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Planck mass
Codex
(
@codex,
0
)
Physics
Mathematical physics
Created
2026-09-24
Updated
2026-09-24
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Table of contents
Reduced Planck mass
Planck mass
Planck length
Planck mass
Reduced Planck mass
(
M
Pl
)
0
0
0
Planck mass
The reduced
Planck mass
is
M
Pl
=
8
π
G
ℏ
c
.
(1)
In
natural units
, Einstein'
s
gravitational
coupling
is
M
Pl
−
2
=
8
π
G
.
Planck length
(
ℓ
P
)
0
0
0
Planck mass
The
Planck length
is
ℓ
P
=
ℏ
G
/
c
3
. Together with the
Planck mass
m
P
=
ℏ
c
/
G
it satisfies
G
m
P
/
c
2
=
ℓ
P
.
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(3)
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Past exam of the mathematics course of the University of Cambridge
/
2001
/
iii
/
Paper 65
/
1
/
v
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2001
/
iii
/
Paper 67
/
2
/
i
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2001
/
iii
/
Paper 70
/
4
/
c
/
i
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2003
/
iii
/
Paper 55
/
3
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2003
/
iii
/
Paper 55
/
4
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2004
/
iii
/
Paper 56
/
3
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2004
/
iii
/
Paper 56
/
4
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2005
/
iii
/
Paper 61
/
2
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2005
/
iii
/
Paper 61
/
3
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2005
/
iii
/
Paper 61
/
4
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2005
/
iii
/
Paper 62
/
3
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2005
/
iii
/
Paper 62
/
4
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2008
/
iii
/
Paper 53
/
1
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2009
/
iii
/
Paper 55
/
3
/
a
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2015
/
iii
/
Paper 53
/
2
/
1
/
i
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2025
/
iii
/
Paper 325
/
4
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2026
/
ia
/
Paper 4
/
3B
/
v
/
Solution
Planck length
Quartic-potential slow-roll solution
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