Astronomy C

[0sm0sis]

Attempt (Click to Show Hidden Text)

1. Pauli exclusion principle
2. An neutron star draws in matter from a companion star, which strikes the surface parallel to the star's motion, providing a "push" on the star, and speeding it up.
3. Gamma ray emissions

Nice job, all three answers are correct. Your turn!

[RiverWalker88]

Consider a binary system consisting of a 1.35 solar mass neutron star and a 0.6 solar mass white dwarf. These stars are separated by a 0.28 AU. A 3km long 10 kg string is between them, held in place by the gravitational pull on either side.
a) At what point between the stars must the center of gravity of the string be placed such that it stays in place?
b) Where on the string is the center of gravity?

These should be solvable, but I didn't test them.

[OrigamiPlanet]

Part a) I think I have right but part b) might be me overthinking it... a lot, but here we go (I uh didn't do the math for part b) because if I am wrong, then I will have wasted a lot of time)

Click to Show Answer

a) Since at least one of the points on the string will be in the center of gravity, we can just make everything point masses for simplicity's sake, but we need to convert all units to kg and meters for this to work. Using Newton's Universal Law of Gravitation and some algebra, we get an approximate result of r=1.68x10^10 meters away from the smaller star.
b) Since the string has a mass across the entire bit, the forces will be changing based on distance, so we need to account for all points on the string to be balanced. I really don't want to do the number crunching for this one cause if it's wrong I'll be wholly devastated. So, say the center of gravity is L meters away from one end of the string, so that it is 3-L meters away from the other end. The total magnitude of all the forces on one side will be equal to the magnitude of the forces on the other side (F1=-F2), so we just need to worry more about getting the correct numbers in. We'll make the mass of the string m1. We'll make the 0.6 solar mass star m2 (now in kg) and the 1.35 solar mass neutron star m3 (also now in kg), and we will make the distance from m1 to the center of gravity r (to which is my listed answer in part a) and is in meters). F1 = (G(m1m2)/((r+3-x)^2)) - (G(m1m2)/((r-x)^2)). F2 = (G(m1m3)/((4.189E+10-r+x)^2)) - (G(m1m3)/((4.189E+10-3+x)^2)).
If that's wrong then welp I have overanalyzed this entire situation and it may just be 1.5 meters into the string (aka halfway). I'm pretty sure it's one of those two answers. 

[OrigamiPlanet]

Alright, time to actually do the number crunching.
a. To start, I'll define a few quantities to make this easier. R_s = Orbital Separation = 420,000km, M_W = Mass of white dwarf = 1.194e30kg, M_N = Mass of neutron star = 2.687e30kg, R_N is the distance from the string to the neutron star. The point I was looking for was the one in which the center of gravity of the string would be in equilibrium between the two stars, so we can use Newton's Law of Gravitation between the string and each star to find the force acting on it (note: the 10kg string is negligent in this). You get and You can set these equal to each other because you want the force acting on the string to be the same on both sides. You then get Some basic rearranging later, you get Then when everything is plugged in and solved, you end up with 2.52e5km from the Neutron Star and 3.78e5km from the white dwarf (and I didn't specify units, so I won't bother converting km to anything else)
b. I'll post an answer when I come up with one (sorry, I don't quite have the time to reason it out right now).

Your Turn!

[OrigamiPlanet]

Alrighty then!
Imagine that stars are now for some reason cubes instead of spheres. Scientists are observing a peak wavelength of 965 nm from Star Cube, and they estimate it’s side length to be 5.00 x 10^8 km. You can assume that Star Cube is a blackbody.
a) Where would this star likely be located on an HR diagram?
b) What’s the surface temperature of the object?
c) What is the luminosity of the object?

[Aimer]

Alrighty then!
Imagine that stars are now for some reason cubes instead of spheres. Scientists are observing a peak wavelength of 965 nm from Star Cube, and they estimate it’s side length to be 5.00 x 10^8 km. You can assume that Star Cube is a blackbody.
a) Where would this star likely be located on an HR diagram?
b) What’s the surface temperature of the object?
c) What is the luminosity of the object?

I used the answers for b) and c) to answer a), so I'll answer a) last:

b) Using wien's law, I got a surface temperature of 3003 K.
c) I used L = σAT^4 where A is the surface area of the star and in this case is equal to 6*(5.00*10^11 m)^2, and got a luminosity of 6.9171*10^30 W.
a) Because star cube has a surface temperature of 3003 K and a luminosity of 6.9171*10^30 W, it would most likely be located in the upper right side of an hr diagram and would be a red supergiant.

[OrigamiPlanet]

Yup, everything looks good! Your turn!

[Aimer]

Star A has a B - V index of -0.20 and a radius of 2.089*10^9 m. Assume Star A is a perfect blackbody.

a) What is the surface temperature of Star A?
b) What class would Star A be found in? (OBAFGKM)
c) What is Star A's luminosity?

Planet Z orbits Star A at a distance of 1.5 AU and has an albedo of 0. Assume Planet Z is a perfect blackbody.

d) What is the equilibrium temperature of Planet Z?

[EKT26]

Star A has a B - V index of -0.20 and a radius of 2.089*10^9 m. Assume Star A is a perfect blackbody.

a) What is the surface temperature of Star A?
b) What class would Star A be found in? (OBAFGKM)
c) What is Star A's luminosity?

Planet Z orbits Star A at a distance of 1.5 AU and has an albedo of 0. Assume Planet Z is a perfect blackbody.

d) What is the equilibrium temperature of Planet Z?

Yikes been a while since I did Astronomy math, but uh this is what I got:

Click to Show Answer

A. 13,600 k
B. This would make it a B class star
C. 1.1 * 10^29 w
D. 928 k

[Aimer]

Everything looks good! Your turn!