Question 1

Light, leaving a point source, spreads out so that the apparent brightness, b, of light per unit area varies with distance d according to which law ( $\alpha$ means "proportional to")?

Accepted Answer

The apparent brightness of light from a point source follows the inverse square law, meaning it is inversely proportional to the square of the distance from the source.

Question 2

Suppose that, at night, the brightness of a light bulb is measured from a certain distance and then the light bulb is moved to a distance twice as far away. How bright will the light appear compared to the earlier measurement?

Accepted Answer

The brightness of a light follows the inverse square law, meaning that as the distance from a light source doubles, its apparent brightness becomes 1/4 of what it was at the original distance.

Question 3

The intensity of sunlight per square meter reaching Venus is approximately what fraction of the intensity of sunlight at Earth's orbital distance?

Accepted Answer

The intensity of sunlight is inversely proportional to the square of the distance from the Sun. Since Venus is closer to the Sun than Earth, the intensity is greater by a factor of (1/0.721)^2.

Question 4

What is the intensity of sunlight per square meter reaching Saturn compared to the intensity at Earth's orbital distance?

Accepted Answer

The intensity of sunlight decreases as distance from the Sun increases. Saturn is approximately 9.5 times farther from the Sun than Earth is, so the intensity of sunlight per square meter at Saturn is 1/9.5 (or approximately 0.105) times the intensity at Earth's orbital distance. Therefore, the answer is A) 1/91, which is the reciprocal of 0.105.

Question 5

If Mercury is at 0.4 au, the Moon is at 1.0 au, and the inverse-square law holds, how much more light falls on a unit area of Mercury's surface than on an equivalent area of the Moon?

Accepted Answer

The inverse-square law states that the intensity of light (or other forms of energy) is inversely proportional to the square of the distance from the source. Therefore, if Mercury is at 0.4 au and the Moon is at 1.0 au, the light intensity on Mercury would be (1/0.4)^2 = 2.5^2 = 6.25 times greater than that on the Moon.

Question 6

Which of the following statements is TRUE of the population of stars in our neighborhood?

Accepted Answer

The majority of stars in our neighborhood, and indeed in the galaxy, are red dwarfs. These stars are much fainter than the Sun and other more luminous stars, making faint stars far more common than bright ones.

Question 7

The luminosity of a star is:

Accepted Answer

The luminosity of a star refers to the total energy it emits at all wavelengths into all space from its whole surface. It is a measure of the star's total energy output, rather than its apparent brightness (apparent magnitude), which can be affected by distance and other factors. The V filter band referred to in option D is a specific range of wavelengths used in astronomical observations, but it represents only a small fraction of the total energy emitted by a star.

Question 8

The luminosity of a star is:

Accepted Answer

Luminosity refers to the total energy output of a star, emitted at all wavelengths into all space. It is not dependent on the star's distance from Earth, as is apparent brightness. Choice A refers to a specific amount of surface space, while choice D specifies a particular distance for measurement, so neither fully capture the meaning of luminosity.

Question 9

A luminosity function is a plot of the:

Accepted Answer

A luminosity function is a plot that shows the number of stars in a given volume as a function of their luminosity. It helps astronomers understand the distribution of stars in a certain volume and can provide information on the formation and evolution of galaxies.

Question 10

Figure 17-5 shows a typical luminosity function. This shows that:

Accepted Answer

The luminosity function shows that faint stars are more numerous.

Question 11

The absolute magnitude of the Sun is +4.8 and its luminosity is 3.9 × 10²⁶ watts. The luminosity of a star whose absolute magnitude is +3.8 is:

Accepted Answer

The luminosity of a star can be related to its absolute magnitude through a specific formula that involves a base-10 logarithmic scale. For every decrease of 1 in the absolute magnitude, the luminosity of a star increases by about 2.512 times (the inverse of the Pogson ratio). Given that the star in question has an absolute magnitude that is 1 magnitude lower than the Sun's (+3.8 compared to +4.8 for the Sun), its luminosity would be approximately 2.512 times that of the Sun. Since the Sun's luminosity is given as 3.9 × 10^26 W, the star's luminosity would be 3.9 × 10^26 W * 2.512 ≈ 9.8 × 10^26 W.

Question 12

The absolute magnitude of the Sun is +4.8 and its luminosity is 3.9 × 10²⁶ watts. The absolute magnitude of the star $v$ (Nu) Hydrae is -0.2. What is the luminosity of $v$ Hydrae?

Accepted Answer

Using the formula for absolute magnitude:
M = -2.5 log(L/Lsun) + 4.8
Solving for L/Lsun:
L/Lsun = 10^((M - 4.8)/-2.5)
For the Sun:
L/Lsun = 1
For $v$ Hydrae:
L/Lsun = 10^((-0.2 - 4.8)/-2.5) = 158.49
Multiplying by the luminosity of the Sun:
Luminosity of $v$ Hydrae = 3.9 × 10^31 W x 158.49 = 6.18 × 10^33 W, which is closest to option C.

