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**Table of Content**

The time dilation calculator quantifies the difference in the passage of time between two frames of reference. This is due to relative motion or differences in gravitational fields explained by the theory of relativity.

**“Time dilation is a measure of differential time interval observed by two persons at different frames of reference to each other and relative to the speed of light.”**

This phenomenon is only notable at speeds close to that of light. The gravitational time dilation calculator is specially developed to calculate the Interstellar objects according to time dilation theory. In deep space, the time dilation becomes increasingly pronounced as described by Einstein’s theory of relativity.

It is possible to calculate the relative motion of the Interstellar objective by the time dialation formula:

The time dilation equation requires the time-traveling viewer’s velocity for v in the Lorentz factor formula.

\[ \Delta t’ = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}} \]

**Where:**

- Δt’ = Dilated time
- Δt = Proper time
- v = Relative velocity between the two frames.
- c = Speed of light = 299,792 km/s (Approx)

**Given:**

Δt = Proper time interval =7 years

v = Velocity of the object = 50000 km/s

c = Speed of light = 299,792 km/s (Approx)

Δt’ = Dilated time interval=?

**Solution:**

The time dilation equation is:

\[Δt’ = Δt \sqrt{1 – \frac{v^2}{c^2}}\]

First covert the velocity from km/s to the speed of light units

\[v = 50000 \text{ km/s} \div 299792 \text{ km/s} \approx 0.167c\]

Insert the values in the time dilation formula:

\[Δt’ = 7 \text{ years} \sqrt{1 – \left(\frac{0.167c}{c}\right)^2}\]

Then simply the fraction inside the square root:

\[Δt’ = 7 \text{ years} \sqrt{1 – 0.027889\]

In this step calculate the value inside the square root:

\[1 – 0.027889 = 0.972111\]

Then

\[Δt’ = 7 \text{ years} \sqrt{0.972111}\]

Now solve the square root:

\[Δt’ = 7 \text{ years} \times \sqrt{0.972111} \approx 7 \text{ years} \times 0.9860 \approx 6.9027 \text{ years}\]

The dilated time interval (Δt’) will be nearly about 6.9027 years. while the proper time interval (Δt) is 7 years. Confirm the values of the dilation time with our speed of light time dilation calculator.

It may be possible users may need the answer in different units. The relativistic time dilation calculator calculates the time dilation in the other units simultaneously.

No, When an observer travels at the speed of light. Then the time dilation is undefined (1/0) due to the Lorentz factor.

It is the property that remains unchanged under Lorentz transformations, regardless of the relative motion of observers.

The key Lorentz invariant in special relativity is the spacetime interval. It is denoted Δs² and is written as:

Δs² = c²Δt² – Δx² – Δy² – Δz²

The theory of relativity describes where gravity is stronger then time passes slowly. The time dilation formula is based on the relativity theory for two objects at various frames of reference.

From Wikipedia.org: Time dilation

From phys.libretexts.org: Relative time