# Physics

posted by .

Some spacecraft design uses a solar sail made of aluminized plastic. As sunlight reflects off the sail, radiation pressure drives the spacecraft outward away from the sun.

a. If the sail material has a density of 700.0 kg/m3, what is the maximum thickness of the sail for which the force due to radiation pressure exceeds the gravitational force on the sail?

b. If the collector's area is 2e6 m^2. its thickness is 1 μm, and the craft carries a 100.0 kg payload, what is its acceleration at the radius of the Earth's orbit?

• Physics -

You need to know the radiation pressure due to solar radiation. This varies with (1/R^2), but so does the gravity force.

The solar flux at the Earth's distance from the sun is about
I = 1300 W/m^2, as I recall. You'd better look it up yourself. Divide that by c for the momentum flux.

(a) Let the sail area be A. (This will cancel out) and the thickness be d. For a balance with radiation pressure,
A*density*d*G*M/R^2 = 2*A*(1300/c)*(Re/R)^2

I am sure you recognize G as the universal constant of gravity. A cancels out. So does R^2.

The factor of 2 assumes perfect reflection of all incident light, for the momentum change.

M is the mass of the sun and Re is the radius of the earth;'s orbit. Solve for d

b. Use
2*A*(1300/c)*(Re/R)^2 for the force on the sail and the appropriate mass for that sail thickness.
Then use a = F/m for the acceleration

• Physics -

Thanks drwls. I'm having trouble with part b though. What is R? For the appropriate mass, am I suppose to use the density times the thickness to get the mass of the sail and with that, add the mass from payload?

## Similar Questions

1. ### Physics

During 2004, japanese scientists successfully tested two solar sails. One had somewhat complicated shape that we shall model as a disk 9 m in diameter and 7.5 um thick. The intensity of solar energy at this location was about 1400 …
2. ### Algebra 2

Are a of a sail. The area in square meters for a triangular sail is given by A(x) = x2 + 5x + 6. a) Find A (5). b) If the height of the sail is x +3 meters, then what is the length of the base of the sail?
3. ### math 209

Area of a sail. The area in square meters for a triangle is given by A(x)=x^2 +5x +6. a.) Find A(5) b) if the height of the sail is x+3 meters, then what is the length of the base of the sail when area is x^2 +5x+6m^2?
4. ### calculus

Area of a sail. The area in square meters for a triangular sail is given by A(x) = x2 + 5x+ 6. a) Find A(5). b) If the height of the sail is x+3 meters, then what is the length of the base of the sail?
5. ### Physics

Some spacecraft design uses a solar sail made of aluminized plastic. As sunlight reflects off the sail, radiation pressure drives the spacecraft outward away from the sun. a. If the sail material has a density of 600.0 kg/m3, what …
6. ### Physics

A solar sail is used to propel a spacecraft. It uses the pressure (force per unit area) of sunlight instead of wind. Assume the sail and its spacecraft have a mass of 245 kg. If the sail has an area of 62,500 m2 and achieves a velocity …
7. ### Physics

Suppose you're an astronaut and you're sitting in a 6000kg space capsule riding on a 4000 m x 8000 m sail (whose mass is included in the 6000 kg). You're orbiting in the vicinity of a distant bright hot star giving off light with an …
8. ### maths

A speed boat at the shore wants to overtake a sail boat that is 3 km out at sea. If the sail boat is travelling away from the shore at 1.5km/hr, how fast should the speed boat travel to overtake the sail boat in 5 minutes fro the shore?
9. ### College Algebra

A sailboat has a triangular sail with an area of 20 square feet. The height of the sail is 6 feet more than the length of the base of the sail. Find the height of the sail.
10. ### physical science

John is using a pulley to lift the sail on his sailboat. The sail weighs 150 N, and he must lift it 4.0 m. How much work must be done on the sail?

More Similar Questions

Post a New Question