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I'm reading Physics for Entertainment by Yakov Perelman and in it he says under "When we move around the sun faster" that at midnight the speed of the rotation of the earth is added to that of earth's translation effectively saying we move faster at night than during the day.

He further goes on to say "Since any point travels about the earth at half a kilometer a second, the difference there between midday and midnight speeds is about a whole kilometer a second."

Does this happen because the gravity of the sun? Is this just a phenomenon of any object, like a wheel (I heard someone explain it on a quora but I wasn't sure if it was related)?

Anyways I don't understand please explain in easy way for me or tell me what to study so I understand it.

A excerpt of the book:

Excerpt from book

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  • $\begingroup$ This is the result of adding the Earth's rotation about its own axis to its much faster revolution about the Sun. $\endgroup$ – probably_someone Dec 12 '18 at 1:41
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Sjruru,

The wheel is indeed a great analogy for this. Imagine a single wheel with centre O that rolls along the ground. Take two opposite points on the wheel (on the top and on the bottom) and call them T and P respectively.

This one is from Physics StackExchange - I take no credit for it.

Have a look at diagram (a), where the wheel is rotating purely about the origin O. At any given moment, at point P will have velocity -v and T will have velocity +v (with velocity tangent to the circumference of the wheel).

In (b), when the wheel is purely moving forwards (translating) at velocity +v, it follows that all points of the wheel have velocity +v too.

Therefore, as (c) is a wheel both rotating and moving forwards at the same velocity (v), it is a combination of the processes occurring in both (a) and (b). It is where at any given moment, P (in contact with the ground) will have an instantaneous velocity of zero (since it is both rotating at -v and translating at +v, which cancels out to 0). Therefore = 0.

Point O travels forward at velocity +v, since it is not rotating, but purely translating.

Finally, point T, however, is not only rotating forward at velocity +v, but it is also translating forwards at +v too. v + v = 2v, so at any given instant T has a velocity of +2v. Therefore = 2.

Now, replace the wheel with the Earth, and a point (Q) underneath the floor is where the Sun lies. Both the wheel situation and the Earth's orbit is similar because both the wheel and the Earth are rotating and translating at the same time. Also, we know the Earth rotates clockwise if the viewer stands below the Earth's orbit, watching it translate towards the right.

Earth's rotation around the Sun

Therefore, in the same way, the outer side of the Earth (facing away from the Sun) would travel faster than the inner side (facing towards the Sun.)

Without knowing the velocity of the pure translation of the Earth, according to Yakov Perelman in your extract, the magnitude of the velocity of the rotation of the Earth (at point P and T) is around v = 0.5km/s. Since the pure translation only adds to the velocities of P and T equally (say translation velocity = t km/s)

Therefore,

Total velocity of P (inner) = t - v km/s

Total velocity of T (outer) = t + v km/s

The difference between the two sides of the Earth (T - P) = 2*v km/s = 2*0.5 km/s = 1 km/s.

And of course, the inner side (P) would be day time, and the outer side (T) would be the outer side.

It is quite something to realise that at night time we are actually flying across the solar system at twice the speed as our daytime counterparts.

Great question, and hope this helps!

Yours, Eugene.

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The surface of the Earth is undergoing two different motions simultaneously. The whole planet is revolving around the sun, and the planet is also rotating. At midnight, these two motions are in the same direction; at noon, they are in opposite directions, and at other times, the two directions are oblique. At night, the smaller rotational velocity adds to the net speed, while during the day it subtracts.

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