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# Solar System tests of general relativity

Lecture of the course "General Relativity With Astrophysical Applications", taught by Prof. Rodrigo Nemmen (USP).

• Parametrized-Post-Newtonian metric (PPN)
• Precession of the perihelion of Mercury measurement
• Deflection of light by the Sun
• The 1919 total eclipse expedition and observations

Credit for the slides/figures belongs to Rodrigo Nemmen, unless otherwise stated.

## Rodrigo Nemmen

November 13, 2018

## Transcript

1. ### AGA0319 Rodrigo Nemmen Solar System Tests of General Relativity Astrophysical

Applications of GR I
2. ### Comparing GR with other theories of gravity We need a

way of testing GR with observations Speciﬁcally: quantify possible deviation from GR in data Standard way: parametrized-Post-Newtonian (PPN)
3. ### Parametrized-Post-Newtonian (PPN) framework Begin with general static, spherically symmetric metric

ds2 = − A(r)(cdt)2 + B(r)dr2 + r2(dθ2 + sin2 θdϕ2) A(r) = 1 − 2GM c2r + ⋯ B(r) = 1 + ⋯ Agreement with Newton requires Deﬁne γ and β A(r) = 1 − 2GM c2r + 2(β − γ) ( GM c2r ) 2 + ⋯ B(r) = 1 + 2γ ( GM c2r ) + ⋯ If γ=1 and β=1 → recover general relativity PPN metric
4. ### Parametrized-Post-Newtonian (PPN) framework ds2 = − A(r)(cdt)2 + B(r)dr2 +

r2(dθ2 + sin2 θdϕ2) A(r) = 1 − 2GM c2r + 2(β − γ) ( GM c2r ) 2 + ⋯ B(r) = 1 + 2γ ( GM c2r ) + ⋯ If γ=1 and β=1 → GR is correct PPN metric If γ≠1 and β≠1 → Einstein is wrong
5. ### Relativistic effects in the PPN metric Δϕ def = (

1 + γ 2 ) ( 4GM c2b ) Deﬂection angle of light ray passing by mass M Δϕ prec = 1 3 (2 + 2γ − β) 6πGM c2a(1 − ϵ2) Precession of perihelion of planet per orbit

7. ### Precession of Mercury’s perihelion GR prediction Δφprec = 43″ /

century Δϕ prec = 6πG c2 M a(1 − ϵ2) 0.8 0.9 1.0 1.1 1.2 38 40 42 44 46 48 γ Δφprec (″/century)
8. ### Precession of Mercury’s perihelion GR prediction Δφprec = 43″ /

century Observed precession = 5599.74″±0.65 / century Δϕ prec = 6πG c2 M a(1 − ϵ2) Effect Δφ (") Precession of equinoxes 5025.64 Perturbation other planets 532 Oblateness of Sun 0.03 Total 5557 Data - effects 43 γ = 1.000 ± 0.002 β = 1.000 ± 0.003 PPN parameters
9. ### Deﬂection of light by the Sun GR prediction Δφdef =

1.75″ Δϕ def = 4GM c2b https://grupos.unican.es/glendama/Historical_intro.htm
10. ### Deﬂection of light by the Sun GR prediction Δφdef =

1.75″ Δϕ def = 4GM c2b https://grupos.unican.es/glendama/Historical_intro.htm
11. ### Deﬂection of light by the Sun Δφ def = 1.75″

https://medium.com/@GatotSoedarto/how-to-show-gravity-aﬀects-light-ee9e8dfd33af

in the sky

in the sky M

17. ### LUZES TODAS TORTAS NOS CÉUS Cientistas inquietos pelos resultados das

observações do eclipse Estrelas não estão onde deveriam estar, mas ninguém precisa se preocupar TEORIA DE EINSTEIN TRIUNFA UM LIVRO PARA DEZ SÁBIOS Ninguém mais no mundo consegue compreende-lo New York Times, 10 Nov. 1919
18. ### Deﬂection of light by the Sun GR prediction Δφdef =

1.75″ γ Δφdef (″) Δϕ def = 4GM c2b 0.8 0.9 1.0 1.1 1.2 1.60 1.65 1.70 1.75 1.80 1.85 1.90 β=1 γ = 1.007 ± 0.009 β = 1.000 ± 0.003 PPN parameters