How Does Jane Receive 30 Messages from Dick in the Twin Paradox Scenario?

[bilkul_king]

please help its urgent

hi

can someone please solve this paradox related to the twin paradox??
jane continues to be on Earth and dick goes to a planet 20 light years away at a speed of 0.8 c. Every year dick sends a message to Jane. Now for Jane due to time dilation the time taken by dick to reach the planet is 25 years and back to Earth another 25 years. Also the frequency the Jane receive the messages while dick is receding away should be equal to one message per three years and while he is coming back it should be equal to three messages per year. Now to due to length contraction dick feels that he is twelve light year away from the planet. Hence he should take 15 years to reach the planet and 15 years back to earth. That means he has sent out a total of 30 messages. Please explain tome how Jane receives these 30 messages.


Please note that all the units and formula e were in accordance with Einstein's special theory of relativity and the formula e and the results were according to the same. Please help me as this question is perplexing my mind since the last 51 hours.

Thanking you,



(LAKSHAY BEHL)

 

[jtbell]

Hint: Dick sends his 15th message at the turnaround point (at the distant planet). Assuming the message travels at the speed of light, when does it reach Jane (according to her)?

 

[bilkul_king]

I DIDN'T GET THAT.see
1) according to dick, while he receding for the 15 years he gets five messages in total in 15 yrs @ 1 msg per 3 yr
and while coming back he is receiving 3 messages per year and for 15 yrs, he will receive 45 messages
that mean a total of 50 messages which is same as the number of messages sent out by jane in 50 yrs wrt earth.2)
now if i perform the same calculations on jane, she should get 25*(1/3) messages from dick while he is receding and 25*3 messages while he is coming back.
but that does not amount to a total of 30 messages sent out by dean.PLZ PLZ PLZ PERFORM THESE CALCULATIONS FOR ME HERE.

AND IN A BOOK WHERE I FOUND THE QUESTION IS FOUND IT PUT AS:--

receding 25*(1/3)

because the planet is 20 lght yrs away jane on Earth continues to receive dick's msgs @ 1/3 per year FOR TWETY more years.

PLZ EXPLAIN HOW THIS STATEMENT IS VALID...

 

[robphy]

Doppler Effect

 

[bilkul_king]

why is no one replying?