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The eccentricity of the orbit of Mercury is 0.206. How much does the apparent magnitude of...

The eccentricity of the orbit of Mercury is 0.206. How much does the apparent magnitude of the Sun vary as seen from Mercury? How does the surface brightness of the Sun vary?

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Answer #1

a) Let a be the length of semi major axis of mercury.

Then, the aphelion distance is a(1+e)

The perihelion distance is a(1-e)

The apparent magnitude and distance is related by

Where M is the absolute magnitude.

So,

at aphelion,

At perihelion,

So,

their difference is

Here, e = 0.206.

So,

b) The ratio of surface brightness is given by the equation

Using the value from the part a,

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