APM3713 Assignment 3 2025 (Chapter 1&2) Due 2025.

APM3713

Assignment 3

ACCURATE SOLUTIONS

Due 2025

, APM3713 Assignment 3 2025: Question 1
Problem Statement: In the future, NASA will launch its first manned mission to
Pluto. The distance between Earth and Pluto is about 4 light-hours, meaning it takes a
photon (traveling at speed c) 4 hours to travel from Earth to Pluto. The spaceship
travels at a constant speed of 0.4c to Pluto. Assume Earth and Pluto are stationary
with respect to each other. The hint states that the distance can be written as 4c · hour.
(a) What is the duration of the journey to Pluto according to people on Earth? [4]
(b) How long will the journey take according to the astronauts on the spaceship? [4]
(c) What will the distance of their journey be according to the astronauts in the
spaceship? [3]
(d) During the journey, the astronauts communicate with the control center on Earth
by sending signals at a frequency (measured in the spaceship’s rest frame) of 300 MHz.
To what frequency must Earth receivers be tuned to receive these signals? [3]


Part (a): Duration of the journey according to people on Earth

Step 1: Understand the Earth’s frame and given quantities In the Earth’s
reference frame (assumed to be inertial), the distance to Pluto is given as 4 light-hours,
expressed as d = 4c · hour, where c is the speed of light. The spaceship travels at a
constant speed of v = 0.4c. To find the duration in Earth’s frame, we use the formula
distance
t= speed
.
Step 2: Calculate the time in Earth’s frame The distance is:


d = 4c · hour


The spaceship’s speed is:
v = 0.4c

The time taken is:
d 4c · hour
t= =
v 0.4c
The c terms cancel:
4
t= · hour = 10 hours
0.4


1