Why does a radio signal take longer when it grazes the Sun?

In GR the gravitational potential slows coordinate time and lengthens the spatial path relative to flat spacetime. The Shapiro formula is the integrated excess travel time along the null geodesic; it is not a refractive plasma effect. A common misconception is that the delay is only from geometric bending — most of Δt comes from the gravitational time dilation along the path.

What does the Cassini bound on γ_PPN mean?

In the parameterized post-Newtonian framework, γ measures how much space curvature a mass produces. GR predicts γ = 1. Cassini’s 2003 conjunction limited |γ − 1| to less than about 2 × 10⁻⁵, the tightest weak-field constraint to date. The simulator’s delay readout scales with that factor when you change the geometry.

Is the round-trip delay just twice the one-way formula?

For a symmetric uplink–downlink at conjunction, yes to leading order: you add the excess for each leg. Real missions also fold in Earth motion, spacecraft ephemeris, and plasma calibration; those corrections are not modeled here. The display focuses on the GR excess in microseconds against the Newtonian baseline.

Shapiro Time Delay (4th GR Test)

A radio signal grazing the Sun picks up an excess one-way travel time Δt ≈ (2GM/c³) ln[(r_E + r_E cos α)(r_R + r_R cos β)/b²] on top of the Newtonian light-time. Cassini, Mariner and Viking presets, with the round-trip delay readout in microseconds and an animated bent-photon path against a straight Newtonian baseline. The Cassini 2003 conjunction constrains |γ_PPN − 1| < 2 × 10⁻⁵ — the strongest weak-field GR test to date.

Geometry

Preset

Lens mass M (M⊙)1 M⊙

Emitter distance r_E (AU)1 AU

Receiver distance r_R (AU)9.539 AU

Impact parameter b (R_⊙)1.6 R_⊙

Photon position0.5

Shapiro time delay is one of the four classical tests of general relativity: a radio signal that grazes a massive body picks up an extra travel time Δt ≈ (2GM/c³) ln[(r_E + r_E cos α)(r_R + r_R cos β)/b²], on top of the Newtonian light-time. For Cassini's 2003 superior conjunction (b ≈ 1.6 R_⊙) the round-trip excess is hundreds of microseconds and constrains the post-Newtonian γ-parameter to |γ − 1| < 2 × 10⁻⁵, the strongest weak-field GR constraint to date. Slide presets to compare Mariner, Viking, Cassini and a binary-pulsar geometry.

Measured values

Δt one-way132.429 μs

Δt round-trip264.858 μs

b1.113e+6 km

Naive path5259.01 s

About this model

This simulator implements the Shapiro time delay — the fourth classical test of general relativity — for a radio signal that grazes the Sun. On top of the Newtonian light-time, the excess one-way delay is Δt ≈ (2GM/c³) ln[(r_E + r_E cos α)(r_R + r_R cos β)/b²], where M is solar mass, r_E and r_R are Earth and receiver distances, α and β are angles to the ray asymptotes, and b is the impact parameter. The model uses the weak-field Schwarzschild metric in the PPN parameterization; higher-order multipoles, plasma delays, and spacecraft clock noise are omitted. Presets for Cassini, Mariner, and Viking show the animated bent-photon path against a straight Newtonian baseline, with round-trip delay in microseconds. The Cassini 2003 solar conjunction constrains |γ_PPN − 1| < 2 × 10⁻⁵.

Who it's for: Advanced undergrad and graduate GR, experimental relativity, and radio-astronomy students studying weak-field tests.

Key terms

Shapiro time delay
fourth GR test
PPN parameter gamma
solar conjunction
Cassini relativity
gravitational light delay

How it works

Shapiro time delay simulator (4th classical GR test). A photon grazing the Sun acquires an excess one-way travel time Δt ≈ (2GM/c³) ln[(r_E + r_E cos α)(r_R + r_R cos β)/b²]. Built-in Cassini, Mariner and Viking presets; round-trip delay readout in microseconds, plus an animated bent photon path versus straight Newtonian baseline.

Frequently asked questions

Why does a radio signal take longer when it grazes the Sun?: In GR the gravitational potential slows coordinate time and lengthens the spatial path relative to flat spacetime. The Shapiro formula is the integrated excess travel time along the null geodesic; it is not a refractive plasma effect. A common misconception is that the delay is only from geometric bending — most of Δt comes from the gravitational time dilation along the path.
What does the Cassini bound on γ_PPN mean?: In the parameterized post-Newtonian framework, γ measures how much space curvature a mass produces. GR predicts γ = 1. Cassini’s 2003 conjunction limited |γ − 1| to less than about 2 × 10⁻⁵, the tightest weak-field constraint to date. The simulator’s delay readout scales with that factor when you change the geometry.
Is the round-trip delay just twice the one-way formula?: For a symmetric uplink–downlink at conjunction, yes to leading order: you add the excess for each leg. Real missions also fold in Earth motion, spacecraft ephemeris, and plasma calibration; those corrections are not modeled here. The display focuses on the GR excess in microseconds against the Newtonian baseline.