# Gravitational time dilation on cylinderical objects

• Pretty Pony
In summary, the conversation discusses the formula for calculating time dilation on cylinders with uniform density and suggests an arbitrary precision calculator that can assist with this calculation. The calculator has advanced features but must be installed and used through the command line. It also mentions the need for more information in order to fully define the problem and offers to help with the calculation at the appropriate level based on the person's math and science background.
Pretty Pony
I am simply looking for the formula to work out the time dilation on cylinders with uniform density. Also, any links to arbitrary precision calculators would be appreciated.

For the arbitrary precision calculator you could try http://pari.math.u-bordeaux.fr/
I have used it the past and it has some very advanced features, but you have to install it and it is a command line calculator.

Are you asking for (1) the time dilation resulting from an exact solution of the Einstein field equations, or (2) the time dilation in the weak-field limit, where the field is essentially Newtonian?

If it's 1, then I don't think you've specified enough to fully define the problem.

If it's 2, then you just need to calculate the potential of the cylinder by integrating. If you don't know how to do that, please tell us more about your math and science background, and we can try to help you at the correct level.

-Ben

## 1. What is gravitational time dilation?

Gravitational time dilation is a phenomenon where time appears to pass slower in a region with a stronger gravitational field, as predicted by Einstein's theory of general relativity. This means that clocks in a stronger gravitational field will tick slower compared to clocks in a weaker gravitational field.

## 2. How does gravitational time dilation affect cylindrical objects?

Gravitational time dilation affects cylindrical objects in a similar way as any other objects. The closer an object is to a massive body, the stronger the gravitational field and the slower time will pass for that object. This means that a cylinder near a massive object will experience time dilation compared to a cylinder farther away.

## 3. Is the effect of gravitational time dilation significant on cylindrical objects?

It depends on the mass and size of the cylindrical object and the strength of the gravitational field it is in. For everyday objects on Earth, the effect of gravitational time dilation is very small and not noticeable. However, for objects near massive bodies like black holes, the effect can be significant and can result in significant differences in time between two objects in different gravitational fields.

## 4. Can gravitational time dilation be observed on Earth?

Yes, gravitational time dilation can be observed on Earth. It is a well-established phenomenon and has been confirmed by various experiments and observations. For example, atomic clocks on Earth have been shown to tick slower in stronger gravitational fields, such as at higher altitudes.

## 5. How does gravitational time dilation affect space travel on cylindrical objects?

Gravitational time dilation is a crucial factor to consider in space travel, especially for long-distance journeys. As a cylindrical object travels through different gravitational fields, time will pass differently for the object compared to a stationary observer on Earth. This means that astronauts on a space mission may experience time differently compared to people on Earth, and this must be accounted for in calculations and communication with Earth.

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