Suppose that the sun shrank in size but that its mass remained the same. What would happen to the orbit of the earth?
1 answer:
Answer:
Nothing
Explanation:
The radius of the orbit of the Earth does not depend on the radius of the sun.
In fact, the gravitational attraction between the Earth and the Sun provides the centripetal force that keeps the Earth in orbit:
where
G is the gravitational constant
M is the mass of the sun
m is the mass of the Earth
r is the radius of the orbit of the Earth
v is the orbital speed of the earth
Re-arranging the equation for r:
Also,
where is the angular velocity of the Earth's orbit. So we can rewrite the equation as
As we see, the radius of the orbit of the Earth, r, does not depend on the mass of the Sun, so if the sun shrank in size, the orbit remains the same.
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<span>A.Wavelengths measured would match the actual wavelengths emitted.
In fact, the stars are not moving relative to Earth, so there is no shift in the measured wavelength.
2) In this second case, the correct answer is
</span><span>A.Wavelengths measured would be shorter than the actual wavelengths emitted.
</span>in fact, since the stars in this case are moving towards the Earth, then apparent frequency of their emitted light will be larger than the actual frequency, because of the Doppler effect, according to the formula:
where f0 is the actual frequency, f' the apparent frequency, c the speed of light and vs the velocity of the source (the stars) relative to the obsever (Earth). Vs is negative when the source is moving towards the observer, so the apparent frequency f' is larger than the actual frequency f0. But the wavelength is inversely proportional to the frequency, so the apparent wavelength will be shorter than the actual wavelength.