APM3713
Assignment 3
Due 2025
, APM3713 Assignment 3 (2025):
1 Question 1
Problem Statement: In the future, NASA will launch its first manned mission to
Pluto. The distance between Earth and Pluto is approximately 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. You may express the distance as 4c · hour.
Questions:
(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: Use the basic kinematic relation The distance in the Earth frame is given
by:
d = 4c · hour
The spaceship travels at a constant speed:
v = 0.4c
Using the formula t = vd , we compute:
4c · hour 4
t= = · hour = 10 hours
0.4c 0.4
1
Assignment 3
Due 2025
, APM3713 Assignment 3 (2025):
1 Question 1
Problem Statement: In the future, NASA will launch its first manned mission to
Pluto. The distance between Earth and Pluto is approximately 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. You may express the distance as 4c · hour.
Questions:
(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: Use the basic kinematic relation The distance in the Earth frame is given
by:
d = 4c · hour
The spaceship travels at a constant speed:
v = 0.4c
Using the formula t = vd , we compute:
4c · hour 4
t= = · hour = 10 hours
0.4c 0.4
1
