Astronomy C

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Re: Astronomy C

Postby Name » November 18th, 2018, 8:03 pm

PM2017 wrote:
Name wrote:1. A star with the same radius and twice the temperature of our sun is found. What is its luminosity (in solar luminosity)?
2. The parallax of a type 1a supernova was found to be .05 milliarcsec. What its distance (in parsecs)?
3. What is the supernovas apparent magnitude?
4. The apparent magnitude of the star in part 1 and the supernova in part 2/3 is the same. What is the distance of the star?


attempt
1. 8 (stefan boltzmann)
2. 20,000 (1000/parallax)
3. -2.8 (distance modulus; abs mag is -19.3)
4. really close, or 0.859 parsecs (Abs mag = 2.53, because the 2.5th root of 8 is ~2.30 4.83 - that is 2.53; apparent magnitude is -2.83)


Sorry, I was being lazy and did all this on a computer and no paper or pencil, and I just felt lazy, so lazy in fact that I decided to make this sentence a run on sentence.

1. Stefan boltzmann is sqrt (solar lumo) times (1/solar temp)^2 =solar radius(1). (1/2)^2 is 1/4 or 4= sqrt lumo. Square both sides it's 16 solar lumos.
2. Yup
3. Yup
4. Absolute mag is 1.82, knowing the apparent mag is -2.79 so distance is 1.19 parsecs
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Re: Astronomy C

Postby Steuben42 » January 7th, 2019, 5:31 pm

It seems to me that the thread's dried up, so I guess I'll post a question that I think is new.

A star has been observed to have a radius of 3.42 solar radii and a temperature of 6141 K. What is the star's luminosity?
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Re: Astronomy C

Postby pb5754[] » January 7th, 2019, 6:08 pm

Steuben42 wrote:It seems to me that the thread's dried up, so I guess I'll post a question that I think is new.

A star has been observed to have a radius of 3.42 solar radii and a temperature of 6141 K. What is the star's luminosity?

attempt
L/Lsun = (R/Rsun)^2(T/Tsun)^4
L = (3.42)^2(6141K/5772K)^4
L = 15.0 solar luminosities

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Re: Astronomy C

Postby Steuben42 » January 7th, 2019, 7:11 pm

pb5754[] wrote:
Steuben42 wrote:It seems to me that the thread's dried up, so I guess I'll post a question that I think is new.

A star has been observed to have a radius of 3.42 solar radii and a temperature of 6141 K. What is the star's luminosity?

attempt
L/Lsun = (R/Rsun)^2(T/Tsun)^4
L = (3.42)^2(6141K/5772K)^4
L = 15.0 solar luminosities


Looks good to me, your turn!
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Re: Astronomy C

Postby pb5754[] » January 8th, 2019, 6:46 am

1. What is the gravitational potential energy of a star with twice the mass of the sun and 3 times the radius?
2. What is the total kinetic energy of the star?

Hint: The star is in a virialized state.

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Re: Astronomy C

Postby SciolyHarsh » January 13th, 2019, 8:27 am

pb5754[] wrote:1. What is the gravitational potential energy of a star with twice the mass of the sun and 3 times the radius?
2. What is the total kinetic energy of the star?

Hint: The star is in a virialized state.


Potential Energy= -3.032x10^41 J
Kinetic Energy=1.52x10^41 J

I'm new to Astro math, so if I get this wrong, could you please show me the work in order to get the correct answer?
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Re: Astronomy C

Postby pb5754[] » January 13th, 2019, 8:21 pm

SciolyHarsh wrote:
pb5754[] wrote:1. What is the gravitational potential energy of a star with twice the mass of the sun and 3 times the radius?
2. What is the total kinetic energy of the star?

Hint: The star is in a virialized state.


Potential Energy= -3.032x10^41 J
Kinetic Energy=1.52x10^41 J

I'm new to Astro math, so if I get this wrong, could you please show me the work in order to get the correct answer?

Looks good!

Your turn.

