# Homework Help: Need conversion and specific heat?

1. Apr 10, 2012

It's not really homework its more of my own thing, but I don't know where else I'd put it

1. The problem statement, all variables and given/known data

category Main belt (Flora family)
Orbital characteristics
Epoch 6 March 2006 (JD 2453800.5)
Aphelion 2.594 AU (388.102 Gm)
Perihelion 1.825 AU (272.985 Gm)
Semi-major axis 2.210 AU (330.544 Gm)
Eccentricity 0.174
Orbital period 3.28 a (1199.647 d)
Average orbital speed 19.88 km/s
Mean anomaly 53.057°
Inclination 4.102°
Longitude of ascending node 253.2lllll18°
Argument of perihelion 129.532°
Proper orbital elements
Physical characteristics
Dimensions 18.2×10.5×8.9 km [1]
Mean radius 6.1 km[2]
Mass 2–3×10^16 kg (estimate)
Mean density ~2.7 g/cm³ (estimate) [3]
Equatorial surface gravity ~0.002 m/s² (estimate)
Escape velocity ~0.006 km/s (estimate)
Rotation period 0.293 d (7.042 h) [4]
Albedo 0.22 [5]
Temperature ~181 K
max: 281 K (+8°C)
Spectral type S
Absolute magnitude (H) 11.46

1199.647*24 because 24 hours, then times 60 because 60 minutes in an hour,
then times another 60 because 60 seconds in a minute, and we get about
1.03*10^8 seconds.

19.88km/s-0km/s)/(1.03*10^8s-0s)= approximately 1.93^-7km/s/s

E(sub k) = 1/2mv^2

Kinetic energy = (1/2)(2.5*10^16kg)(19.88km/s)
2. Relevant equations

E(sub k) = 1/2mv^2
(v2-v1)/(t2-t1)
and the other stuff I'm looking for

3. The attempt at a solution

The solution is kind of what I'm asking for, I need a way to convert kinetic energy directly into thermal energy, and then I also need to find how much energy it takes to raise the entire Earth's atmosphere by 1 degree of something or 1 kelvin, preferably degree.

2. Apr 10, 2012

### Staff: Mentor

Hi Forumasker, Welcome to Physics Forums.

It's not entirely clear what your problem statement is, but I can surmise that you're trying to determine how much heat energy would be end up in Earth's atmosphere due to an impact by a asteroid or comet. Is that true?

Rigorous analysis would be difficult because there are several potential paths for energy to take from such a collision depending upon its nature; Depending upon the size, composition, and initial speed of the body it may wholly or partially disintegrate in the atmosphere due to friction. A big bow-shock pressure wave in front of the body also stirs up the atmosphere mechanically. If a large portion of the body makes it to the surface and undergoes "lithobraking", then its KE is dumped into the Earths surface via a cratering event. Some portion of that energy will still make it into the atmosphere as the "hot spot" cools.

The body for which you've provided data doesn't cross the Earth's orbit: it has a perihelion of 1.825 AU compared to the Earth's 1 AU nearly circular orbit. Perhaps you're just looking for sample characteristics for estimation purposes?

Supposing that the body was somehow perturbed into crossing the Earth's path, it's orbital velocity would be a function of its position in its orbit (distance from the Sun). You can work out its speed for any distance from the Sun using the concept of conservation of total mechanical energy. The total mechanical energy held by any body in orbit around the Sun is
inversely proportional to the length of the body's major axis: $\xi = -\mu/(2a)$.

If the body is "captured" by the Earth then it will gain additional energy from gravitational potential energy converted to kinetic energy as it falls into the Earth's local gravitational well. Whether or not this will be a significant contribution will depend upon the initial speed of the body w.r.t. the Earth -- is the body approaching the Earth "from behind" (prograde orbit) or from "in front" (retrograde orbit) or perhaps its trajectory is nearly perpendicular to the plane of the Earth's orbit? Maybe you're just looking for the maximum approach speed?

You should be able to search the web for values for the specific heat of air, as well as total mass estimates and volume of the atmosphere.

The atmosphere is in a container whose "lid" is provided by gravity. That means when energy is added it will not only go into raising its temperature but also expanding the atmosphere against its "lid" -- The atmospheric volume will get larger. So adding energy to the atmosphere is not quite the same thing as adding energy to air sealed in a fixed size container. For a given "dose" of energy, temperature changes will be moderated by some energy going into gravitational potential energy as the atmosphere expands.

3. Apr 10, 2012