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Math Review for Space Travel
How to work out how long space travel will take:
When dealing with problems involving long distances to travel, and the time it takes to travel them, you
may encounter different units of measure (light years vs. kilometers), as well as scientific notation.
If your problem has different units of measure, it is important to convert your units to the same unit of
measure before beginning your problem. The most common units of measure used in astronomy are
AU (Astronomical unit), and light years. The table below shows the distance for AU and ly expressed in
different ways:
Astronomical Unit 150 million kilometers
150,000,000 km
1.5x108 km
Light Year
9.5 trillion kilometers
9,500,000,000,000 km
9.5 x1012 km
3
6
9
12
Tip: 10 means thousand, 10 means million, 10 means billion, 10 means trillion
Because light years are such a long distance, you often need to use scientific notation in your
calculators. Different calculators provide this in different ways.
Casio, Sharp, & Micronta
To get the number 9.5 x 1012,
press:
Texas instruments
To get the number 9.5 x 1012,
press:
9.5
9.5
EXP
12
2nd
10x
12
To convert from AU to km multiply the number of AU by 150 million
To convert from ly to km, multiply the number of ly by 9.5 trillion
Working out the Time
Then, if you know the distance, and the speed of travel, you can easily work out how long it takes to
get to the destination:
Distance in km
Speed in km/h
=
Time in h
Converting Time
With any space problem, the time in hours is not a practical way to express your answer. For example,
you would never tell someone you are 131400 hours old. It is often easiest to convert from hours to
days first, and then converting from days to months or years.
Converting from:
Hours to Days (h--->d)
Divide the hours by 24h/day
Eg.
Days to months (d-->mon)
Divide days by 30.4 days/mo
Eg.
Days to years (d-->a)
Divide days by 365
Eg.
131400 h
24h/day
5475 h
30.4d/mo
5475 h
365d/year
= 5475 days
= 180.1 mo
= 15 years
Using mixed units for time:
Often, when converting from times, you will not get a whole number. For example, 6842 days is equal
to 18.74 months. It is clearer to express this in months, and days (and perhaps even hours and
minutes).
6842 days
365 days/year
= 18.74 years
.88 months x 30.4
days/months
26.75 days
.74 years x 12
months/year
= 8.88 months
.75 days x 24h/day
= 18h
Final answer can then be expressed as 18 years, 8 months, 26 days, and 18h
Math Review for Space Travel
Practice Questions
1. Mars is 1.5 AU from the sun. How many kilometers is it from the sun?
2. Alpha Centauri is 4.1 ly from Earth. How many kilometers is it from earth?
3. The circumference of Earth’s orbit is 938 million kilometers. How fast does Earth travel in
km/h?
4. NASA hopes to send people to Mars. The total distance to travel to Mars is 195 million km. If
the spacecraft travels 31,250 km/h, how long will it take to get to Mars? (in h and a)
5. The European Space Agency (ESA) is planning to send a satellite to Pluto. Pluto is 39 AU away
from the sun. If the satellite travels a speed of 27500 km/h, how long will it take to get to
Pluto? Express your answer in years, months, and days.
6. Astronomers recently discovered a planet orbiting the star Vela, which is 36 light years away
(which is relatively close). The planet, now named HD85512b, may be habitable (ie. The
temperature is just right for water to exist as a liquid). Someone claiming to be a 600 year old
alien arrives from this planet, and says the spacecraft can travel a speed of 3 million km/h. How
long would it have taken this traveler to get to Earth? (in years) How old is the alien?