Physics HL Satellite Task - Portfolio HELP

[SwedishPersian]

Hi we got a satelite task for our portfolio and i was wondering if anyone has done it. Its only required to be in the portfolio so it doesn't have to be that fancy, but i still need some help with getting started since I really don't know how to do it. We arent given any firgures and Task 1 should be the "easiest". Then for task 2 and 3 we're suppose to make up our own figures. Here are the tasks:

Task 1:

The IB has decided to launch a geosynchronous communication-satellite. Calculate the radius of the satellite's orbit.

Task 2:

Describe the lauch process, and calculate the amount of fuel needed to put the satellite into its orbit.

Task 3:

The IB has realised that fuel is expensive. They would like to know the kinetic energy, the gravitational potential energy and the total energy of your satellite for different orbital radii.

Please note that this is not the energy situation during the launch, but for different orbits (e.g transitionary orbit) where the satellite is moving with a constant speed and the engines are shut off.

[sweetnsimple786]

Ooh I remember doing something like this last year. Okay so you're using mechanics related to gravitation & circular motion.

I'll try to help you through this, but I won't give you answers.

What have you done to start for task 1? Hint. F=ma. Gravitation. Circular orbit. Plug stuff in!

[SwedishPersian]

I actually managed to solve task 1 by considering the circular motion and gravitational force formulas:

mv^2/r = GmM/r^2

v^2 = GM/r v = 2(pi)r/T T =period

(2(pi)r/T)^2 = GM/r

r^3 = GMT^2/4(pi)^2

replacing G, M (mass of earth) and T (peroid of earth [24 hrs]) we get:

R ~ 42000000 meters

its task 2 and 3 which ineed help with getting started on. what fuel can i use, how much do i have to investigate in terms of energy density and accounting for mass loss ass the fuel is burned etc.

[sweetnsimple786]

So you're comfortable describing the launch. Alright well for fuel, I'm not sure how much IB expects. What I'd be asked for would be the change in energy and things like that. They wouldn't ask for fuel because that'd require research. So I'd say U = -W = -GMm (1/r1 - 1/r2) I don't know how to convert energy into fuel. I'd assume it was asking for energy. When I looked the concept up, I found this http://www.physicsfo...php/t-9033.html and http://exploration.g...ket/rktpow.html The only place I've dealt with energy density is electrostatics and capacitance, so sorry. And the way my teacher explained the virial theorem is that it's used for a lot of things we wouldn't get into unless we were taking astrophysics, but it's like PE = -2(KE) in a system like this. If you've been dealing with that kind of stuff, then you'll know what to do with it more than I do If you've never seen that before, sorry. For 3 they want general formulas, right? You can find the velocity of the satellite using what you did to find the radius, so the KE shouldn't be too hard. I got something to the third order of magnitude for just the velocity. There's already a formula for it, and the total is KE + U. I guess I'm missing something if this is supposed to be the most difficult. I'd use calculus, but these formulas have already been derived.