Units

Newton and Einstein form

“Wavelength”-form

Mass form

Gravitational constant

G 6.67408 × 10 11

G p = l p 2 c 3

Newton’s gravitational force

F = G m 1 m 2 r 2

F = c r 2 l p 2 λ ¯ 2

F = c r 2 m 2 m p 2

Escape velocity

v e = 2 G m r

v e = l p λ ¯ c 2

v e = 2 m m p c

Orbital velocity

v o = G m r

v o = l p λ ¯ c

v o = m m p c

Gravitational parameter

μ = G m

μ = l p 2 λ ¯ c 2

μ = m m p l p c 2

Gravitational acceleration field

g = G m r 2

g = l p 2 λ ¯ 3 c 2

g = m 2 m p 2 c 2 λ ¯

Gravitational time dilation

t 0 = t f 1 2 G m r c 2 = 1 v e 2 c 2

t o = t f 1 2 l p 2 λ ¯ 2

t o = t f 1 2 m 2 m p 2

Orbital time dilation

t 0 = t f 1 3 G m r c 2 = 1 3 2 v e 2 c 2

t o = t f 1 3 l p 2 λ ¯ 2

t o = t f 1 3 m 2 m p 2

Light deflection

δ = 4 G m c 2 r

δ = 4 l p 2 λ ¯ 2

δ = 4 m 2 m p 2

Schwarzschild Radiusa

r s = 2 G m c 2

r s = 2 l p 2 λ ¯

r s = 2 l p m m p

Gravitational redshift GR

lim r + z ( r ) = 1 1 2 G m r c 2 1

lim r + z ( r ) = 1 1 2 l p 2 λ ¯ 2 1

1 1 2 m 2 m p 2 1

Gravitational redshift ABSb

lim r + z ( r ) = G m c 2 r

lim r + z ( r ) = l p 2 λ ¯ 2

m 2 m p 2