Question about the orbit between Mars and Earth

[Coda]

Hallo, i have a question here, hope someone can answer it. :)

As we know, two object attract each other. The closer the object, the stronger the force of attraction. This explain why Earth is attract by sun, but moon is attract by earth. (i guess.)

But here i got a question, we know that at certain times, Mars get so much closer to the Earth when she orbit the sun. Now, why Mars orbit line didnt affect by earth? (example: Mars being suck towards earth.)



reference: http://janus.astro.umd.edu/javadir/orbits/ssv.html

Maybe this is a foolish question, hope you don't mind. ;)

 

[D H]

Actually, the gravitational force on the Moon by the Sun is greater than that exerted by the Earth.

As far as Mars and Earth are concerned, the gravitational force exerted by the Sun on Mars is about 16,000 times that exerted by the Earth, and that is when Earth and Mars are at their closest. The force exerted by the Earth is tiny compared to that exerted by the Sun.

That said, those who make their career in accurately predicting the behaviors of the planets incorporate the interactions amongst all of the major bodies in the solar system in their models.

 

[Coda]

I see. But then why moon didnt orbit the sun but Earth itself?

 

[Janus]

I see. But then why moon didnt orbit the sun but Earth itself?

Becuase the Moon and Earth orbit the Sun together. Or put another way, the Sun's pull on the Earth and its pull on the Moon causes an almost identical acceleration for both. There is a slight difference due to the fact that the Moon goes from being closer to or further from the Sun the the Earth.

It is this differential that would result in the Sun pulling the Moon away. But the differential is smaller than the Earth's grip on the Moon.

 

[D H]

I see. But then why moon didnt orbit the sun but Earth itself?

Some mainstream (i.e., non-crackpot) astronomers and physicists say exactly this. They represent a tiny minority, however.

Note well: I am not in that camp. The Earth and Moon obviously orbit each other, and the two together orbit the Sun.

There is a slight difference due to the fact that the Moon goes from being closer to or further from the Sun the the Earth.

It is this differential that would result in the Sun pulling the Moon away. But the differential is smaller than the Earth's grip on the Moon.

An Earth-centered frame presents a much more sensible point of view. In this (accelerating) reference frame, the net gravitational acceleration due to the Sun at some is space is the difference between the Newtonian gravitational acceleration toward the Sun at the point in question and the acceleration of the Earth as a whole toward the Sun. From this perspective, the effect of the Sun is perturbative only. The Moon is in orbit about the Earth because it is gravitationally bound to the Earth.

Going back to a Sun-centered point of view, the point at which the Sun's gravitational force on an object exceeds that exerted by the Earth on the object is 2/3 of the way between the Earth and the Moon. Saying that the Moon is not in orbit about the Earth is tantamount to saying that this 2/3 point is the dividing line between an Earth orbiting and something that is in orbit about the Sun rather than the Earth. From either a heliocentric or geocentric point of view, there is no qualitative difference something orbiting the Earth at 0.66 lunar radii and 0.68 lunar radii. It seems downright silly to say that one of these constitutes an Earth orbit and the other does not.

The Moon is gravitationally bound to the Earth. Compare the Moon's trajectory about the Earth to that of J2000E3, most likely the third stage of the Apollo 12 mission. J2000E3 is not gravitationally bound to the Earth.

http://neo.jpl.nasa.gov/j002e3/j002e3d.gif

 

[Coda]

Hello D H, can you explain to me how moon "gravitationally bound to Earth"?

My physics is not so good, as I know moon can orbit Earth because it's accelerate speed is at the correct distant from the earth. And I guess, the mass attration from the moon have some effect too.

Is this what you mean by "gravitationally bound"?

 

[eachus]

Gravitationally bound means that it would take energy to remove the moon from the Earth's vicinity, and that there is no such source.

Except that there is. One of the effects of the lunar tides on Earth is to move the moon away from the earth, at the rate of approximately 38 millimetres per year. ;-) Since this will still be in progress when the sun reaches red giant stage in around five billion years, you can see why the question of whether or not the moon is gravitationally bound to the Earth is one that astronomers can and do disagree on.

IMHO, the moon should be considered a (dwarf) planet along with Pluto. The moon is 3476 km in diameter, while Pluto is only 2302 km in diameter. Since the moon's orbit around the sun is everywhere convex, also (roughly speaking in sol-centric space) doesn't cross its orbital path until it completes one orbilt around the sun. It is the only moon in the solar system for which this is true.