Question

The starship *Enterprise* leaves a distant earth colony,
which is nearly at rest with respect to the earth. The ship travels
at nearly constant velocity toward earth. When the
*Enterprise* reaches earth 1.02 y has elapsed, as measured
on the ship. Clocks in the earth's reference frame show that the
voyage lasted 2.89 y.

How far from earth is the colony, as measured in the reference
frame of the earth?

Unit: light years

(b) How far from earth is the colony, as measured in the reference
frame of the ship?

Unit: light years

Answer #1

By time dilation

more time = gamma *less time

2.79 = gamma * 1.02

gamma = 2.89/1.02 = 2.83333333

and we know

gamma = 1/ sqrt( 1- v^2/c^2)

2.83333333 = 1/ sqrt( 1- v^2/c^2)

**v≈0.935646 c**

Then the distance from the earth to colony as measured in theframe of reference of earth is

= 2.89y***0.935646 c =2.70401694 ly**

B)

And the distance from the earth to colony as measured inthe frame of reference of ship is

= 1.02y* **0.935646c =0.95435892 ly**

**Goodluck for exams Comment in case any doubt, will reply
for sure..**

The starship Enterprise leaves a distant earth colony,
which is nearly at rest with respect to the earth. The ship travels
at nearly constant velocity toward earth. When the
Enterprise reaches earth 1.10 y has elapsed, as measured
on the ship. Clocks in the earth's reference frame show that the
voyage lasted 3.29 y. How far from earth is the colony, as measured
in the reference frame of the earth?
(b) How far from earth is the colony, as measured...

The starship Enterprise leaves a distant earth colony,
which is nearly at rest with respect to the earth. The ship travels
at nearly constant velocity toward earth. When the
Enterprise reaches earth 1.03 y has elapsed, as measured
on the ship. Clocks in the earth's reference frame show that the
voyage lasted 3.26 y.
How far from earth is the colony, as measured in the reference
frame of the earth?
(b) How far from earth is the colony, as measured...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 8 minutes ago

asked 10 minutes ago

asked 31 minutes ago

asked 51 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago