How can I apply Wien's and Stefan's laws to solve these astronomy questions?

[kylewoodloveast]

I am having a hard time with these astronomy questions. Our teacher gives us no help and I am lost with this stuff. If anybody could help me out not just with the answer but on How to do it I would be most appreciative.

What would be the frequency of an electromagnetic wave having a wavelength of 1.37 Earth's diameter (12,800 km) to the nearest Hz?

The blackbody emission spectrum of one object peaks in the ultraviolet region of the spectrum at 185 nm. A second object's spectrum peaks in the red region at 650 nm. To two decimal places, according to Wien's law, how many times hotter is it?

To one decimal place, in the previous problem, according to Stefan's law, how many times more energy per unit area does the hotter body radiate?

If your body surface area is 1.98 m2, to the nearest watt, how much energy do you radiate to your environment per second?

To the nearest hundredth of a micron, at what wavelength does a protostar with a temperature of 979 K radiate most strongly?

Radiation from an approaching nearby star is observed to be reduced in wavelength (after correcting for Earth's orbital motion) by a factor of 0.999926. To the nearest tenth of a km/s, what is the radial velocity of the star relative to the Sun?

Imagine you are observing a spacecraft orbiting a distant planet in an orbit with a radius of 100,000 km. You happen to be located in the plane of the spacecraft 's orbit. You find that the spacecraft 's radio signal varies periodically in wavelength between 3 + and - 0.000023 meters. Assuming the radio is broadcasting at constant frequency, to the nearest tenth of a MHz, what is that frequency?

In the previous problem, what is the mass of the planet? Enter the answer in the form n.nneyy, which is "computer speak" for n.nn x 10yy, that is, 5.37 x 1020 should be entered as 5.37e20.




If you can just help on one that would be great.

 

[cristo]

Welcome to PF, kyle. Note that our forum rules prevent us from ever handing out solutions to homework questions, and from giving help before we have seen some effort from the student. So, please tell us what you think about any of these questions. Do you have any formulae you know, or any way in which you think you can proceed on any of the questions?

 

[kylewoodloveast]

well for the first question i know frequency=1/period...which doesn't make any sense to me.

on the 2nd i know that the ultraviolet is hotter but i don't how to find the temperature to put it into wiens formula

the next problem assumes i got the previous question right. i didn't

with the next problem I can not find a formula to find out the watt's a human body gives off. do i have to know the temp of my body before knowing the energy it emits?

ps. i am a music ed major. this is my one science that i am required. help

 

[Math Is Hard]

Note: moved from Astronomy to HW/coursework under Other Sciences. - MIH

 

[Kurdt]

For the first question, the equation you've given is not going to help. You will need to use $c = f\lambda$ which relates the wave speed, c, with its frequency, f, and the wavelength lambda.

For the second, You do not need to know T. You are just comparing the temperature for different peak wavelengths. Use Wien's law to work out the temperature then see if you can work out which one is greater than the other by a particular factor.

For the third. Yes you will have to have worked out the temperature to compare the two valuse from Stefan's law.

You would probably use stefans law again for the fourth question with the average human body temperature. Rememberit gives you watts per unit area so you'll have to be careful. Consider why they give you the surface area of a human body.