Engineering Answers

In the optical transmission, a rectangular waveguide with a = 2b = 4.8 cm is filled with Teflon (r = 2.11, loss tangent of 3 X 10-4) is used. Assume that the walls of the waveguide are coated with gold (σc = 4.1 X 107 S/m) and that a TE10 wave at 4 GHz propagates down the waveguide. Compute the value of attenuation due to conduction and ohmic losses.

The James Webb Space Telescope (JWSP) was finally launched into space on December 25, 2021,

and is about to become one of the most important scientific instruments of our time. Name the

major components of the JWSP shown in the figure below:

The James Webb Space Telescope is positioned around 1.5 million kilometres from the Earth on

the side facing away from the Sun. The telescope remains at this distance and orbits around the

Sun with the Earth’s orbital velocity.

(a) Why is it important to position the JWST behind the Earth?

(b) Determine the angular velocity ω of the telescope as it orbits around the Sun.

The centrifugalFω and gravitational forceFG are acting on objects orbiting the Sun: F = Fω−FG

(c) Based on this, how much should the telescope accelerate towards or away from the Sun?

(d) Why is the orbit of the telescope stable nonetheless? What otherforces need to be considered?

Neutron stars are some of the densest objects in the universe. They form during supernova ex-

plosions and are very small compared to other astronomical objects. You can assume 5 x 1017

kg/m3 as the average density of a neutron star. The Earth has a total mass of about 5.97 x 1024 kg.

What would be the diameter of the Earth if it had the density of a neutron star?

Assume that a gravitational anomaly in the solar system has shied afield of asteroids into Earth’s

orbit, and the field is now moving directly towards Earth. The asteroid field has a density of ρ

(asteroids/volume), and each asteroid has an average mass of m. The asteroid field stretches

over a distance d in Earth’s path. Assume that the Earth moves with a velocity of v, the asteroids

with u, and that v  u. Let R be the radius of the Earth. The Earth collides with the asteroid field:

v u

Show that the slow-down ∆v of the Earth due to the asteroid collisions is given by:

∆v = v



1 −

1

1 + πR2dρ m

M

The electromagnetic spectrum contains various types of radiation with dierent properties. The

James Webb Space Telescope is not like an optical telescope at home and does not capture visible

light; instead, it observes the sky in the infrared spectrum.

Explain what infrared radiation is and answer the following questions: How is infrared radiation

dierent from visible light? Why does the JWST observe infrared light, and what are the scientific

advantages for astronomers?