Questions & Answers
Browse all 24 questions from the
Astrophysical Algebra study set below.
Each question shows the correct answer — select a study format above to practice interactively.
1
If the orbital period T of a planet in years is given by T = a^(3/2) where 'a' is the semi-major axis in AU, what is the semi-major axis of a planet with an orbital period of 64 years?
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A
4 AU
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B
8 AU
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C
16 AU
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D
32 AU
2
The luminosity L of a star is proportional to the square of its radius R and the fourth power of its temperature T (L ∝ R²T⁴). If a star's radius is doubled and temperature halved, by what factor does its luminosity change?
3
The escape velocity v from a planet is given by v = sqrt(2GM/r). If mass M is increased by 8 and radius r by 2, by what factor does the escape velocity increase?
4
Using the equation d = vt, where d is distance and v is velocity, calculate the distance in km to a star if light (300,000 km/s) takes 5 years to reach Earth (Assume 1 year = 31,536,000 seconds).
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A
4.73 x 10^13 km
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B
9.46 x 10^13 km
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C
1.42 x 10^14 km
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D
2.84 x 10^14 km
5
The magnitude system for star brightness uses the formula m1 - m2 = -2.5 * log10(F1/F2). If the flux ratio F1/F2 is 100, what is the difference in magnitude?
6
A satellite orbits at a radius r. The centripetal acceleration is a = v²/r. If velocity v is tripled and radius r is doubled, what is the new acceleration factor?
7
The gravitational force F between two bodies is F = G(m1*m2)/r². If the distance r between Earth and the Moon were halved, how would the gravitational force change?
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A
Halved
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B
Doubled
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C
Quartered
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D
Quadrupled
8
The Drake Equation estimates N = R*fp*ne*fl*fi*fc*L. If all variables are constants except L (the lifetime of a civilization), and L increases by a factor of 10, how does N change?
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A
Remains same
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B
Increases by 10
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C
Increases by 100
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D
Decreases by 10
9
Hubble's Law states v = H0 * d. If H0 is 70 km/s/Mpc, at what distance in Mpc is a galaxy moving away at 7,000 km/s?
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A
10 Mpc
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B
50 Mpc
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C
100 Mpc
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D
700 Mpc
10
The surface area of a spherical planet is 4πr². If the radius of Mars is approximately 3,390 km, what is the expression for its surface area?
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A
11,492,100π km²
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B
45,968,400π km²
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C
12,852,100π km²
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D
38,556,300π km²
11
The redshift z is defined by 1+z = λobs / λemit. If a galaxy has a spectral line observed at 600nm that was emitted at 400nm, what is the redshift z?
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A
0.25
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B
0.5
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C
0.75
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D
1.5
12
For an object in circular orbit, orbital velocity v = sqrt(GM/r). If a planet moves to a new orbit where the radius is 4 times larger, what is the factor of change in orbital velocity?
13
The mass-luminosity relation for main sequence stars is L ∝ M^3.5. If a star is 4 times as massive as the Sun, how many times more luminous is it?
14
A rocket's mass ratio is R = mi/mf. Using the Tsiolkovsky rocket equation Δv = ve * ln(R), if Δv = 2*ve, what is the mass ratio R?
15
The Stefan-Boltzmann law states P = AσT⁴. If the temperature of a blackbody increases from 2,000K to 4,000K, by what factor does the power output increase?
16
The orbital angular momentum L = mvr. If a satellite's mass is doubled, its velocity is halved, and its distance from the planet is tripled, what is the new angular momentum?
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A
1.5 times the original
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B
2 times the original
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C
3 times the original
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D
4.5 times the original
17
Kepler's Second Law implies that for a planet in an elliptical orbit, the product of velocity and distance at perihelion equals the product at aphelion (v1*r1 = v2*r2). If r1=1AU and r2=3AU, what is the ratio v1/v2?
18
The density of a spherical planet is ρ = M / (4/3 * π * r³). If the radius of a planet is doubled while mass remains constant, what is the factor of change in density?
19
If the Sun's mass is 1.989 x 10^30 kg and Earth's mass is 5.97 x 10^24 kg, what is the approximate ratio of the Sun's mass to Earth's mass?
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A
3.33 x 10^5
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B
3.33 x 10^4
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C
3.33 x 10^6
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D
3.33 x 10^3
20
The Schwarzschild radius Rs of a black hole is 2GM/c². If the mass M of a black hole is doubled, what is the factor of change in the Schwarzschild radius?
21
The energy E of a photon is E = hc/λ. If the wavelength λ is cut in half, what happens to the energy E?
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A
Divided by 2
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B
Multiplied by 2
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C
Multiplied by 4
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D
Remains same
22
A light-year is the distance light travels in a year. Given c = 3 x 10^8 m/s, approximately how many meters is one light-year?
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A
9.46 x 10^15 m
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B
3 x 10^12 m
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C
3.15 x 10^7 m
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D
9.46 x 10^12 m
23
If the period of a pulsar is 0.033 seconds, what is its frequency in Hertz (f = 1/T)?
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A
3.03 Hz
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B
10.3 Hz
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C
30.3 Hz
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D
303 Hz
24
The flux of light from a star follows the inverse square law F = L / (4πd²). If the distance d is increased by 10, how does the flux F change?
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A
Decreases by 10
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B
Decreases by 100
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C
Increases by 10
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D
Increases by 100