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Re: Astronomy C

Postby SciolyHarsh » January 14th, 2019, 8:17 am

Given that the apparent magnitude of a type 1a supernova is 5.75, and the redshift is 0.67, find the age of the universe, assuming the Hubble constant is 70 (km/s)/Mpc.
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Re: Astronomy C

Postby pb5754[] » January 14th, 2019, 4:14 pm

SciolyHarsh wrote:Given that the apparent magnitude of a type 1a supernova is 5.75, and the redshift is 0.67, find the age of the universe, assuming the Hubble constant is 70 (km/s)/Mpc.

attempt?
The age of the universe I believe is T = 1/H.
This gives us T = (0.014286 Mpc*s/km)(3.086*10^19 km/Mpc) = 4.41*10^17 s = 14.0 billion years.

Did you really need the apparent magnitude and redshift? or am I doing this wrong?

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Re: Astronomy C

Postby PM2017 » January 14th, 2019, 6:08 pm

pb5754[] wrote:
SciolyHarsh wrote:Given that the apparent magnitude of a type 1a supernova is 5.75, and the redshift is 0.67, find the age of the universe, assuming the Hubble constant is 70 (km/s)/Mpc.

attempt?
The age of the universe I believe is T = 1/H.
This gives us T = (0.014286 Mpc*s/km)(3.086*10^19 km/Mpc) = 4.41*10^17 s = 14.0 billion years.

Did you really need the apparent magnitude and redshift? or am I doing this wrong?

.
I think the question accidentally added the Hubble constant. It should have been an attempt to derive it on your own.
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Re: Astronomy C

Postby SciolyHarsh » January 15th, 2019, 3:55 pm

Did you really need the apparent magnitude and redshift? or am I doing this wrong?

yeah i meant to derive it lol but I added the hubble constant for some reason.

Anyway, using the Hubble constant you got it right. Your turn
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Re: Astronomy C

Postby pb5754[] » January 24th, 2019, 3:23 pm

Sorry I completely forgot about this :oops:

A planet with mass 2.4*10^23 kg orbits a star of mass 2.7 solar masses at a radius of 10 AU with velocity 100 m/s. Find the semimajor axis.

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Re: Astronomy C

Postby SciolyHarsh » February 5th, 2019, 4:13 pm

I wasn't sure how exactly to solve this, but I did my best.
Here are my steps:
1. I converted the mass of the planet to solar masses, but it's so small that it's nearly negligible. That said, for the problem's sake, I used it in the calculations.
2. Next, I used the radius of the star to solve for the circumference of the planet. I found it to be 20pi AU.
3. I then converted the velocity from m/s to AU/year, and I solved for the orbital period by finding out how long it would take to orbit the star completely once using the given velocity which I converted to AU/year.
4. I used the orbital period and the masses of both the planet and the star to solve for the semi-major axis using Kepler's Third Law.


My answer for the semi-major axis was 288.394 AU. If I'm wrong, could you post the steps to solve this?
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Re: Astronomy C

Postby pb5754[] » February 6th, 2019, 2:22 pm

SciolyHarsh wrote:I wasn't sure how exactly to solve this, but I did my best.
Here are my steps:
1. I converted the mass of the planet to solar masses, but it's so small that it's nearly negligible. That said, for the problem's sake, I used it in the calculations.
2. Next, I used the radius of the star to solve for the circumference of the planet. I found it to be 20pi AU.
3. I then converted the velocity from m/s to AU/year, and I solved for the orbital period by finding out how long it would take to orbit the star completely once using the given velocity which I converted to AU/year.
4. I used the orbital period and the masses of both the planet and the star to solve for the semi-major axis using Kepler's Third Law.


My answer for the semi-major axis was 288.394 AU. If I'm wrong, could you post the steps to solve this?

This is how I would do it...
Answer
Use the vis-viva equation (which can be obtained by applying the principle of conservation of mechanical energy): v = sqrt(GM((2/r)-(1/a))), where v = orbital velocity (m/s), M = mass of the star (central body) (kg), r = radius (m), a = semimajor axis (m)
At this point, you can manipulate this equation to obtain the formula a = (GMr)/(2GM-(v^2)r)
Now plugging the values (and remembering to convert to the proper units) in you get a = 5.00 AU.

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Re: Astronomy C

Postby SciolyHarsh » February 6th, 2019, 3:04 pm

Ah! I didn't know about that equation. Thank you for that. I'm not sure what to do now that I've gotten it wrong though
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