If the time discrepancy is 0.1 nanoseconds, what is the distance error in meters?

If the time discrepancy is 0.1 nanoseconds, what is the distance error in meters?

• A. 0.001 m
• B. 0.03 m
• C. 0.15 m
• D. 0.3 m

Answer: (B)

Time errors translate directly into distance errors by using speed times time. For signals used in geodesy, the distance error equals the speed of light times the time discrepancy: Δd = c × Δt. With Δt = 0.1 nanoseconds = 1×10⁻¹⁰ s and c ≈ 3.0×10⁸ m/s, Δd ≈ 3.0×10⁸ × 1×10⁻¹⁰ = 3.0×10⁻² m, which is about 0.03 m. So the distance error is 0.03 meters.

Time errors translate directly into distance errors by using speed times time. For signals used in geodesy, the distance error equals the speed of light times the time discrepancy: Δd = c × Δt. With Δt = 0.1 nanoseconds = 1×10⁻¹⁰ s and c ≈ 3.0×10⁸ m/s, Δd ≈ 3.0×10⁸ × 1×10⁻¹⁰ = 3.0×10⁻² m, which is about 0.03 m. So the distance error is 0.03 meters.