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Communications satellites. Communications satellites are used to bounce radio waves from the earth's surface to send messages around the curvature of the earth. In order to be available all the time, they must remain above the same point on the earth's surface and must move in a circle above the equator. (a) How long must it take for a communications satellite to make one complete orbit around the earth? (Such an orbit is said to be geosynchronous.) (b) Make a free-body diagram of the satellite in orbit. (c) Apply Newton's second law to the satellite and find its altitude above the earth's surface. (d) Draw the orbit of a communications satellite to scale on a sketch of the earth.

(a) 86400 s = 24 h (b) see explanation (c) 3.58$\times$10$^7$m (d) see explanation

Physics 101 Mechanics

Chapter 6

Circular Motion and Gravitatio

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Dibyajyoti G.

March 15, 2021

In january 2005 the huygens probe landed on saturn's moon titan, the only sattelite in the solar system having a thick atmosphere.Titan's diameter is 5150km, and its mass is 1.35×10^23 kg.The probe weighed 2520N on the earth

In january 2005 the huygens probe landed on saturn's moon titan, the only sattelite in the solar system having a thick atmosphere.Titan's diameter is 5150km, and its mass is 1.35×10^23 kg. The probe weighed 2520N on the earth.

Simon Fraser University

Hope College

University of Winnipeg

McMaster University

Lectures

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In physics, kinematics is the description of the motion of objects and systems in the frame of reference defined by the observer. An observer has to be specified, otherwise the term is meaningless.

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In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

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Communication satellites a…

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A communication satellite …

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A communications satellite…

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Communications satellites …

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Hello. In problem 37 we stood yet special type of satellite which are used for communications. And so those satellites must remain above the same point on Earth's surface on at all times. That means they have to rotate, seems cheetahs. The earth rotate. So in a once, you know that, um the question is, how long must take for communications. I'd like to make one complete orbit around Earth if the satellite has to remain at the same point on the earth's surface than it will, um, do one full orbit in the same time that the earth this one for tradition and that takes exactly 24 hours. And so in seconds, This is 6400 seconds. Now would be were asked me free body diagram of the satellite. So the only force that is that we actually consider here is the gravity from the earth. That's it for forces. We could also draw on dhe speed here, So there is a tangential speed and also an acceleration from the Earth. But in terms of forces, there's only F g. And so I didn't see this will become useful because they're telling us, applying Newton's second law to the satellite andan. With this, we will be able to find its altitude. So what is Newton's lie? Sigan Notice for some of forces equals mass times the exploration. So this there's only one force here play gravity and Grady's mg. So we have mg calls. Well, not not so fast. Not so fast. Mg. That's only a earth's surface Right here. Um, we're not on the surface of earth were in orbit, So we have to use the more general ah force of gravity, which is g m em. Two different masses over r squared over earth. This would be, um, and the mass of the satellite, and then the second mass would be it's mess. Okay, so we have this forest equal to M A because of Newton's second law. And here, since this is a circular, orbit the exploration. So the acceleration, eh? Is V squared over r. That whole thing's equal to m v squared over r. And this is actually what you have in it is fury in chapter 6.5, and ah, this is there just asking you in this problem thio to do the same thing they did, um page 176 so we can do it, Um, as well. And so basically, what's done here is that from those two parts of the equation, we extracts equation for speed, which is that this PC called square root off G times the mass earth's over our and are here is the radius orbit of the satellite, not the riches of the earth and not the altitude, either. It's really, um Hydra the earth here. And this is the satellite. This is the Regis are that we're considering. It's descends between the satellite and the center of the earth. So with this equation in mind, since one of the altitude will want you calculate the radius and from the Regis Weaken subject from the regis of the orbit, we can subtract the radius of the earth to get the altitude. So, um, using also the fact that V is two pi r Over tea, you can write r equals on DDE tee times, vite over to pyre. And then we have we will replace this equation for the year, so t over to Pie V is the square root of g m e over our But this we're not done here because we have are on this side and earned this side. So remember that square root of our is just arch times 1/2 So here it could have our times are when has equals the restaurant. And so those two together that's equal to our tree efs That's hole Well supplying exponents work now you have to some them. So this is our to the one rate. So one plus 1/2 history house and so d'oh final equation for the regis would be, um, to apply exponents of 2/3 on each side. And that's just one of the explore entry atthe on the left side just like that. So right, Duncan here are equals tea over to pie screwed of G mass of the Earth to the power of 2/3. We have all we need now, on this equation, the period is 86 1004 100 seconds. You have to use Siggins as the unit G is 6.6742 times 10 to the minus 11. And you didn't meet her square or killed him squared. And then we have to match the mass of the Earth. The mass of the earth is five point 97 times 10 to 24 kilograms. Okay, you So if you, um Philip What? All those numbers you end up with a regis of 4.2 Q times, 10 to 27 meters. This is only the radius of the orbit, right, Which I run here. And we know the Regis of the Earth as well. So Regis of the Earth is six point treat eight times tend to six years and then to find attitude, which, um, just write down this word here altitude. You have to do the Regis of orbit minus the Regis of the Earth. And so if she's affect those two numbers, you will get in altitude of, um treat 0.58 times, tended it seven meters and then in D. They're asking us to drop draw the same sketch I drew here but to scale because this is not to scale because I have no idea what the answer would be. Now we know the answer and his cheap point fire of eight times seven, and we want to compare it to 6.38 times, 10 to 6. So those are really big numbers. They're hard to imagine and hard to compare. One thing we can do to help us is divided by 10 to 6. So now we'll have, um, millions of meters. And this one is also its roughy 36 millions of Meteors. This one is rough e six means of meters so we can see that there's, ah times six difference between two. Um, so let's tread Earth gun right here. This is one Regis of the Earth orbit. It's six times big, six times to Regis of Earth that it won't to treat for 56 And this is where or satellite orbits the earth. So personally, I was impressed by how for it was I thought Sal eyes would be a lot closer to Earth. But in order for them to rotate to do a full rotation in 24 hours, they need to be that far. So yeah, it was a critical brown because it got too got us to learn about to get a sense of scale communications, satellite, how far they can be from the Earth

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