Gravitational forces between Earth and the Sun

Any change in mass will have an effect on the orbit.

1. The gravitational pull of the earth on the sun is exactly equal to the gravitational pull of the sun on the earth. This will always be true. It is Newton's third law.

2. If you double the mass of the earth you will double the force between them, however since the mass doubles the amount of force required to maintain the current orbit, they cancel out.

Changing the mass of the earth doesn't impact the orbit.

It is also useful to consider that the planets have angular momentum, and it appears that this differs from planet to planet. Venus has the most nearly circular orbit (with Mercury not far behind), and Venus has slowed so much that her rotational spin has also reduced--one day on Venus is longer than one year (it now takes the planet longer to rotate once on its axis than does to make one revolution around our star. Earth and Mars have very elliptical orbits, with that of Mars being very pronounced. One must also consider axial tilt. The planets and the star all are tilted on their axes. The Sun is tilted about 7 degrees. Earth is tilted (if I recall correctly) 23 and a half degrees. Mars has an axial tilt of twenty-five degrees. Uranus has an axial tilt of almost 98 degrees--it is more like a ball rolling on a billiard table than a top spinning. Axial tilt is a reference to the plane of the eciptic.

I recommend universetoday-dot-com as a good place to browse for descriptions of star systems, and primarily ours, because that is the one we know best. This is an image from that site:

If the mass goes up but the speed doesn’t change then the orbit will decay.

Would you like to show me the mathematics behind that claim?

The easiest way to approach this is to set the function for gravitational force between two bodies equal to the function for centripetal force in an orbit.

GMm/(r^2) =mv^2/r

Where M is the mass of the sun, and m is the mass of the orbiting planets.

You should see that 'm' cancels out.

Ok. I'll take you at your word and try to learn something. Could you explain how that is possible without using math (because I don't understand the math).

I don't see how two objects of vastly different mass could be in exactly the same orbital plane going the same speed (which is what your answer implies).

The language of physics is math. Once you try to explain physics without math, you run the risk of misunderstanding. I can tell you it is true, and I can point out that the math has been used to put countlesss satellites into orbit; the math works.

I don't know if Kepler's laws would interest you. You might want to read about them. You will notes that the mass or size of the planet is irrelevant in Kepler's laws.

The fact that Newton's equations replicated Kepler's laws was a huge success.

I found a very informative video with perhaps the prettiest astrophysicist I've ever seen.

It appears that my original answer was actually correct, Mass does affect the orbit, but only in the most detailed of ways (because things actually orbit around a barycenter). In general usage, the minute affect of mass is not relevant in most natural orbital systems. So I learned something. And thank you Max for making me aware of this.

Please see video below for details:
https://www.youtube.com/watch?v=bFdzuTwYo3g

You admit you don't understand the math... so you Google for a video that you think proves you are correct, in spite of the fact that after watching said video you still don't understand the math.

I can't argue against that.

In celestial mechanics, when both orbiting bodies' masses have to be taken into account, the orbital period T can be calculated as follows



A small change in the Mass of the very much smaller body has a minuscule effect on the orbits.

https://en.wikipedia.org/wiki/Orbital_period

In a simple two-body case, the distance from the center of the primary to the barycenter, r1, is given by:



https://en.wikipedia.org/wiki/Barycenter

An astrophysicist with a plunging lithp, hubba hubba.



Heaven, I'm in heaven,
At two masses barycenter so to speak
And I seem to find the gravity I seek
Celestial meets bestial for the meek

Heaven, I'm in heaven,
If those astronomic wonders worth a peek
Seem to vanish like a Halley's comet streak
Then they're out together dancing, cheek to cheek

In the case of the earth and the sun, the sun has the mass of about 330,000 earths.

Again I would invite anyone to do the math (rather than science by Google searches).

Don't just google 330,000 earths use the googled formulae to go through a pointless, except for the barycenter, calculation.

If the OP is taking a physics class, she will be learning to work with actual formulas. You are right, generally we ignore calculations involving the barycenter when mass is significantly larger than the other. In this caseypu can work with centripetal force.

When the masses are equivalent, this simplification isn't valid. In the case of the earth and sun the masses are very different. Generally in beginning physics classes we use the simpler equations.

The more important point is the conflict between mathematics and intuition. Very often the mathematics of physics are different than the intuitive answer. In science when this happens intuition must be discarded.

Are you saying the video is incorrect or inaccurate?

The video is correct and accurate. It she makes my point quite well. She clearly explains why when the sun is very much larger than the planet, the mass of the planet is *negligible".

The interesting part of this discussion is how intuition is often wrong. Let's make this point.

In a true two body problem, where the two objects orbiting each other are about the same mass.... What do you think happens when you increase the mass of one of the objects. Does its speed increase or decrease?

This topic is so complicated, isn't it?

Thanks. That's all I needed to know.

A pleasure chatting with you, as always.