1. What is Gravitational Time Dilation?

Gravitational time dilation is a phenomenon predicted by Einstein's theory of general relativity where time passes at different rates in regions of different gravitational potential. The higher the gravitational potential (the farther away from a source of gravitation), the faster time passes.

2. How Does the Calculator Work?

The calculator uses the gravitational time dilation formula:

Where:

• \( \Delta t' \) — Dilated time (seconds)
• \( \Delta t \) — Proper time (seconds)
• \( g \) — Acceleration due to gravity (m/s²)
• \( h \) — Height difference (meters)
• \( c \) — Speed of light (299,792,458 m/s)

Explanation: The equation shows how time runs slower in stronger gravitational fields (or equivalently, under acceleration).

3. Importance of Time Dilation Calculation

Details: Understanding time dilation is crucial for GPS satellite systems, astrophysics, and testing general relativity. Even small effects become significant over large distances or long periods.

4. Using the Calculator

Tips: Enter proper time in seconds, acceleration in m/s², and height in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: How significant is this effect on Earth?
A: For Earth's gravity (9.8 m/s²), a 1 meter height difference creates a time dilation of about 1 part in 10¹⁶ - tiny but measurable with atomic clocks.

Q2: Does this apply to acceleration without gravity?
A: Yes, according to Einstein's equivalence principle, acceleration produces equivalent effects to gravity.

Q3: What's the most extreme time dilation observed?
A: Near black holes, where time can appear almost frozen to distant observers.

Q4: Why does time slow down in stronger gravity?
A: In general relativity, gravity curves spacetime, and this curvature affects the passage of time.

Q5: How does this relate to GPS satellites?
A: GPS satellites experience both gravitational and velocity time dilation, which must be corrected for accurate positioning.