textbook. For reference, the diameter of the Earth is about 13,000 km, and the diameter of the Sun is 1,400,000 km (1.4X106 km), a bit more than 100 times the size of the Earth. Spaceship travel times should be described in hours, days, years, centuries; whichever allows the most comfortable numbers---between 1 and 1000 if possible.

Object Diameter (km) Diameter (spaceship travel-time)
Moon
Earth 13,000 km
Sun 1.4X106
Solar System
Milky Way Galaxy
Virgo Cluster 1.67X1019 km

2. Suppose that during your lifetime, technology improves, and space travel of 100,000 km/hr becomes feasible. At this speed, how long would it take humans to reach Pluto from Earth?
3. Suppose someone asks you how far it is from the Earth to the Sun. You could answer "93 million miles", or you could say "8 light minutes". If you know how fast light travels (186,000 miles per second or 300,000 km/s), then the second answer replaces an uncomfortably large number with a more reasonable one.

Distances in the astronomical realm are huge. Using miles or kilometers becomes silly when you are consistently talking about "four hundred million trillion miles". It makes sense to switch to much more reasonable units. The normal choice is the light travel time. Fill in the blanks in the table. Light travel times can be given in light-hours, light-days, or light-years; whichever allows the use of the most comfortable numbers.

Object Distance (km or A.U.) Distance (light travel time)
Sun 1 A.U.=1.5X108km
Pluto 38 A.U.
Nearest Star (not the Sun)
Nearest Large Galaxy (M31)   2 Mly = 2 million light years
Nearest Cluster of Galaxys