Questions & Answers
Browse all 15 questions from the
Algebraic Principles in Astrophysics 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 is proportional to the 3/2 power of its semi-major axis a (T = ka^(3/2)), and a dwarf planet has a semi-major axis 4 times that of Earth, what is its orbital period in Earth years?
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A
4 years
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B
8 years
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C
16 years
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D
32 years
2
The apparent magnitude m and absolute magnitude M of a star are related by m - M = 5log10(d) - 5, where d is the distance in parsecs. If a star has m=5 and M=0, what is its distance d in parsecs?
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A
10 pc
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B
50 pc
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C
100 pc
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D
500 pc
3
The Schwarzschild radius Rs of a black hole is calculated by Rs = 2GM/c^2. If mass M is doubled, by what factor does the radius Rs increase?
4
The Stefan-Boltzmann law states luminosity L = AσT^4. If a star's radius is doubled while its surface temperature T remains constant, by what factor does its luminosity L increase?
5
Escape velocity v is proportional to the square root of the mass M of a planet (v = k√M). If planet A has 9 times the mass of planet B, how many times greater is the escape velocity of A compared to B?
6
Using the equation d = vt, if a radio signal travels at 300,000 km/s and takes 500 seconds to reach Earth from the Sun, what is the distance in kilometers expressed in scientific notation?
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A
1.5 x 10^7 km
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B
1.5 x 10^8 km
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C
3.0 x 10^8 km
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D
1.5 x 10^9 km
7
The orbital velocity v of a satellite is given by v = √(GM/r). If the distance r from the center of the planet is increased by a factor of 4, what happens to the orbital velocity v?
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A
It decreases by half
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B
It decreases by a quarter
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C
It increases by half
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D
It remains the same
8
The gravitational force F between two bodies is F = G(m1*m2)/r^2. If the distance r between two planets is tripled, the gravitational force F changes by what factor?
9
If a galaxy's redshift z is related to its recessional velocity v by v = cz, and c is 300,000 km/s, what is the velocity of a galaxy with a redshift of 0.05?
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A
1,500 km/s
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B
15,000 km/s
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C
30,000 km/s
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D
150,000 km/s
10
The total energy E of a photon is E = hc/λ. If the wavelength λ is halved, what happens to the energy E of the photon?
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A
It is halved
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B
It remains the same
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C
It doubles
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D
It quadruples
11
The density ρ of a planet is M/V. Given V = (4/3)πr^3, if the radius r of a planet is doubled while keeping mass M constant, the density ρ changes by what factor?
12
Using the formula for the circumference of an orbit C = 2πr, if the average distance of Mars from the Sun is 228 million km, approximately how far does it travel in one complete circular orbit?
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A
716 million km
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B
1.43 billion km
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C
2.86 billion km
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D
4.56 billion km
13
The time dilation factor γ is 1/√(1 - v^2/c^2). If v = 0.6c, what is the value of γ?
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A
1.25
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B
1.33
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C
1.5
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D
2.0
14
If the brightness of a star follows the inverse-square law B = L/(4πd^2), and distance d is increased by a factor of 10, how does the brightness B change?
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A
It becomes 1/10
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B
It becomes 1/20
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C
It becomes 1/50
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D
It becomes 1/100
15
Using the formula for kinetic energy KE = 1/2mv^2, if an asteroid's velocity v is tripled, what happens to its kinetic energy?
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A
It increases by 3 times
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B
It increases by 6 times
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C
It increases by 9 times
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D
It increases by 27 times
