# Increase of mass effect on orbit

Just a some easy questions from a newbie here, in hopes of settling an argument.

If the mass of the earth were to suddenly double, what effect would that have on it's spin and it's orbit around the sun?

• Would the length of a year change and how much? (Shorter)
• Would the length of a day change and how much? (??)
• Would the distance from the earth to sun change and how much? (Yes, more eliptical orbit?)
• Would the shape of earths orbit change and how? (Yes)

**BTW I am not cheating on my homework or anything. I've been out of school for years and have forgotten most of what little physics I ever knew.

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Chris Hillman
Conservation of mass ensures that the mass of an object such as the Earth cannot "suddenly double". You could ask instead for a comparison of a similar object, E, orbiting at the same mean distance R from some object, S, where S has the same mass as our Sun but E has mass only one half the mass of the Earth. Then, Kepler's laws tell you the answer.

“ceteris paribus” all other things being equal
Including the motion of the new mass being added in, is coming in equal to the motions of mass being doubled i.e. not added any new forces.

Then NONE of the orbital characteristics you list would change

Janus
Staff Emeritus
Gold Member
“ceteris paribus” all other things being equal
Including the motion of the new mass being added in, is coming in equal to the motions of mass being doubled i.e. not added any new forces.

Then NONE of the orbital characteristics you list would change

Well, not exactly. Both the period and the eccentricity would change ever so slighty. (The length of the year would change by less than a minute.) This is because the Earth does not orbit the center of the Sun, but both orbit a commom barycenter (Granted, this barycenter is still inside the Sun). Doubling the mass of the Earth would slighty shift this barycenter, and slighty alter the oribtal characteristics.

Thanks for the answers. I must admit I was off in my thinking.

Well, not exactly. Both the period and the eccentricity would change ever so slighty. (The length of the year would change by less than a minute.) This is because the Earth does not orbit the center of the Sun, but both orbit a commom barycenter (Granted, this barycenter is still inside the Sun). Doubling the mass of the Earth would slighty shift this barycenter, and slighty alter the oribtal characteristics.
Sounds right, to get the barycenter back in position would require doubling the Sun as well.

Hello,

A couple of friends and I were having a similar discussion and now its turned into a heated debate, so I wonder if you can set the record straight for us.

The Argument is if you suddenly increased the mass of the Earth (lets say doubled it) would its orbital path around the sun change, ie move closer or away from the sun by a significant amount, lets say out of the livable zone where liquid water is possible.

Would the same affect occur is the Mass and the Size of the earth changed but its speed remained the same?

We have read the previous post where it is stated that its orbital length will change by a few seconds a year and have taken it to mean different things. Does changing its orbital time mean that its orbital path will move, or will it simply move along the same path but a tad slower?

Hope you can help before it really gets ugly.

Thanks!

What the previous posts said was that: while something with a mass 2M will experience a greater gravitational force than a mass of M, mass is also a measure of inertia, and in effect the mass of 2M would require twice the force to keep it in orbit, and these things "cancel out". It's the same principle that makes a bowling ball fall at the same rate as a pingpong ball (neglecting air friction).

EDIT: then they made it more exact by saying "it doesn't cancel out exactly", but this difference (due to the symmetry being slightly different) is minute in comparison to what you guys are thinking of

Hello,

If you have the time, can you please provide a statement in laymans terms as i would like to reduce the wriggle room available, no doubt my friends will try and find something as a get out clause. (as you can see this is a tense matter !! :) )

If you dont have the time then thank you for the post.

Dale
Mentor
2020 Award
The only way for the mass of the earth to double is for it to collide with an object with the same mass as the earth. So the length of the day and year after the collision depends strongly on the details like the initial linear and angular momentum of the other object. There may be some specific exact combination that would leave it unchanged, but all other combinations would change them.

rcgldr
Homework Helper
In case it wasn't clear, the orbit of the earth and sun is a function of the combined mass of earth and sun (ignoring other planets and moons). Doubling the mass of the earth would have little effect on the total mass.

If you doubled the mass of the sun, then you'd have a huge increase in the total energy (potential and kinetic) of the two body system, with a corresponding change in the orbital path and velocities.

Then instead if you kept doubling the mass of the earth untill it's mass was more than the sun's.The sun would then orbit the earth.

Hello, Thank you for your posts, unfortunately the debate still rages and qualifications are now being questioned.

Is anyone who has already commented a qualified physicist / mathematician / Scientist etc .. ?

lol sorry to hassle !!

Janus
Staff Emeritus
Gold Member
Hello, Thank you for your posts, unfortunately the debate still rages and qualifications are now being questioned.

Is anyone who has already commented a qualified physicist / mathematician / Scientist etc .. ?

lol sorry to hassle !!

You can find the orbital velocity of the Earth (taking the Earth's mass into account) by the formula:

$$V_o = \sqrt{\frac{M_s^2 G}{(M_s+M_e)r}}$$

Ms and Me are the masses of the Sun and Earth respectively, G is the Gravitational constant and r the distance between the Earth and Sun.

Using 2e30kg for Ms, 6e24 kg for Me and 1.5e11 m for r, this gives us an answer of

29828.35336 m/s

Doubling "Me" gives an answer of

29828.30862

Since this is slower than the Earth's present orbital velocity, if it suddenly doubled its mass (and everything else remained the same), the Earth would being moving faster than it needed to in order to maintain its present orbital distance and as a result, would move into a slightly more elliptical orbit with an average distance a little further from the Sun. But only slightly. 0.045 m/s is a pretty small difference, much smaller than the amount the Earth's orbital speed varies due to the eccentricity of its present orbit.

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Dale
Mentor
2020 Award
Hello, Thank you for your posts, unfortunately the debate still rages and qualifications are now being questioned.

Is anyone who has already commented a qualified physicist / mathematician / Scientist etc .. ?
Yes, several are. But appeal to authority is a logical fallacy.