SME
Grade 8 Science · Problem type
Farther out, longer year
Use this for “Mars is 1.5 times as far from the sun as Earth. How long is its year?”
Table
Distance from the sun (d)
(AU)
Length of its year (T)
(Earth years)
This is an example. Type your own values to start a new problem.
T (Earth years)
=
(
d (AU)
)
3
Formulas
T
=
√
d
3
(length
of
its
year
=
√(distance
from
the
sun³))
1.874
=
√
1.52
3
Assumptions
•
A year is one trip round the sun. Earth’s is 1 year at 1 AU.
•
Farther from the sun the pull is weaker, so a planet moves slower and has farther to go.
•
Kepler found the pattern 400 years ago: the year squared equals the distance cubed, in Earth years and AU.
Step-by-step
WE KNOW
d = 1.52 AU (distance from the sun)
FIND
length of its year (T)
Step 1 · Find length of its year (T)
Use T = √(d³) (length of its year = √(distance from the sun³))
Cube the distance, then take the square root: farther planets move slower on longer paths.
T
=
√
1.52
3
T
≈
1.874
Earth
years
Check
Put the numbers back in. Both sides should match.
1.874
≈
√
1.52
3
✓
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