homer's physics corner

[Homer]

Why doesn't the gravitational field of earth do any work on the satellites? Wouldn't it like pull them down? 

[paulsterio]

Why doesn't the gravitational field of earth do any work on the satellites? Wouldn't it like pull them down? 

They do not do work on satellites, as there's no change in energy. However, the force pulls them towards the centre, if they didn't the satellites would just float away into space and not orbit the earth.

Think about it this way, you throw a ball really hard, it flies far away, but think about it, it doesn't fly straight, in fact, it flies on a curved path, similar to the Earth's own curvature.

Throw it a little harder and it flies a little further.

Throw it harder again and it'll fly even further.

Now if you were superman, you could just thrown the ball and it would just follow the curvature of the Earth all the way around and hit you in the ass.

Now imagine if you were't there blocking it's path, that's right, it would just orbit around the Earth forever and ever like a satellite.

P.S. Try the ATARNotes Physics book - it'll explain this + most other physics concepts in a lot of detail.

[b^3]

I'm a little rusty here but in this sense we have work=force*displacement (in the direciton of the force). If we have a purely circular orbit as we come across in vce physics, then there is no displacement in the direction of the force, since that displacement is towards the center of the earth and the satellite is not moving further away or closer since for the circular orbit we have a constant radius. This also means our Gravitational potential energy of the satellite will be constant, and so will be the kinetic energy of the satellite. i.e. GPE+K=constant. Thus the energy of the system is not changing, so no work is being done on the satellite by the earth's gravitational field.

We should also note that this is a very simplified problem. In the context of real life, the orbit won't be perfectly circular, and over the course of time and due to orbital decay, the 'height' of the orbit will slowly decrease as the (low number of) particles that are still up there (I'm talking around ISS orbital levels) does bring the satellite down a little. Hence why every so often the ISS has to be boosted up a little (or to avoid dangerous other bits of junk floating around up there).

[Homer]

Thanks guys! But I'm still a little confused. Paul as you said that the force pulls it towards the centre, which other force keeps it from crashing into the centre? Also the answer states that "since the gravitation force of attraction between the earth and the satellites is always perpendicular to the satellites velocity, the speed of the satellite remains constant and therefore its change in kinetic energy is zero." I am not sure what that means either :-/

[Homer]

also why is it not possible to place a satellite in orbit so that it is always directly over Melbourne?

[b^3]

Thanks guys! But I'm still a little confused. Paul as you said that the force pulls it towards the centre, which other force keeps it from crashing into the centre? Also the answer states that "since the gravitation force of attraction between the earth and the satellites is always perpendicular to the satellites velocity, the speed of the satellite remains constant and therefore its change in kinetic energy is zero." I am not sure what that means either :-/

To keep an object travelling in a circular path, we need to have a force that is perpendicular to the direction that the object is travelling in, in order to change the direction that the object is moving in. Think of it this way, if you have a rock tied to the end of a string and you whirl it around you. To keep the rock moving in the circular path, you're applying a force towards you from the rock, as you're pulling on the string.

For the satellite to move in a circular orbit, we need this constant force towards the centre of the circle to be perpendicular. If it were not perpendicular then the speed would change as we would do work on the object, and well the balance of GPE and kinetic energy would be thrown out and so the height of the satellite would change, we would send it out of the circular orbit. If the speed is constant, then there is no change in kinetic energy, which for a circular orbit, GPE+K=constant, so the height wouldn't change either.

also why is it not possible to place a satellite in orbit so that it is always directly over Melbourne?

The only way to keep a satellite directly above a point on the earth is to put it in a Geostationary Orbit, where the period of the satellite matches that of the rotation of the earth, i.e. ther period will be one day. But the earth is spinning along an axis, so this orbit has to be above the equator, otherwise it will spin with the rotation of the earth, but it will be moving up and down the latitutudes of the earth (i.e. long N-S direction).

That wasn't the best explanation for it, but I hope it helps... would really help if I could draw orbit paths out on here..

EDIT: What I'm trying to get at with the last bit is say with the diagram below, we can have the first three options, but we can't have the fourth. If we were to have the satellite always stay above melbourne, then we would have to have the fourth option, but we cannot actually get the fourth option, as to keep the satellite moving in this path, we need the net force to be towards the centre of the circle, but the net force is towards the centre of the earth, which in that case is not in the centre of the circle. Hence we cannot have that path and so we cannot have a geostationary orbit that stays above melbourne.


EDIT2: Fixed diagram

[paulsterio]

Thanks guys! But I'm still a little confused. Paul as you said that the force pulls it towards the centre, which other force keeps it from crashing into the centre? Also the answer states that "since the gravitation force of attraction between the earth and the satellites is always perpendicular to the satellites velocity, the speed of the satellite remains constant and therefore its change in kinetic energy is zero." I am not sure what that means either :-/

The velocity is what keeps it in a circular orbit.

Think about it this way, we say that the force is always towards the centre, however, think about the object for a second, the direction of the force on it is constantly changing. It WANTS TO move off at a tangent to the circle, but the force pulls it towards the centre, think about having a straight line, if you bend it, you will eventually get a circle.

Crude explanation, but I can't think of a proper explanation right now that's not extremely long and requires diagrams.

[availn]

There is no force holding up satellites, the only force acting on them is gravity pulling them down. However, think of them as going sideways very quickly (at a constant velocity, no force is making them go sideways). Because they're going sideways, they gain a teensy bit of height. However gravity pulls them down, making them lose that bit of height, and making sure that the satellite always goes sideways to the earth so that it doesn't fly out into space. This happens constantly, so in reality, they don't gain or lose any height; they just orbit.

It is really the same reason our planets don't get eaten by the sun. Earth is falling towards the sun, but continually misses.

[Homer]

AWESOME! explanations, b^3, availn and Paul. The image makes it crystal clear! hehe

[Homer]

Gracie places a toy on the palm of her outstretched hand as she performs a jump on her trampoline. What is the apparent weight of the toy during the jump?

I dont understand why it is zero. I agree that it would be zero when shes going down, but when she is going up wouldn't it be something else?

[paulsterio]

Gracie places a toy on the palm of her outstretched hand as she performs a jump on her trampoline. What is the apparent weight of the toy during the jump?

I dont understand why it is zero. I agree that it would be zero when shes going down, but when she is going up wouldn't it be something else?

It wouldn't be zero when she's accelerating at anything other than 10m/s^2 down.

So you're right, when it's accelerating up, it won't be zero.

[Homer]

this is what the book says "the toy and gracie's hand both move with an acceleration of 9.8 ms-2 down and so the normal force on the toy is zero"

[#1procrastinator]

apparent weight is equal to the normal force

[availn]

this is what the book says "the toy and gracie's hand both move with an acceleration of 9.8 ms-2 down and so the normal force on the toy is zero"

I think the book is referring only to when they are moving down, and not up. But yeah, it could have been worded better.

[Homer]

I'm having trouble understanding the concepts of apparent weight and weightlessness.
Suppose the normal force was greater than the gravity force would that mean the the person would feel lighter or heavier? also what happens to the apparent weight when a person is traveling in a lift? Thanks