[wolfgang]

If there were another two planets looking exactly like our earth,and both of them having the same distance to our sun like our earth,and both rotates around the sun and around their axis at the same speed as our earth did.

Also on both of them there are the same creatures and the same mankind.

The only difference is that ,one of them(LE planet)is two times larger than our earth,and the other planet(SE)is half the size our earth.

If Three babies were born at the same time,each on one of the three planets.

15 years later,the baby on earth celebrates his 15th birthday.

How old would be the other two babies at this time?

Note:

One year=365 days

1 day= complete rotation of a given planet around its axis,One time.

[benjer3]

Are you meaning size by volume or diameter?

[Guest]

All three babies are 15 years old. The question stated that the other planet revolve around there axis at the same speed.

[Guest]

if they all rotate at the same speed, the wouldn't all three babies on all three planets be the same age at any given time?

Edit: ninja'd

Edited April 19, 2011 by Akariass

[Guest]

Shouldn't they all be 15 years old? If the three earths are rotating and revolving at the same speed days and years are equivalent. Just consider them different points along a radius of a sphere.

[Guest]

is to trick you into considering the speed in which one would travel if one were standing on the outer edge of each planet (the crust). If that speed were the same,as the puzzle is designed to make you think, then the LE baby would be younger and the SE baby older. However, as the puzzle states that the speed of rotation around the axis is the same, this means that they complete a rotaion (a day) in the same amount of time. Hence a day on earth is the same length as a day on either LE or SE. And each baby is the same age.

[curr3nt]

Sure they would be the same "age". But due to relativity wouldn't the one on the larger planet be an older or younger 15 than the other two because they are traveling faster? I can never remember the direction...

[Guest]

The determinant for a year is the time for the planet to complete a cycle around the star, which is equivalent for all three planets. The age is fifteen years for all three children. The rate of the planet's rotation about its axis is immaterial.

Edited April 19, 2011 by thirdtimescharm

[Guest]

The baby on the smaller planet would be older and the larger planet younger. The planets rotate at the same speed, but the larger takes longer for a rotation, the smaller shorter. If we're working with halves, wouldn't the SE baby be 30 years old and the LE baby 7.5 years old???

[Guest]

The determinant for a year is the time for the planet to complete a cycle around the star, which is equivalent for all three planets. The age is fifteen years for all three children. The rate of the planet's rotation about its axis is immaterial.

I was composing my post simultaneously with yours ...

You're right, of course ... whether a day is 12 or 48 hours, it doesn't make a difference in the length of a year. A year is a complete rotation around a star.

EXCEPT ...

Wolfgang posted "One year=365 days; 1 day= complete rotation of a given planet around its axis,One time."

This does make it a math question.

Edited April 19, 2011 by JAPrufrock

[Guest]

is to trick you into considering the speed in which one would travel if one were standing on the outer edge of each planet (the crust). If that speed were the same,as the puzzle is designed to make you think, then the LE baby would be younger and the SE baby older. However, as the puzzle states that the speed of rotation around the axis is the same, this means that they complete a rotaion (a day) in the same amount of time. Hence a day on earth is the same length as a day on either LE or SE. And each baby is the same age.

If the crust speed were the same as maurice mentions, then LE would not make as many rotations(days), and SE would make more rotations(days), and both babies would still be 15 years old, but the LE baby would be fewer days old, and vice versa for the SE baby. This is because a year on LE would have fewer than 365.242 days while a year on SE would have more, but per the OP requirement that the time for the planet to travel around the sun (a year) is the same, they would still be 15 years old.

Now the fun part: Because it is stated that the rotational velocity is the same, the velocity of the crust is actually greater for LE and less for SE. So on each of there respective planets each baby would be precisely 15 years old; however, per Einsteins special theory of relativity, when all viewed in the same reference frame, the baby from LE would have lived the shortest amount of time while the baby from SE, the longest. I guess I should mention that the actual time difference in there life would be so incredibaly imperceptable that it really doesn't matter. Even if a fourth baby was born at the same time, completely motionless, in an abolute reference frame and just watched as the 3 earths traveled around their 3 suns 15 times, even the relatively large velocities of the suns moving in their Milky Way galaxies and the galaxies moving in space would only cause the 3 babys to be a couple minutes "younger" than the 4th baby.

[Guest]

as an aside on this problem, I don't think that the described system would be plausible, as a planet twice the size of earth would be sucked into the sun and out of orbit, and one half the size of earth would be flung away from the sun, given equal speeds and starting distances. I guess the physics don't bear too much investigation.

How was that for geekiness?

[benjer3]

as an aside on this problem, I don't think that the described system would be plausible, as a planet twice the size of earth would be sucked into the sun and out of orbit, and one half the size of earth would be flung away from the sun, given equal speeds and starting distances. I guess the physics don't bear too much investigation.

Actually, orbit speed is independent of the mass of the satellite, as the increase in gravity is balanced by the decrease in acceleration due to greater inertia. I figured that out doing a lab in astronomy. It's pretty cool, though.

[Guest]

Note:

One year=365 days

1 day= complete rotation of a given planet around its axis,One time

If the crust speed were the same as maurice mentions, then LE would not make as many rotations(days), and SE would make more rotations(days), and both babies would still be 15 years old, but the LE baby would be fewer days old, and vice versa for the SE baby. This is because a year on LE would have fewer than 365.242 days while a year on SE would have more, but per the OP requirement that the time for the planet to travel around the sun (a year) is the same, they would still be 15 years old.

