Question

A space probe (mass m) is designed to explore the outer edges of the solar system. It is propelled by a solar sail, which is made of a large circular sheet of highly reflective fabric. Assume the sun radiated with power P.

1. How much could the propulsion be increased if the radius of the sail were three times larger?

2. Jupiter is about five times as far from the sun as the earth. When the probe reaches jupiter, how much would the propulsion have changed?

3. What minimum radius r would be required for the sail to overcome the gravitational pull of the sun if the probe is supposed to fly directly away from the sun? Let M be the mass of the sun. Hint: the gravitational force is given by GMm/R^2, where R is the distance from the center of the sun and G is the gravitational constant

Answer #1

The space probe is propelled by Sun because of radiation pressure exerted by it on the solar sail. Given that the solar sail is made up of circular sheet. The area is given as .

1) Propulsion is directly proportional to area. Therefore If the radius is increased three times the propulsion will increase 9 times.

2) The radiation pressure or the propulsion is inversely proportional to the square of the distance. Therefore if the distance is increased 5 times, the propulsion will decrease by 25 times.

3) Force exerted on an ideal sail having perfect reflectance is
equal to 9.08 uN/m^{2} (from Wikipedia). If the sail has a
radius r, then

Hence.

The escape speed from an object is v2 = 2GM/R, where M is the
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gravitational constant 6.67 × 10-11 m3 kg-1 s-2. What is the
approximate escape speed, in km/s, from the Solar System starting
from an orbit at 0.6 AU? In this case, the mass of the Sun, 2.2e+30
kg, can be used as the mass of the Solar system.

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