Questions & Answers
Browse all 21 questions from the
Cosmic Algebraic Constants study set below.
Each question shows the correct answer — select a study format above to practice interactively.
1
The Schwarzschild radius R of a non-rotating black hole is calculated as R = 2GM/c^2. Given G is approximately 6.674 × 10^-11 m^3 kg^-1 s^-2 and c is 299,792,458 m/s, approximately how much does the radius change if the mass M is doubled?
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A
It remains the same
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B
It doubles
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C
It quadruples
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D
It decreases by half
2
In Kepler’s Third Law, p^2 = a^3, where p is the orbital period in Earth years and a is the semi-major axis in AU. If an object has a semi-major axis of 4 AU, what is its orbital period in years?
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A
2 years
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B
4 years
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C
8 years
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D
16 years
3
The luminosity L of a star is related to its radius R and temperature T by the formula L = 4πR^2σT^4. If a star's radius is doubled and its temperature is halved, by what factor does its luminosity change?
4
The escape velocity v of a planet is given by v = sqrt(2GM/r). If a planet's mass M is quadrupled and its radius r is doubled, what is the factor change in its escape velocity?
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A
sqrt(2)
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B
2
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C
sqrt(4)
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D
4
5
The absolute magnitude M of a star is given by M = m - 5(log10(d) - 1), where d is the distance in parsecs. If m=5 and d=100, what is the absolute magnitude M?
6
Hubble's Law is expressed as v = H0 * D. If the Hubble constant H0 is 70 km/s/Mpc and a galaxy is 50 Mpc away, what is its recessional velocity in km/s?
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A
350
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B
3500
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C
700
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D
7000
7
The gravitational force between two bodies is F = G(m1*m2)/r^2. If the distance r is tripled while keeping the masses constant, what is the new force as a fraction of the original?
8
In the equation for the Drake Equation N = R* · fp · ne · fl · fi · fc · L, if all variables equal 0.1 except R* which equals 1, what is the value of N?
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A
0.000001
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B
0.0001
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C
0.01
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D
0.1
9
The apparent brightness b of a star follows the inverse square law b = L / (4πd^2). If the distance d to a star is increased by a factor of 10, how does the brightness change?
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A
Decreases by 1/10
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B
Decreases by 1/20
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C
Decreases by 1/100
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D
Decreases by 1/1000
10
The wavelength λ of a photon is related to frequency f by c = λ * f. If the frequency of light is doubled, what happens to the wavelength?
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A
It is halved
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B
It is doubled
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C
It stays the same
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D
It is squared
11
Using the formula for orbital velocity v = sqrt(GM/r), if the orbital distance r is quadrupled, how does the velocity v change?
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A
It doubles
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B
It halves
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C
It stays the same
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D
It triples
12
The Stefan-Boltzmann law states Power = Area * σ * T^4. If the temperature T of a black body is tripled, the power output increases by a factor of:
13
A light-year is approximately 9.46 × 10^15 meters. Expressed in scientific notation, what is the result of multiplying 2 light-years by 3?
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A
5.676 × 10^16
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B
1.892 × 10^16
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C
2.838 × 10^16
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D
9.46 × 10^16
14
The density ρ of a sphere is ρ = M / ((4/3)πr^3). If the radius r is halved while the mass M remains constant, what happens to the density?
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A
It becomes 2x
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B
It becomes 4x
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C
It becomes 8x
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D
It becomes 1/8x
15
The formula for time dilation is t' = t / sqrt(1 - v^2/c^2). As v approaches c, what happens to the value of t'?
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A
It approaches 0
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B
It approaches 1
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C
It approaches infinity
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D
It stays constant
16
The mass-energy equivalence is E = mc^2. If mass is increased by 5 kg, how much does energy E increase (c = 3 × 10^8 m/s)?
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A
1.5 × 10^17 J
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B
4.5 × 10^17 J
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C
9 × 10^17 J
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D
4.5 × 10^18 J
17
The angular size θ of an object is approximately θ = s / d, where s is size and d is distance. If distance d doubles, what happens to θ?
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A
It doubles
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B
It halves
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C
It is squared
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D
It is quadrupled
18
For circular orbits, the period T = 2π * sqrt(r^3 / GM). If the mass M of the central body is increased by a factor of 4, what happens to the period T?
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A
It doubles
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B
It halves
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C
It stays the same
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D
It becomes 1/4
19
In the relation Z = (λ_obs - λ_rest) / λ_rest, if a spectral line is shifted from 500nm to 600nm, what is the redshift Z?
20
The Drake Equation has N = R*fp ne fl fi fc L. If R* = 1 and all other terms are 1, what is N?
21
If a rocket consumes fuel at a rate dm/dt, the thrust is F = ve * (dm/dt). If both fuel consumption and exhaust velocity double, by what factor does thrust increase?
