Welcome back, everyone. Hopefully, you had a chance to work this problem out on your own. So we're told in this problem that a spacecraft with reflective sail-like material may eventually be used for low-cost space travel. This is a real technology that's actually being used, and the science is sound. We're told that a 400-kilogram satellite near Earth is equipped with these super reflective sails.
I want to draw this out here. So what happens is those sails are going to capture sunlight from the sun, and it's going to generate a radiation pressure. So you have the sun like this, and then at some distance where the Earth is, you're going to have this satellite over here with big reflective sails like this. The sunlight that travels is going to hit those reflective sails, and it's eventually going to push them to the right. This is going to be a force from radiation pressure.
Eventually, what happens is that the satellite is going to pick up speed, and that's actually one way that we could generate large amounts of velocity for a spacecraft with very little fuel. You're only using the light from the sun.
The area of each of these reflective sails is 5,000 meters squared. So, in other words, the area is equal to 5,000, but what happens is the total amount of area is going to be twice of 5,000 because there are 2 of them, both completely reflective. So this total area is going to equal 10,000.
We are using our reflective radiation pressure equations and not our absorbing radiation equations, and the intensity of sunlight is approximately 1350. So let's figure out what the force that's exerted on the satellites is. We use the equation: F r e f l e c t e d = 2 × I A c where I is 1350, A is 10,000, and c is 3 × 10&sup8;. You should get F reflect ≈ 0.09 Newtons.
For the second problem, assuming that the satellite starts from rest, how fast is it moving after 1 year? We use the kinematic equation: V f i n a l = V i n i t i a l + a × t Given that V initial is 0, we find acceleration using F = ma, thus a = F reflect / m = 0.09 / 400 kg, giving us an acceleration of 2.25 × 10⊃-4 m/s². For t = 1 year × 365 days × 24 hours × 60 minutes × 60 seconds, calculate V final ≈ 7,100 m/s.
Even though the force is very small, after acting for a long time, it can produce significant velocity changes. This technology could send the satellite out, and years later, it would be traveling extremely fast out of the solar system. That's it for this one, folks. Let me know if you have any questions. I'll see you in the next video.