Question 13

By approximately how many magnitudes is the star Sirius fainter than the full moon in our sky? (See Figure 17-6.(in the text))

Accepted Answer

The full moon is about 11 magnitudes brighter than Sirius, as the magnitude scale is logarithmic, with each magnitude being about 2.5 times brighter than the next.

Question 14

Two stars that differ from each other by five magnitudes have a ratio of brightness of:

Accepted Answer

The brightness ratio between two stars is given by the formula:

Brightness ratio = 100^( (magnitude difference)/5)

Here, magnitude difference = 5

So, brightness ratio = 100^(5/5) = 100^1 = 100.

Therefore, the answer is D)100.

Question 15

What is the magnitude of a star that appears twice as bright as a 3.0 magnitude star?

Accepted Answer

The magnitude scale is logarithmic, with a difference of 5 magnitudes corresponding to a brightness factor of 100. A difference of 1 magnitude corresponds to a brightness factor of approximately 2.512. To find the magnitude that appears twice as bright as a 3.0 magnitude star, we can use the formula $m_1 - m_2 = -2.5 \log_{10}(B_1/B_2)$, where $B_1/B_2 = 2$. Solving for $m_1$ gives a magnitude of approximately 2.25.

Question 16

Two stars orbit each other in a binary system. Each star by itself has an apparent magnitude of 4.0. What is the apparent magnitude of the two seen together as a single object?

Accepted Answer

The apparent magnitudes of two stars combined can be calculated using the formula for combining magnitudes: m = -2.5 * log10(10^(-m1/2.5) + 10^(-m2/2.5)). For two stars each with a magnitude of 4.0, the combined magnitude is approximately 3.25.

Question 17

The star γ Phoenecis has an apparent magnitude of 3.4 and an absolute magnitude of -4.6. The North Star (Polaris) has an apparent magnitude of 2.0 and an absolute magnitude of -4.6. Assuming that no light has been absorbed or scattered by interstellar dust, we can say for sure that:

Accepted Answer

The apparent magnitude of a star is how bright it appears from Earth, while the absolute magnitude is how bright it would appear at a standard distance of 10 parsecs. Since both stars have the same absolute magnitude but Polaris has a brighter apparent magnitude, it means Polaris is closer to Earth than γ Phoenecis.

Question 18

A star with an apparent magnitude of m = +2.5 is at 100 pc from Earth. What is its absolute magnitude, M?

Accepted Answer

The absolute magnitude, M, of a star is defined as the magnitude the star would have if it were placed at a distance of 10 parsecs from Earth. The formula to calculate M from the apparent magnitude, m, and the distance in parsecs, d, is M = m - 5(log10(d) - 1). Plugging in m = +2.5 and d = 100 pc, we get M = 2.5 - 5(log10(100) - 1) = 2.5 - 5(2 - 1) = 2.5 - 5 = -2.5.

Question 19

The star β Arietis has an apparent magnitude of +2.7 and a distance of 52 ly. What is its absolute magnitude, M?

Accepted Answer

The absolute magnitude, M, of a star can be calculated using the formula: $M = m + 5 - 5 \log_{10}(d)$, where $m$ is the apparent magnitude and $d$ is the distance in parsecs. First, convert the distance from light years to parsecs (1 ly = 0.306601 parsec), so 52 ly is approximately 15.943 parsecs. Plugging the values into the formula gives $M = 2.7 + 5 - 5 \log_{10}(15.943) \approx 1.7$.

Question 20

Several optical glass filters are used to select specific portions of a star's light for photometry. Which of the following filters most closely matches the sensitivity of the eye, with peak wavelength sensitivity at about 550 nm? (I = infrared, B = blue, U = ultraviolet, V = visual)

Accepted Answer

The V filter has a peak wavelength sensitivity at about 550 nm, which is consistent with the peak sensitivity of the human eye. Therefore, the V filter is the best choice for selecting specific portions of a star's light for photometry, as it closely matches the spectral sensitivity of the eye.

Quiz 17: The Nature of the Stars

Light, leaving a point source, spreads out so that the apparent brightness, b, of light per unit area varies with distance d according to which law ( $\alpha$ means "proportional to") ?

Suppose that, at night, the brightness of a light bulb is measured from a certain distance and then the light bulb is moved to a distance twice as far away. How bright will the light appear compared to the earlier measurement?

The intensity of sunlight per square meter reaching Venus is approximately what fraction of the intensity of sunlight at Earth's orbital distance?

What is the intensity of sunlight per square meter reaching Saturn compared to the intensity at Earth's orbital distance?

If Mercury is at 0.4 au, the Moon is at 1.0 au, and the inverse-square law holds, how much more light falls on a unit area of Mercury's surface than on an equivalent area of the Moon?

