A tricky Physics question I thought about (1 Viewer)

[TheAstronomer]

Consider this thought experiment:
Twin brothers, Andrew and Michael, are situated in a geostationary orbit and the equator respectively. After a period of one year at their respective positions, which of the two will become older (i.e. age faster)? Assume that at this very instant, both of them have the exact same age. You may use relevant equations to support your answer.

 

[cub3root]

the one that went up will be slightly younger because of special relativity. the formula t_o = t_v/squt(blah) shows that the person up in the sky will be travelling at 11000/kph

my explanation is not exactly through but it is a straightforward question

2ez

 

[TheAstronomer]

Yes that's what I thought, but don't you have to incorporate the effects of general relativity to this question as well?

 

[cub3root]

Yes that's what I thought, but don't you have to incorporate the effects of general relativity to this question as well?

general relativity is much more advanced beyond the hsc and your answers don't have to say that. pretty much include this in your answer:

- which one is younger (the one that went up)
- because either mathematical proof or qualitative description

 

[TheAstronomer]

Yeah so my point is, what will be the actual answer in and beyond the domain of the HSC? This is not a past exam question I found btw, just a thought a while ago.

 

[cub3root]

tbh; i am not really sure how to include general relativity into this question. as far as i understand, general relativity is concerned with space-time and i have no idea beyond that. I don't see how that would come into play in the HSC but then again I don't have much knowledge beyond HSC phys + 1 uni subject lol

good luck

 

[someth1ng]

The one on the ground would tick slower - gravitational time dilation. I don't think there's relative motion between them.

 

[anomalousdecay]

the one that went up will be slightly younger because of special relativity. the formula t_o = t_v/squt(blah) shows that the person up in the sky will be travelling at 11000/kph

my explanation is not exactly through but it is a straightforward question

2ez

Are you sure?

I mean the Earth rotates just as fast, so wouldn't the person on Earth be moving just as fast?

So using HSC methods they would be the same age imo.

The one on the ground would tick slower - gravitational time dilation. I don't think there's relative motion between them.

This is not HSC, so again my point stands that by HSC methods they would be the same age.

And the cool thing is that a downside of being fat is that you live longer! lel.

 

[Squar3root]

Are you sure?

I mean the Earth rotates just as fast, so wouldn't the person on Earth be moving just as fast?

So using HSC methods they would be the same age imo.

no the person traveling at the equator will be at speed 1670 kph and the guy at the equator will be at 11000 kph.

think of it like this. there are 2 circles and one is bigger than the other. obviously for the larger circle you have to travel faster to be in direct contact with the smaller circle

 

[someth1ng]

no the person traveling at the equator will be at speed 1670 kph and the guy at the equator will be at 11000 kph.

think of it like this. there are 2 circles and one is bigger than the other. obviously for the larger circle you have to travel faster to be in direct contact with the smaller circle

Not relevant - that is the speed relative to the centre of the Earth - aging depends on speed relative to each other.

 

[anomalousdecay]

no the person traveling at the equator will be at speed 1670 kph and the guy at the equator will be at 11000 kph.

think of it like this. there are 2 circles and one is bigger than the other. obviously for the larger circle you have to travel faster to be in direct contact with the smaller circle

The motion is relative to each other. Not the reference of the earth....

Not relevant - that is the speed relative to the centre of the Earth - aging depends on speed relative to each other.

Pretty much this.

Also Chuck Norris is always right. Its Chuck Norris!!!

 

[Squar3root]

Not relevant - that is the speed relative to the centre of the Earth - aging depends on speed relative to each other.

So then the relative motion would just be 11000-1670?

 

[anomalousdecay]

So then the relative motion would just be 11000-1670?

"relative to each other"

zero.

 

[Squar3root]

"relative to each other"

zero.

so if there is zero relative motion that means that neither "get younger"?

 

[anomalousdecay]

so if there is zero relative motion that means that neither "get younger"?

Yes using HSC methods.


Extracurricular:

There is gravitational dilation which affects both (as someth1ng explained), but will affect the person on Earth more. Hence the person on Earth will be younger after the specified time period.

 

[Squar3root]

Yes using HSC methods.


Extracurricular:

There is gravitational dilation which affects both (as someth1ng explained), but will affect the person on Earth more. Hence the person on Earth will be younger after the specified time period.

but how does that make sense? the person in the sky has speed 11000 kph = 1.0e-5 m/s

the question says 1 year so = 31536000 seconds

now the time dilation formula.

t_v = t_o/sqrt(1 - v^2/c^2)

we want t_o = 31535999.9999...... which makes him slightly younger (not even by a second but just slightly)


ohh wait; but since the guy in the sky is in circular motion he is experiencing a centripetal force towards the centre which makes him in a non-inertial frame of reference. Don't know if that changes anything though

 

[anomalousdecay]

but how does that make sense? the person in the sky has speed 11000 kph = 1.0e-5 m/s

the question says 1 year so = 31536000 seconds

now the time dilation formula.

t_v = t_o/sqrt(1 - v^2/c^2)

we want t_o = 31535999.9999...... which makes him slightly younger (not even by a second but just slightly)


ohh wait; but since the guy in the sky is in circular motion he is experiencing a centripetal force towards the centre which makes him in a non-inertial frame of reference. Don't know if that changes anything though

No what you are saying is that the Earth doesn't spin.

One will be travelling faster relative to Earth (the one in a higher orbit) in terms of circular motion.

However, relative to each other they still keep the same distance between each other at ALL TIMES.

Hence if there is no change in distance, there is no relative velocity between the two!

So they don't have a difference in time on the basis of speed.

 

[Squar3root]

No what you are saying is that the Earth doesn't spin.

One will be travelling faster relative to Earth (the one in a higher orbit) in terms of circular motion.

However, relative to each other they still keep the same distance between each other at ALL TIMES.

Hence if there is no change in distance, there is no relative velocity between the two!

So they don't have a difference in time on the basis of speed.

okay I understand what you mean know; Just read the whole question wrong lol. gg inglish

 

[anomalousdecay]

okay I understand what you mean know; Just read the whole question wrong lol. gg inglish

Just....please pass the supplementary.

And read the questions properly so that you can pass it.