Question

HELP
In sunlight, the force on 2 sail, each of area 2km^2, is of the order of 10N each at a distance fro the sun equal to the Earth's orbital radius. Discuss the viability of using such sails to propel space vehicles. already in orbit, to reach the outer planets of the solar system.

Answer 1

@oOKawaiiOo help?

Answer 2

i dont know

Answer 3

The sails would provide a slow acceleration given the force of 1 AU (the distance from the Sun to the Earth). That force, however, would start to decrease as the ship moved further from the Sun. The force on the sales varies directly with the intensity of the light hitting the sales. The intensity of that light, unfortunately, decreases with the square of the distance to the sun. That means if the distance doubles to 2AU, the intensity and thus the force on the sales will fall by a factor of 4.

If the ship is on a trip to Mars, by the time the ship gets to Mars (1.5 AU), the force on its sales will have reduced by a factor of 1.8. If you want to go to Saturn(9.5AU) and visit one of its moons, then the force on the sails will have dropped by a factor of 90. Lastly, if you were intent on getting to Pluto (39.5 AU), the force on your sails will have dropped by a factor of 1560 to a paltry 0.013N, a force equal to about 3/100 the weight of a paperclip.

The good news is that on all of your trips, you'd be accelerating for your entire trip, something that rocket powered ships cannot do. That means you might arrive at your destination quicker than a rocket might. If you played your cards right and used a couple of planets or moons as gravitational slingshots, you could increase your speed even more.

Answer 4

woah thank you very much.

Can you help me with this question?
Why is the fact that light can transport linear momentum surprising ?

Answer 5

It's surprising because a photon has no mass. Linear momentum is generally defined as: p=mv where p is momentum; m is mass; and v is velocity. The momentum of a photon, however, is defined as:\[p=\frac{ h }{ \lambda } =\frac{ h \nu }{ c }\]where h is Planck's constant; λ is the wavelength of the photon; ν is the photon's frequency; and c is the speed of light. Even more surprising might be the fact that light can have angular momentum.

Answer 6

Thank you...I understand completely now. Since you mentioned the formula for the momentum of a photon, can you help me with this problem?:

By considering the equation p= E/c, show that the momentum of a single photon of yellow light of energy E for which the wavelength is 560nm, is about 10^-27 N s.

I've been stuck on this problem for a while.

Answer 7

The energy of a photon is given by:\[E=h\]where E is energy; h is Planck's constant; and ν is the photon's frequency.

If we substitute that equation for energy into the equation for momentum that you have we get:\[p=\frac{ h \nu }{ c}\]That's one of the expressions I gave earlier for momentum. That expression is equal to:\[p=\frac{ h }{ \lambda }\]For your problem you're given λ, so you only need to know Planck's constant to solve the equation. Planck's constant is:\[h=6.626\times 10^{-34}kg∙m ^{2}/s\]

Answer 8

Okay so I'm supposed to get back 10^-27 N s.
But, I'm not getting that.

Answer 9

I suspect that you need to convert 560nm to meters.

Answer 10

Okay. So I used the formula p= Planck's constant / wavelength in m and I got back the answer. Thanks!!