SME
Grade 12 Science · Problem type
An exoplanet’s orbit from its period
Use this for “A planet circles a star of 0.5 solar masses every 1,461 days. How far is it from its star?”
Diagram
Each shaded sector is swept in 1/8 of the period: equal areas in equal times.
a³ = M × T² for a star of M = 0.5 Suns: a = ∛(M × T²) = ∛(0.5 × 4²) = 2 AU
This is an example. Type your own values to start a new problem.
(
a (AU)
)
3
=
M (M☉)
×
(
T (years)
)
2
P
Period in days
example · days
Formulas
T
=
P
365.25
4
=
1,461
365.25
a
3
=
M
×
T
2
2
3
=
0.5
×
4
2
Assumptions
•
The planet’s mass is tiny beside its star’s.
•
With M = 1 this is the solar system’s T² = a³.
•
A heavier star pulls harder, so the same period means a wider orbit.
Step-by-step
WE KNOW
P = 1,461 days, M = 0.5 M☉
FIND
period in years (T), orbit size (a)
Step 1 · Find period in years (T)
Use T = P ÷ 365.25
A year is 365.25 days: count the years.
T
=
1,461
365.25
T
=
4
years
Step 2 · Find orbit size (a)
Use a³ = M × T²
Kepler’s
third
law
with
the
star’s
mass:
a
is
the
cube
root
of
M
×
T
2
.
a
=
∛(
M
×
T
2
)
a
=
∛(0.5
×
4
2
)
a
=
∛8
a
=
2
AU
Check
Put the numbers back in. Both sides should match.
4
=
1,461
365.25
✓
2
3
=
0.5
×
4
2
✓
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Exoplanets and the search for life
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The habitable zone and a planet’s temperature
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