Space 2004 HSC Q19 A) (1 Viewer)

[cybob101]

Can someone show me how they did this? i can't figure it out

 

[Dumbledore]

it might be helpful to show the question, or is my computer failing again?

 

[anom1ly]

i've looked at the question, what is it specifically your having trouble with?

 

[Dumbledore]

ehh crap, i looked at it and got stumped 2...
i know the earth will be about opposite in its orbit as ~half a year passes, but the position of mars is harder to figure out without knowing the relative radius of orbit in comparison to the earths as further out objects orbit slower

 

[anom1ly]

ehh crap, i looked at it and got stumped 2...
i know the earth will be about opposite in its orbit as ~half a year passes, but the position of mars is harder to figure out without knowing the relative radius of orbit in comparison to the earths as further out objects orbit slower

i havnt seen the marking criteria, but i think your reading into it too much.
its only asking for approximate positions, so its safe the say that earth will be ahead of mars. other than that, and the trajectory of the satellite, im not sure if it needs anything else.

 

[cybob101]

question is on board of studies. with the given information all i can figure out is that mars has changed position less than 180degrees. i don't think that would cut it. the markoing criteria said 1/3 orbit, where did they get it from?

 

[Dumbledore]

i don't suppose the radius of mars is on the physics data sheet? if we knew it as a % of the earths radius, we could use keplars 3rd law to determine the orbital period... other than that, no idea

 

[anom1ly]

question is on board of studies. with the given information all i can figure out is that mars has changed position less than 180degrees. i don't think that would cut it. the markoing criteria said 1/3 orbit, where did they get it from?

i wouldn't worry too much about it. most teachers would accept anywhere in the 1/3 ballpark.

 

[Dumbledore]

actually forget it, u need the mass aswell

 

[Dumbledore]

i wouldn't worry too much about it. most teachers would accept anywhere in the 1/3 ballpark.

i hope thats ok.. if i were to do this question i wouldn't have put 1/3 though, all i would know is its less

would they accept like 2/3 or something?

 

[cybob101]

hows this i think this might work....
keplers law of periods= (R^3)/T^2=k if orbiting around same centre(sun).......
using a ruler radius of earths orbit=2.5 mars=4.3 period of earth = 1
so (2.5^3)/1^2 =15.625=(4.3^3/t^2) rearrange to 15.625/(4.3^3)= t^2=0.19652.....
sqr root=0.4433

 

[cybob101]

um...2/3 is bigger than 1/2

 

[Dumbledore]

um...2/3 is bigger than 1/2

lol i meant 2/3's of the distance of the orbit travelled by the earth >.< i guess thats 1/3 then though

 

[Dumbledore]

hows this i think this might work....
keplers law of periods= (R^3)/T^2.......
using a ruler radius of earths orbit=2.5 mars=4.3 period of earth = 1
so (2.5^3)/1^2 =15.625=(4.3^3/t^2) rearrange to 15.625/(4.3^3)= t^2=0.19652.....
sqr root=0.4433

i seriously don't think u would ever use a ruler in the physics exam, the diagram is definatly not drawn to scale as the sun takes up like 90% of the volume in the solar system

also i know its close but the mass of the earth is not exactly the mass of mars which would make a slight difference as keplars law is not independant of mass

 

[TranscendK]

actually, keplar's law is independant of mass. its just dependant on the mass of the central object the sun.

 

[youngminii]

Easy. As Dumbledore said, Earth will be around halfway through it's orbit in half a year, so it'll be somewhere on the opposite side.

also i know its close but the mass of the earth is not exactly the mass of mars which would make a slight difference as keplars law is not independant of mass

I can't believe you just said that.
As TranscendK said, Kepler's Law of Periods is completely independent of the mass that's doing the orbiting. Now since Mars is further away, r is greater which means t will also have to be greater to keep the value constant (r^3/T^2 = GM/4pi) which means Mars will have a greater period, which means that it won't have orbitted as much as Earth. So it'll be somewhere around the middle of half an orbit and where it is now, which is around 1/4 or 1/3 of it's orbit. Tada, there's your answer.

Oh and the satellite will obviously be launched in the direction of Earth's motion to gain relative velocity, but you have to show it exiting Earth in a sort of parabolic motion until it 'leaves' its gravitational field.

Also, I do believe they are moving anticlockwise and this is the bit where it gets tricky (if I'm right). Imagine the planets are moving clockwise. Since Earth orbits faster than Mars, Mars won't catch up to Earth (as in be aligned to the Sun), and so Earth will have to do a whole circle and finally catch up to Mars heaps later. You're only given a 6 month window where the satellite is launched. But as you SHOULD know, satellites are always launched to gain relative velocity from Earth's relative motion to the sun. Now if it's moving clockwise, then how is it going to launch a satellite in the clockwise direction and have it land on Mars? No, it has to be launching the satellite in the opposite direction, am I right? (We aren't considering the rotational velocity of the Earth here). So if it's launching the satellite in the opposite direction, then that has to be the direction the Earth is moving so that the satellite can gain the relative velocity and hence both planets are moving anticlockwise.

I may be wrong in that last bit, 'cause it seems overly complicated and there must be a reason they give the North Pole.. I just can't spot it..
Either way, it's either got to do with Earth's relative velocity to the Sun or Earth's rotational velocity.

 

[k02033]

The earth spins anti clockwise when viewed from the top, looking at its north pole.
And you can get an exact answer for the 1st part, in terms of angular displacement.

= angular displacement of earth



= angular displacement of mars

= period of mars in days

 

[Dumbledore]

yes i can't believe i said that either, i just looked at the forumla and was used to doing calculations on objects orbiting the earth that i forgot its not always the earth mass in the calculation. hopefully i don't do something incredibly stupid like that in the hsc

 

[Dumbledore]

The earth spins anti clockwise when viewed from the top, looking at its north pole.
And you can get an exact answer for the 1st part, in terms of angular displacement.

= angular displacement of earth



= angular displacement of mars

= period of mars in days

the part we were discussing was how to determine the period of mars though

 

[k02033]

do they give your radius of mars orbit?