SME
Grade 12 Science · Earth & Space Science
Exoplanets and the search for life
Use this for “A planet passes in front of a Sun-sized star and dims it by 1%. How big is the planet?”
Diagram
The
planet
covers
(
r
109 × R
)²
of
the
star’s
disk:
(
10.9
109 × 1
)²
=
0.01,
so
the
light
dips
by
δ
=
1%.
The dip starts as the planet touches the star’s edge and is deepest once it is wholly in front.
This is an example. Type your own values to start a new problem.
δ
%
=
100
×
(
r (R⊕)
÷
(109
×
R (R☉)
))
2
Formulas
δ
=
100
×
(
r
109 ×
R
)²
1
=
100
×
(
10.9
109 × 1
)²
Assumptions
•
The dip is the share of the star’s disk the planet covers.
•
The orbit must be nearly edge-on to us, or there is no transit.
•
Repeated dips a period apart confirm a planet.
•
1 R☉ = 109 R⊕: the Sun is 109 Earths wide.
Step-by-step
WE KNOW
δ = 1%, R = 1 R☉
FIND
planet’s radius (r)
Step 1 · Find planet’s radius (r)
Use δ = 100 × (r ÷ (109 × R))²
Undo the square: the radius ratio is the square root of the dip’s share.
r
=
109
×
R
×
√(
δ
100
)
r
=
109
×
1
×
√(
1
100
)
r
=
109
×
√
0.01
r
=
109
×
0.1
r
=
10.9
R⊕
Check
Put the numbers back in. Both sides should match.
1
=
100
×
(
10.9
109 × 1
)²
✓
Topic check
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