Constants In this example we will investigate the viability of using radiation p
ID: 2039447 • Letter: C
Question
Constants
In this example we will investigate the viability of using radiation pressure to propel a spacecraft. Suppose a spacecraft with a mass of 2.50×104kg has a solar sail made of perfectly reflective aluminized film with an area of 2.59×106m2 (about 1 square mile). If the spacecraft is launched into earth orbit and then deploys its sail at right angles to the sunlight, what is the acceleration due to sunlight? (At the earth’s distance from the sun, the pressure exerted by sunlight on an absorbing surface is 4.70×10?6Pa.)
SOLUTION
SET UP We sketch the situation in (Figure 1). Because our sail is perfectly reflective, the pressure exerted on it is twice the value given in the statement of the problem: p=9.40×10?6Pa. Before the sail is deployed, the spacecraft's net radial velocity relative to the sun is zero.
SOLVE The radiation pressure p is the magnitude of force per unit area, so we start by finding the magnitude F of force exerted on the sail:
F=pA=(9.40×10?6N/m2)(2.59×106m2)=24.3N
We now find the magnitude a of the spacecraft's acceleration due to the radiation pressure.
a=F/m=(24.3N)/(2.50×104kg)=9.72×10?4m/s2
REFLECT For this spacecraft, a square mile of sail provides an acceleration of only about 10?4g, small compared with the accelerations provided by chemical rockets. However, rockets burn out; sunlight keeps pushing. Even on its first day, the craft travels more than 3000 km in the radial direction, and on day 12 its radial speed exceeds 1 km/s.
Part A - Practice Problem:
A communications satellite has solar-energy-collecting panels with a total area of 2.0 m2 . What is the average magnitude of total force on these panels associated with radiation pressure, if the radiation is completely absorbed?
Express your answer to two significant figures and include appropriate units.
Constants
In this example we will investigate the viability of using radiation pressure to propel a spacecraft. Suppose a spacecraft with a mass of 2.50×104kg has a solar sail made of perfectly reflective aluminized film with an area of 2.59×106m2 (about 1 square mile). If the spacecraft is launched into earth orbit and then deploys its sail at right angles to the sunlight, what is the acceleration due to sunlight? (At the earth’s distance from the sun, the pressure exerted by sunlight on an absorbing surface is 4.70×10?6Pa.)
SOLUTION
SET UP We sketch the situation in (Figure 1). Because our sail is perfectly reflective, the pressure exerted on it is twice the value given in the statement of the problem: p=9.40×10?6Pa. Before the sail is deployed, the spacecraft's net radial velocity relative to the sun is zero.
SOLVE The radiation pressure p is the magnitude of force per unit area, so we start by finding the magnitude F of force exerted on the sail:
F=pA=(9.40×10?6N/m2)(2.59×106m2)=24.3N
We now find the magnitude a of the spacecraft's acceleration due to the radiation pressure.
a=F/m=(24.3N)/(2.50×104kg)=9.72×10?4m/s2
REFLECT For this spacecraft, a square mile of sail provides an acceleration of only about 10?4g, small compared with the accelerations provided by chemical rockets. However, rockets burn out; sunlight keeps pushing. Even on its first day, the craft travels more than 3000 km in the radial direction, and on day 12 its radial speed exceeds 1 km/s.
Part A - Practice Problem:
A communications satellite has solar-energy-collecting panels with a total area of 2.0 m2 . What is the average magnitude of total force on these panels associated with radiation pressure, if the radiation is completely absorbed?
Express your answer to two significant figures and include appropriate units.
Explanation / Answer
I suppose that we need to solve PART A of the problem.
The radiation pressure on the absorbing surface is 4.7*106 Pa as given
Hence for 2 m2 total sail area
Force on sail = Pressure * Area = 9.4*106 Newtons