Which of the following statements is TRUE of the population of stars in our neighborhood?

The luminosity of a star is:

The luminosity of a star is:

A luminosity function is a plot of the:

Figure 17-5 shows a typical luminosity function. This shows that:

The absolute magnitude of the Sun is +4.8 and its luminosity is 3.9 × 10²⁶ watts. The luminosity of a star whose absolute magnitude is +3.8 is:

The absolute magnitude of the Sun is +4.8 and its luminosity is 3.9 × 10²⁶ watts. The absolute magnitude of the star $v$ (Nu) Hydrae is -0.2. What is the luminosity of $v$ Hydrae?

By approximately how many magnitudes is the star Sirius fainter than the full moon in our sky? (See Figure 17-6.(in the text) )

Two stars that differ from each other by five magnitudes have a ratio of brightness of:

What is the magnitude of a star that appears twice as bright as a 3.0 magnitude star?

Two stars orbit each other in a binary system. Each star by itself has an apparent magnitude of 4.0. What is the apparent magnitude of the two seen together as a single object?

The star γ Phoenecis has an apparent magnitude of 3.4 and an absolute magnitude of -4.6. The North Star (Polaris) has an apparent magnitude of 2.0 and an absolute magnitude of -4.6. Assuming that no light has been absorbed or scattered by interstellar dust, we can say for sure that:

A star with an apparent magnitude of m = +2.5 is at 100 pc from Earth. What is its absolute magnitude, M?

The star β Arietis has an apparent magnitude of +2.7 and a distance of 52 ly. What is its absolute magnitude, M?

Several optical glass filters are used to select specific portions of a star's light for photometry. Which of the following filters most closely matches the sensitivity of the eye, with peak wavelength sensitivity at about 550 nm? (I = infrared, B = blue, U = ultraviolet, V = visual)

Quiz 17: The Nature of the Stars

Light, leaving a point source, spreads out so that the apparent brightness, b, of light per unit area varies with distance d according to which law ( α\alphaα means "proportional to") ?

Suppose that, at night, the brightness of a light bulb is measured from a certain distance and then the light bulb is moved to a distance twice as far away. How bright will the light appear compared to the earlier measurement?

The intensity of sunlight per square meter reaching Venus is approximately what fraction of the intensity of sunlight at Earth's orbital distance?

What is the intensity of sunlight per square meter reaching Saturn compared to the intensity at Earth's orbital distance?

If Mercury is at 0.4 au, the Moon is at 1.0 au, and the inverse-square law holds, how much more light falls on a unit area of Mercury's surface than on an equivalent area of the Moon?

Which of the following statements is TRUE of the population of stars in our neighborhood?

The luminosity of a star is:

The luminosity of a star is:

A luminosity function is a plot of the:

Figure 17-5 shows a typical luminosity function. This shows that:

The absolute magnitude of the Sun is +4.8 and its luminosity is 3.9 × 1026 watts. The luminosity of a star whose absolute magnitude is +3.8 is:

The absolute magnitude of the Sun is +4.8 and its luminosity is 3.9 × 1026 watts. The absolute magnitude of the star vvv (Nu) Hydrae is -0.2. What is the luminosity of vvv Hydrae?

By approximately how many magnitudes is the star Sirius fainter than the full moon in our sky? (See Figure 17-6.(in the text) )

Two stars that differ from each other by five magnitudes have a ratio of brightness of:

What is the magnitude of a star that appears twice as bright as a 3.0 magnitude star?

Two stars orbit each other in a binary system. Each star by itself has an apparent magnitude of 4.0. What is the apparent magnitude of the two seen together as a single object?

The star γ Phoenecis has an apparent magnitude of 3.4 and an absolute magnitude of -4.6. The North Star (Polaris) has an apparent magnitude of 2.0 and an absolute magnitude of -4.6. Assuming that no light has been absorbed or scattered by interstellar dust, we can say for sure that:

A star with an apparent magnitude of m = +2.5 is at 100 pc from Earth. What is its absolute magnitude, M?

The star β Arietis has an apparent magnitude of +2.7 and a distance of 52 ly. What is its absolute magnitude, M?

Several optical glass filters are used to select specific portions of a star's light for photometry. Which of the following filters most closely matches the sensitivity of the eye, with peak wavelength sensitivity at about 550 nm? (I = infrared, B = blue, U = ultraviolet, V = visual)

Light, leaving a point source, spreads out so that the apparent brightness, b, of light per unit area varies with distance d according to which law ( $\alpha$ means "proportional to") ?

The absolute magnitude of the Sun is +4.8 and its luminosity is 3.9 × 10²⁶ watts. The luminosity of a star whose absolute magnitude is +3.8 is:

The absolute magnitude of the Sun is +4.8 and its luminosity is 3.9 × 10²⁶ watts. The absolute magnitude of the star $v$ (Nu) Hydrae is -0.2. What is the luminosity of $v$ Hydrae?