What are the perihelion and aphelion speeds of Mercury? What are the perihelion and aphelion distances of Earth? How would these speeds be calculated?

2 Answers
Gió
Apr 22, 2016

I suppose you wanted the speeds for both Earth AND Mercury.

Explanation:

I would use the radial distances #r# both at perihelion #P# and aphelion #A# into Newton's Second Law #Sigmavec(F)=mvec(a)# using also centripetal acceleration:

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Use the values from the literature for the mass of the Sun, #M_S#, #G#, and the radial distances (you may find them in books, I think).

A. S. Adikesavan
Apr 22, 2016

Mercury;s perihelion speed = 69.8 km's and aphelion speed is 46.0 km/s. Earth's perihelion = 147.1 million km and aphelion = 152.1 million km.

Explanation:

Let #v_a# = speed , when the distance of a planet from the Sun is the semi-major axis a of the planet's orbit., #v_(pe)# = perihelion speed and# v_(ap)# = speed at aphelion. Let e be the eccentricity of the orbit.

Then, approximating #v_a# = average speed v,

#v_(pe)=v_a(1+e)=v(1+e)#, nearly and #v_(ap)=v_a(1-e)=v(1-e)#, nearly.

I can assure you that these approximations give 3-sd values without error, if there are no bugs in the data used..

For Mercury v = 47.4 km/s, a = 57.9 million (M) km and e = 0.2055. .

So, #v_(pe)=47.4(1+0.2055)=69.8 km/s# and
#v_(ap)=47.4(1-0.2055)=46.0# km/s#, nearly.

This way, the perihelion and aphelion speeds of the Earth can be approximated using relevant data from sources like
NASA Planetary Fact Sheet.

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