I have two questions I'm a bit confused on...(adsbygoogle = window.adsbygoogle || []).push({});

1st:

Ten days after it was launched toward Mars in December 1998, the Mars Climate Orbiter spacecraft (mass 629 kg) was [tex]2.87 \times 10^{6} km[/tex] from the earth and traveling at [tex]1.20 \times 10^{4} km/h[/tex] relative to the earth.

a.) At this time, what was the spacecraft's kinetic energy relative to the earth?

b.) What was the potential energy of the earth-spacecraft system?

Common sense will tell me that I can find one, once I figure out the other... Now, the first time I approached this, I used the law of conservation of energy... But don't think I'm going the right way in finding the correct initial kinetic and potential energy. For this type of problem, although the terms are different for finding potential energy, is the method to find kinetic energy still the same:

[tex]K = \displaystyle{\frac{1}{2}}mv^2[/tex]?

If this is true, does this mean that the initial velocity is [tex]1.20 \times 10^{4} km/h[/tex]?

I understand at 10 days, the orbiter is travelling that fast... But that speed can't be constant, can it? Wouldn't it be decreasing as it escapes earth's gravitational pull?

How would I use the velocity at 10 days to find the kinetic energy? If I simply plug in the given velocity into the kinetic energy formula, I get some insane number that can't be correct...

Any pointers??

2nd:

For a problem,

I found the speed of a spacecraft at which it would crash into earth, assuming it were a distance of [tex]\infty[/tex] away, and no other astronomical object's gravitational pull affected it.

[tex]s_{e}=\sqrt{\displaystyle{\frac{2M_{e}G}{R_{e}}}}[/tex]

And this is what I was then asked:

Now find the spacecraft's speed when its distance from the center of the earth is [tex]R=\alpha R_{\rm e}[/tex], where [tex]\alpha \ge 1[/tex].

Express the speed in terms of [tex]s_{e}[/tex] and [tex]\alpha[/tex].

So, this appears to be a simple algebra problem. And after a bout of apparently incorrect algebra, I got

[tex]s_{\alpha}=\displaystyle{\frac{s_{e}}{\alpha}}[/tex]

Eh... What did I do wrong here??

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# Mechanical Energy of a Spacecraft

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