Now the fun part: Because it is stated that the rotational velocity is the same, the velocity of the crust is actually greater for LE and less for SE. So on each of there respective planets each baby would be precisely 15 years old; however, per Einsteins special theory of relativity, when all viewed in the same reference frame, the baby from LE would have lived the shortest amount of time while the baby from SE, the longest. I guess I should mention that the actual time difference in there life would be so incredibaly imperceptable that it really doesn't matter. Even if a fourth baby was born at the same time, completely motionless, in an abolute reference frame and just watched as the 3 earths traveled around their 3 suns 15 times, even the relatively large velocities of the suns moving in their Milky Way galaxies and the galaxies moving in space would only cause the 3 babys to be a couple minutes "younger" than the 4th baby.

You overlooked this note in the OP defining a year. True they will have lived the same revolutions around the sun, but as you state on LE they will have lived fewer days thus fewer years, thus not as many years old. Opposite for SE

[Guest]

You overlooked this note in the OP defining a year. True they will have lived the same revolutions around the sun, but as you state on LE they will have lived fewer days thus fewer years, thus not as many years old. Opposite for SE

quote name='maurice' date='19 April 2011 - 07:00 PM' timestamp='1303254015' post='276939']

For those turning this into a word problem, please stop. Wolfgang defined a year, and it ain't a revolution around a star ... it's 365 days, where a day is a revolution around an axis. Stop applying logic and Newtonian physics and start doing math.

Edited April 20, 2011 by JAPrufrock

[Akriti]

well if they are moving with same speed around same sun then all should have equal ages...........

But if this has something to do with calculations then i might be wrong as well

[Guest]

Bigger planet 7 1/2 yrs old and the smaller planet is 30 yrs old.

[fabpig]

The thing that needs defining is "AT THE SAME SPEED".. Des this mean revolutions/time period, or distance travelled at surface/time period.

[Guest]

For those turning this into a word problem, please stop. Wolfgang defined a year, and it ain't a revolution around a star ... it's 365 days, where a day is a revolution around an axis. Stop applying logic and Newtonian physics and start doing math.

Agreed about the definition of a year, but even without applying any funny business your answer is still wrong

Wolfy also states that they rotate around the axis at the same speed. Thus a day on each planet is the same amount of time. Thus each baby is the same age.

edit - @efpy, I'm pretty sure the implication is rev/s as the OP states that they rotate about their axis at the same speed.

Edited April 20, 2011 by maurice

[Guest]

If there are three people on a merry-go-round, one in the center, one on the outside edge and one inbetween the other two and you spin the merry-go-round will every person make the some number of rotations or will the person on the outside make less rotations? Or better yet imagine a golf ball, a baseball and a basketball with a rod going through their axes. If you spin them they all make the same number of rotations. If surface speed, or circumference around the axis made a difference then wouldn't the location on the planet change the length of a day? As you move toward the poles the distance travelled each rotation shrinks.

[k-man]

We normally don't measure the age of people down to seconds, so in the general sense all three will be the same age. However, if measured to a second the child on SE will be a few seconds older and the child on LE will be a few seconds younger than the child on Earth.

Consider twins born at the same time and one of the twins placed in a satellite orbiting the Earth in sync with the Earth rotation. It's effectively pinned above a particular point on Earth. The time on the satellite moves slower than on the ground, so the twin on the satellite will be younger. That's what's happening with the child on LE.

[Guest]

If there are three people on a merry-go-round, one in the center, one on the outside edge and one inbetween the other two and you spin the merry-go-round will every person make the some number of rotations or will the person on the outside make less rotations? Or better yet imagine a golf ball, a baseball and a basketball with a rod going through their axes. If you spin them they all make the same number of rotations. If surface speed, or circumference around the axis made a difference then wouldn't the location on the planet change the length of a day? As you move toward the poles the distance travelled each rotation shrinks.

The person on the outer edge of the merry-go-round would have further to go but would still make the rotation in the same amount of time. They would go faster, but their day would be the same amount of time. So the length of the day would not change as you moved away from the axis, so long as the speed that one rotates around the axis remains unchanged.

[Peekay]

I guess the problem boils down to a simple definition. By "speed" do we mean "linear speed" or "angular velocity"?

[Guest]

I guess the problem boils down to a simple definition. By "speed" do we mean "linear speed" or "angular velocity"?

I agree. However, the OP states that the planets rotate about the axis at the same speed. Speed of rotation is usually meant to mean angular velocity.

edit - mayhap Wolfy will clarify if he meant linear speed.

Edited April 20, 2011 by maurice

[Guest]

Agreed about the definition of a year, but even without applying any funny business your answer is still wrong

Wolfy also states that they rotate around the axis at the same speed. Thus a day on each planet is the same amount of time. Thus each baby is the same age.

edit - @efpy, I'm pretty sure the implication is rev/s as the OP states that they rotate about their axis at the same speed.

You're confusing speed with time per rotation. That's like saying I can travel from New York to Chicago in the same amount of time as New York to L.A., as long as I'm traveling at 55 MPH the whole way.

Hmmm ... just got your analogy; since the rotation is, for all intents and purposes, on the axis (not the surface), I see where you're going. But, if speed is measured at the surface, rather than the axis, the rotational time would be double and half by definition.

Edited April 20, 2011 by JAPrufrock

[Peekay]

If by "speed" we mean "angular velocity" then all planets will take the same time to rotate about their axis. The "day" will be the same and hence the "year". All of the babies would be 15 years old.

If, however, we are talking about "linear speed" or "surface velocity": the smaller planet would then rotate twice as fast and the larger planet half as fast. So, in the same amount of time (15 Earth years), the smaller planet will have twice the number of days, hence twice the number of years. So the age of the baby will be 30 years. Similarly, for the bigger planet, the age would be 7.5 years.