Physics Dot Point 1.6.4 part (b) (2 Viewers)

[freezeice04]

Physics Dot Point 1.6.4 part (b)

I don't understand how to do this. Heres the question:

Satellite X has its orbit around Earth changed from an altitude of 10,000km to 20,000km. Satellite Y has its orbit around Earth changed from an altitude of 20,000km to 30,000km. Both satellites have a mass of 500kg.

Calculate the amount of work done on each satellite.

Maybe somethings wrong with my calculations? But the answer says something different to mine. I worked out the change in GPE for each and still didn't get the answer.

 

[ohexploitable]

The answers are wrong.

See here: http://community.boredofstudies.org/showthread.php?t=253356

But if you do the calculations they are different from the answers,

Work done on X = 4.63*10⁹ http://www.wolframalpha.com/input/?....67*10^-11*((500*6*10^24)/(6378000+10000000))
Work done on Y = 2.09*10⁹ http://www.wolframalpha.com/input/?....67*10^-11*((500*6*10^24)/(6378000+20000000))

 

[freezeice04]

Ok Thanks! The next Question as well: 1.6.5 a)

Three spacecraft having masses m1>m2>m3 are in the same stable orbit around planet X. Compare their gravitational potential energies and justify your answer.

Isn't the GPE: m3>m2>m1 but the answers have it the other way around?

And god I spent so much time trying to figure out what I did wrong. I hate dotpoint :/

 

[ohexploitable]

 

[freezeice04]

But GPE is a negative value so doesn't mean the larger the negative value, the smaller it is?

 

[ohexploitable]

Alternatively,



Where m_i is the mass of the satellite.

The force required to place an object a certain distance away from the Earth varies directly with its mass. By the principle of conservation of energy, the kinetic energy required to place the object in orbit is equal to its gravitational potential energy. A greater mass requires a greater force and hence, greater energy.

 

[ohexploitable]

But GPE is a negative value so doesn't mean the larger the negative value, the smaller it is?

Yeah, I don't like this solution either, see my alternate solution.