Celestial Mechanics And Stellar Characterization Assessment Practice Tests

Question 1

A spacecraft travels a distance of $12 AU$ in $1400$ days. Calculate its average speed in $\frac{km}{h}$. (Use $1 AU \approx 1.5 	imes 10^8 km$ and assume $1 day = 24 h$). Provide the result in scientific notation.

Accepted Answer

5.36 	imes 10^4 km/h

Question 2

If a planet is at opposition, what is the angular separation between the Sun and the planet as viewed from Earth?

Accepted Answer

180^{\circ}

Answer

0^{\circ}

Answer

90^{\circ}

Answer

270^{\circ}

Question 3

Estimate the total number of stars in a cluster if the cluster has a volume of $10^{12} pc^3$ and a stellar density of $0.05 stars/pc^3$. Express your answer as a power of 10.

Accepted Answer

5 	imes 10^{10}

Question 4

Because the Moon is tidally locked to Earth, an observer standing on the center of the Moon's near side would see the Earth rise and set every 24 hours.

Accepted Answer

False

Answer

True

Question 5

If Earth's axial tilt were increased from $23.5^{\circ}$ to $40^{\circ}$, calculate the zenith angle of the Sun at the Tropic of Cancer ($23.5^{\circ} N$) during the summer solstice.

Accepted Answer

16.5^{\circ}

Question 6

Which of the following processes are primary components of the geochemical carbon cycle on Earth?

Answer

Atmospheric $CO_2$ dissolving in rain to form carbonic acid

Answer

Chemical weathering of silicate rocks

Answer

Subduction of carbonate rocks into the mantle

Answer

Photosynthesis by artificial solar panels

Question 7

A signal is sent from a probe at $80 AU$ from Earth. Calculate the time in hours it takes for the signal to reach Earth. (Use $c = 3 	imes 10^5 km/s$ and $1 AU = 1.5 	imes 10^8 km$).

Accepted Answer

11.11 hours

Question 8

An electron in a hydrogen atom transitions from the $n=4$ energy level to the $n=2$ level. Given the energy of the $n$-th level is $E_n = -\frac{13.6	ext{ eV}}{n^2}$, calculate the wavelength $\lambda$ of the emitted photon in nanometers. Use $h = 4.136 	imes 10^{-15}	ext{ eV s}$ and $c = 3.00 	imes 10^8	ext{ m/s}$.

Accepted Answer

486 nm

Question 9

Two stars, Star A and Star B, have the same surface temperature. Star A has a luminosity $100$ times greater than Star B. Based on the Stefan-Boltzmann law $L = 4\pi R^2 \sigma T^4$, what is the ratio of their radii $\frac{R_A}{R_B}$?

Accepted Answer

Option A

Answer

Option B

Answer

Option C

Answer

Option D

Question 10

On the main sequence of the H-R diagram, a star with a higher surface temperature will necessarily have a lower mass than a star with a lower surface temperature.

Accepted Answer

False

Answer

True

Question 11

Which of the following pressure types are primary factors in preventing the gravitational collapse of different stellar objects?

Accepted Answer

Option A

Answer

Option B

Answer

Option C

Answer

Option D

Question 12

A molecular cloud has a gravitational potential energy $U = -\frac{3}{5}\frac{GM^2}{R}$. If the cloud collapses from an initial radius $R_i$ to a final radius $R_f = \frac{1}{10}R_i$, determine the factor by which the magnitude of the gravitational potential energy increases.

Accepted Answer

10

Question 13

If a star is located in the upper-right region of the H-R diagram, which of the following best describes its physical state compared to a main-sequence star of the same temperature?

Accepted Answer

Option A

Answer

Option B

Answer

Option C

Answer

Option D

Question 14

Determine the frequency $f$ of a photon emitted during an electronic transition where the energy change $\Delta E$ is $4.00 	imes 10^{-19}	ext{ J}$. Use Planck's constant $h = 6.626 	imes 10^{-34}	ext{ J s}$.

Accepted Answer

6.04 	imes 10^{14}	ext{ Hz}

Question 15

If a planet has an escape velocity of $v_{esc} = 12$ km/s and the thermal root-mean-square speed of a specific gas molecule is $v_{rms} = 1.8$ km/s, determine if the planet is likely to retain this gas based on the rule of thumb $v_{rms} < \frac{1}{6} v_{esc}$. Provide the calculated threshold value.

Accepted Answer

2 km/s

Question 16

An exoplanet transits a star with a radius of $R_* = 0.5 R_{\odot}$. If the observed transit depth (the fraction of blocked light) is $0.01$, what is the radius of the exoplanet $R_p$ in terms of solar radii?

Accepted Answer

Option A

Answer

Option B

Answer

Option C

Answer

Option D

Question 17

If Earth's axial tilt were increased from $23.5^{\circ}$ to $40^{\circ}$, the seasonal variation in solar irradiance at high latitudes would decrease.

Accepted Answer

False

Answer

True

Question 18

Given a planet with mass $M = 5.97 	imes 10^{24}$ kg and a radius $R = 6.37 	imes 10^6$ m, calculate the escape velocity $v_{esc} = \sqrt{\frac{2GM}{R}}$ (using $G = 6.67 	imes 10^{-11} 	ext{ m}^3 	ext{kg}^{-1} 	ext{s}^{-2}$).

Accepted Answer

Option A

Answer

Option B

Answer

Option C

Answer

Option D

Question 19

Which of the following factors directly influence the geochemical carbon cycle on a terrestrial planet?

Accepted Answer

Option A

Answer

Option B

Answer

Option C

Answer

Option D

Question 20

A moon is tidally locked to its host planet. If the moon's orbital period (sidereal) is 27.3 days, calculate the length of the solar day (synodic period) on the moon, assuming the planet orbits the Sun in 365.25 days.

Accepted Answer

29.5 days

Celestial Mechanics And Stellar Characterization Assessment Practice Tests

Practice Tests

Celestial Mechanics and Stellar Characterization Assessment

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