22 Jun Do not solve the following ques
Do not solve the following question numerically unless specifically asked to do so. The flux
from the Suns surface is given by LJ = 4pRJ
2 sTJ
4
, where TJ is the temperature on the Suns surface.
(a) [3] What is the incident luminosity from the Sun seen on Earths surface?
(b) [4] Only a part of the luminosity incident on Earths surface is reflected back. The fraction of radiation
reflected from Earths surface, or albedo, is given by A. The other part is absorbed and converted into heat,
which is then emitted as thermal emission from the planet. Write an expression for the luminosity absorbed
by Earth and the luminosity emitted by Earth. Assume Earth has had ample time to come up to thermal
equilibrium. Use the symbol Tsurf to represent the surface temperature of Earth.
(c) [3] Find an expression for the surface temperature of Earth, when the Earth is at thermal equilibrium. Note
that thermal equilibrium means that the amount of radiation absorbed by Earth is the same as the amount of
radiation emitted by Earth.
(d) [3] Calculate the surface temperature for Earth if A = 0.36. If Earths observed maximum temperature is 310
K, does the calculated temperature predict an accurate surface temperature? Explain.
(e) [3] Repeat the calculation to find the surface temperature of Venus (A = 0.76). Venus has an observed
maximum temperature of 750 K. Is the calculated surface temperature for Venus accurate? Why or why not?
4. [8 marks total] Problem 16 in Chapter Three of the text (page 72):
(a) [4] In the past, when the Moon was 0.25 as far from Earth as it is now, estimate how much more massive
Earths average tidal bulge was than it is today.
(b) [4] How much stronger was the net accelerating effect of this bulge on the Moon?
5. [5 marks total] It has been proposed that a spaceship might be propelled in the Solar System by radiation pressure,
using a large sail made of foil. The reflectivity of foil causes the radiation force to be twice what it is normally.
Calculate the area (in square kilometers) that the sail must be for the radiation force to be equal to the Suns
gravitational attraction. Assume that the mass of the ship and sail is 1500 kg and Q=1.1
6. [8 marks total] Problem 17 in Chapter Three of the text (page 72):
An early measurement of the outer radius of Uranuss rings was about 5.0 × 107 m from the center of the planet.
Compare this to the Roche limit for icy bodies near Uranus, using the expression derived here for touching
particles. What is the significance of this result? Would you expect Uranuss ring particles to aggregate into a
satellite?
7. [17 marks total] Consider a small dust grain of mass m = 4.19 × 10-3 kg and radius a = 1 cm, which becomes
separated from a parent body in a circular orbit a distance 2.5 AU fr
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