Reach for the Stars B

[Locoholic]

I would also know the parallax angle, as I have gotten that at an invitational.

I knew I was forgetting something. Parallax also appeared on a couple tests I took.

[Darwinist721]

u should also have the equation relating luminosity/brightness ratios to differences in magnitude (luminosity for absolute magnitude, brightness for apparent)

[Locoholic]

u should also have the equation relating luminosity/brightness ratios to differences in magnitude (luminosity for absolute magnitude, brightness for apparent)

That one actually hasn't appeared for me on actual tests, but it has on practice tests. Yes, that's one to study as well.

Also, isn't brightness the same as apparent magnitude? Or does it have different units/it's on a different scale?

[Darwinist721]

u should also have the equation relating luminosity/brightness ratios to differences in magnitude (luminosity for absolute magnitude, brightness for apparent)

That one actually hasn't appeared for me on actual tests, but it has on practice tests. Yes, that's one to study as well.

Also, isn't brightness the same as apparent magnitude? Or does it have different units/it's on a different scale?

brightness and apparent magnitude measure the same thing but yes on a different scale with different units. Brightness is measured in W/m^2 while magnitudes are unitless. Magnitudes are logarithmic and are lower for brighter stars.

[Locoholic]

brightness and apparent magnitude measure the same thing but yes on a different scale with different units. Brightness is measured in W/m^2 while magnitudes are unitless. Magnitudes are logarithmic and are lower for brighter stars.

I thought that W/m^2 was luminosity flux. Does that mean luminosity flux is brightness?

[Darwinist721]

brightness and apparent magnitude measure the same thing but yes on a different scale with different units. Brightness is measured in W/m^2 while magnitudes are unitless. Magnitudes are logarithmic and are lower for brighter stars.

I thought that W/m^2 was luminosity flux. Does that mean luminosity flux is brightness?

they're very closely related. Flux is a measure of the amount of energy radiated per unit time per unit area (W/m^2). At the surface of a blackbody, including stars, F = σT^4. The total luminosity is found by multiplying the flux by the total surface area of the star, which is A = 4πR^2, for a luminosity of L = 4πR^2σT^4. This should make sense because the luminosity is the energy emitted per unit time (W) and flux is energy emitted per unit time per unit area (W/m^2). However, flux isnt only measured at the surface of a star. At any distance from a star d, the energy per unit time emitted (luminosity) is spread over the surface of a sphere centered on the star with a radius of d. Since the flux is the luminosity received per unit area, the flux (or brightness, they measure the same thing) at a distance d is b = L/(4πd^2), which is just the luminosity divided by the surface area of a sphere with radius d. So the surface flux and brightness measure the same thing, but surface flux is specifically measured at the surface of a star. You might notice that when d = R, the brightness equation simplifies down to b = σT^4, which is the exact value of the surface flux.

summary: flux and brightness measure the same quantity. F = σT^4 is the surface flux of a star, a special case that measures the brightness at the surface of a star.

[Locoholic]

Since the flux is the luminosity received per unit area, the flux (or brightness, they measure the same thing) at a distance d is b = L/(4πd^2), which is just the luminosity divided by the surface area of a sphere with radius d.

So...is d distance or the sphere's radius? Other than that, thanks for the info!

[Darwinist721]

Since the flux is the luminosity received per unit area, the flux (or brightness, they measure the same thing) at a distance d is b = L/(4πd^2), which is just the luminosity divided by the surface area of a sphere with radius d.

So...is d distance or the sphere's radius? Other than that, thanks for the info!

sorry that may have been a little unclear. So the energy emitted from the luminosity of the star travels out radially equally in all directions from the star. You can think of the energy as traveling through an expanding sphere. At any distance d from the star, the energy is spread across a sphere in space with a radius of d. So, the total energy traveling through this expanding sphere is still the luminosity L, but it is spread over the surface of the expanding sphere, which has a radius d at any given distance. So, the energy per time per unit area (aka the brightness) is the total energy per unit time, L, divided by the surface area that the energy is spread over, being the surface area of the sphere of radius d, with A = 4πd^2, so b = L/(4πd^2). Hopefully that clears things up a little but dont be afraid to ask if it needs to be clarified more

[Locoholic]

sorry that may have been a little unclear. So the energy emitted from the luminosity of the star travels out radially equally in all directions from the star. You can think of the energy as traveling through an expanding sphere. At any distance d from the star, the energy is spread across a sphere in space with a radius of d. So, the total energy traveling through this expanding sphere is still the luminosity L, but it is spread over the surface of the expanding sphere, which has a radius d at any given distance. So, the energy per time per unit area (aka the brightness) is the total energy per unit time, L, divided by the surface area that the energy is spread over, being the surface area of the sphere of radius d, with A = 4πd^2, so b = L/(4πd^2). Hopefully that clears things up a little but dont be afraid to ask if it needs to be clarified more

So the distance is basically the radius of the "sphere" of energy coming from the object, right? And from what I gather, luminosity flux is L/4πr^2 where r is the radius of the object, while brightness is L/4πd^2 where d is the radius of the object's sphere of energy (distance to the object), is that also correct? Just making sure I get this.

[opal555]

Hi! Regionals is a few days away so this is urgent. Do we have to know the stars and deep sky objects' position relative to the constellations or do we just have to know about them?