Sending an object to space from earth at different places

[shotme100]

Homework Statement

I have an assignment that I need help with. It asks if Australia is a viable place to launch rockets from. Doesn't say what type or anything like that. I have worked out the speed of the person relative to Earth in a few different spots so I can compare. I am aware that I can not use velocity for this to calculate how fast it would go during the take off. Is there a way to say I need this much energy or speed to get to this height (2000km) (low-earth-orbit) with an object of let's say 200kg? If so how would I go about caculating this all and how would I say I needs this much energy to get to this? I saw that someone on her posted about something similar but i wasn't sure.. I also was wondering how I can use the Earth's relative speed and use that with the speed of the take off or energy that can be calculated? Like if I say its going to need x amount of speed to get to 2000km which i don't think I can say because during the flight the mass with constantly change as the object is burning it. So if I then say it needs x amount of energy how can i factor in the speed I already have from Earth with the x amount of energy?

Sorry if this is a bit messy.. I'm not very good at physics and need some help :)

 

[Simon Bridge]

You know where rockets are launched from don't you?
Why is that a good place? (Research.)

 

[shotme100]

Yes but we have to show how it uses less fuel and stuff like that. It will be better at the equator because you can use the Earth's rotation to your advantage more than you could near the pole. I'm just trying to work out how I can work out what speed or energy is required to get it to a specific orbit. So I can compare

 

[Bandersnatch]

You can and should think in terms of speed, rather than energy, I reckon.
If you can show that you need lower speed, it's easy to connect that with lower energy requirement.

What is the minimum speed a body needs to be imparted with at launch, to enter a circular orbit? (I'm sure you know about escape velocities.)

 

[shotme100]

I do, but will it work? Because the mass will constantly be changing due to the burning of the fuel

 

[voko]

Russia's Plesetsk Cosmodrome is at 63 degree North. Australia's southern extremity is at 55 degree South.

This alone means that Australia is "viable". Unless you have more specific criteria, we can't help you.

 

[Simon Bridge]

What level is this supposed to be at?

The energy needed to get to a specific distance can be worked out from the gravitational potential energy equation. However, that won't put the object in orbit. To be in orbit the object needs a particular angular momentum... but notice that the Earth is spinning, so there is an initial angular momentum from being on the surface.

You'll find these things discussed when you research why certain places are chosen as launch sites.
Like voko shows you - you can compare them.
i.e. http://en.wikipedia.org/wiki/Cape_Canaveral#Rocket_launch_site

 

[Bandersnatch]

You can show how much more fuel a rocket sent out from Australia needs when compared to one launched from the equator.
First, show how to calculate the escape velocity. Then the Earth rotation speeds for both, lattitudes. Then use the Tsiolkovsky rocket equation to calculate the ratio of fuel mass requirements for a given rocket design(i.e. same exhaust velocity).
http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation
Remember to mention the assumptions used in the calculations - no drag and orbit at surface level.

If it's not supposed to be rigorous, you can just use pre-calculated values to make the same argument.


Finally, as others said, the viability is hardly a yes/no question, it's all a matter of cutting the costs.