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PlanetData
FindFormula
Related Categories
Astronomy
Physics
Rediscovering Kepler's Third Law
Example Notebook
Open in Cloud
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Find the orbit period and semimajor axis for all the planets in our Solar System:
I
n
[
1
]
:
=
E
n
t
i
t
y
V
a
l
u
e
p
l
a
n
e
t
s
P
L
A
N
E
T
S
,
{
"
O
r
b
i
t
P
e
r
i
o
d
"
,
"
S
e
m
i
m
a
j
o
r
A
x
i
s
"
}
O
u
t
[
1
]
=
8
7
.
9
6
9
2
6
d
a
y
s
,
0
.
3
8
7
0
9
8
9
3
a
u
,
2
2
4
.
7
0
0
8
0
d
a
y
s
,
0
.
7
2
3
3
3
1
9
9
a
u
,
3
6
5
.
2
5
6
3
6
d
a
y
s
,
1
.
0
0
0
0
0
0
1
1
a
u
,
{
1
.
8
8
0
8
4
7
6
a
,
1
.
5
2
3
6
6
2
3
1
a
u
}
,
{
1
1
.
8
6
2
6
1
5
a
,
5
.
2
0
3
3
6
3
0
1
a
u
}
,
{
2
9
.
4
4
7
4
9
8
a
,
9
.
5
3
7
0
7
0
3
2
a
u
}
,
{
8
4
.
0
1
6
8
4
6
a
,
1
9
.
1
9
1
2
6
3
9
3
a
u
}
,
{
1
6
4
.
7
9
1
3
2
a
,
3
0
.
0
6
8
9
6
3
4
8
a
u
}
Make a log-log plot:
I
n
[
2
]
:
=
L
i
s
t
L
o
g
L
o
g
P
l
o
t
[
%
]
O
u
t
[
2
]
=
The fact that it's close to a straight line implies a power law relationship.
Find a formula for the semimajor axis as a function of the period:
I
n
[
3
]
:
=
F
i
n
d
F
o
r
m
u
l
a
[
%
%
,
p
]
O
u
t
[
3
]
=
0
.
0
1
3
5
5
4
4
0
.
7
Q
u
a
n
t
i
t
y
M
a
g
n
i
t
u
d
e
[
p
,
D
a
y
s
]
a
u
There's an exponent of 0.7, close to the 2/3 of Kepler's third law.
Exoplanets
(
5
)
Pick 10 random exoplanets:
I
n
[
1
]
:
=
R
a
n
d
o
m
E
n
t
i
t
y
[
"
E
x
o
p
l
a
n
e
t
"
,
1
0
]
O
u
t
[
1
]
=
K
e
p
l
e
r
4
7
4
b
,
K
e
p
l
e
r
1
4
2
c
,
K
e
p
l
e
r
1
0
9
9
b
,
K
e
p
l
e
r
1
8
1
b
,
K
2
-
7
5
b
,
H
A
T
-
P
-
2
5
b
,
K
e
p
l
e
r
2
7
2
b
,
K
e
p
l
e
r
6
7
5
b
,
K
e
p
l
e
r
1
0
6
0
b
,
H
D
1
6
0
5
c
Only a few have known semimajor axes:
I
n
[
2
]
:
=
E
n
t
i
t
y
V
a
l
u
e
[
%
,
{
"
O
r
b
i
t
P
e
r
i
o
d
"
,
"
S
e
m
i
m
a
j
o
r
A
x
i
s
"
}
]
O
u
t
[
2
]
=
{
1
3
5
.
9
4
9
2
0
3
h
,
M
i
s
s
i
n
g
[
N
o
t
A
v
a
i
l
a
b
l
e
]
}
,
{
1
1
4
.
3
5
9
1
h
,
0
.
0
5
7
a
u
}
,
{
5
2
.
0
7
8
5
0
8
0
h
,
M
i
s
s
i
n
g
[
N
o
t
A
v
a
i
l
a
b
l
e
]
}
,
{
7
5
.
3
6
0
5
3
h
,
0
.
0
4
a
u
}
,
7
.
8
1
9
6
d
a
y
s
,
0
.
0
8
1
a
u
,
{
8
7
.
7
2
8
1
1
h
,
0
.
0
4
6
6
a
u
}
,
{
7
1
.
3
6
1
3
2
h
,
0
.
0
3
8
a
u
}
,
{
5
6
.
1
3
6
9
3
5
9
h
,
M
i
s
s
i
n
g
[
N
o
t
A
v
a
i
l
a
b
l
e
]
}
,
4
6
.
9
1
0
0
4
4
8
8
d
a
y
s
,
M
i
s
s
i
n
g
[
N
o
t
A
v
a
i
l
a
b
l
e
]
,
{
5
.
7
8
4
a
,
3
.
5
2
a
u
}
FInd results for 100 random exoplanets:
I
n
[
3
]
:
=
d
a
t
a
=
E
n
t
i
t
y
V
a
l
u
e
[
R
a
n
d
o
m
E
n
t
i
t
y
[
"
E
x
o
p
l
a
n
e
t
"
,
1
0
0
]
,
{
"
O
r
b
i
t
P
e
r
i
o
d
"
,
"
S
e
m
i
m
a
j
o
r
A
x
i
s
"
}
]
;
Plot semimajor axis against orbit period:
I
n
[
4
]
:
=
L
i
s
t
L
o
g
L
o
g
P
l
o
t
[
d
a
t
a
]
O
u
t
[
4
]
=
Find a fit to the data, removing all cases in the data that contain missing values:
I
n
[
5
]
:
=
F
i
n
d
F
o
r
m
u
l
a
[
D
e
l
e
t
e
M
i
s
s
i
n
g
[
d
a
t
a
,
1
,
1
]
,
p
]
O
u
t
[
5
]
=
1
.
2
2
1
0
7
0
.
6
Q
u
a
n
t
i
t
y
M
a
g
n
i
t
u
d
e
[
p
,
J
u
l
i
a
n
Y
e
a
r
s
]
a
u
The exponent is extremely close to 2/3, validating Kepler's third law.
See Also
OrbitalProperties
Related Symbols
PlanetData
FindFormula
Publisher Information
Contributed by:
Stephen Wolfram
