In Newton's theory of gravity and pertaining to orbits, if an object's mass changes, does its orbit change?

Question

Newton states that bodies pull towards each other due to gravity. I want to know if a body's mass changes suddenly while in orbit, will its orbit deteriorate or will it simply adjust its orbit according to the new mass? How does this effect orbiting bodies that spin while in orbit such as Earth? If it were to be taken by a great impact, would it be possible to "knock" it out of orbit?

So then, as I understand it, we're needing to include the inertia of the body compared to the weight of the satellite while taking into account the distance of the satellite from the orbiting body. If I am correct, even a small object passing by an orbiting body would have some miniscule effect upon its inertia causing it to vary its orbit even a tiny bit. So, when we put objects into orbit around earth, we are causing the earth to wobble in a ratio almost equal to that of the satellite's mass to the earth's mass (as small as that may be). However, over time, I believe that it could have a large effect on the earth's rotation. It is hightly possible that the moon is causing the earth to slowly change its wobble on its axis even now over millions of years. I'm impressed with your answers everyone! And I want to hear what everyone else has to say.

Answer 1

"If a body's mass changes suddenly while in orbit, will its orbit deteriorate or will it simply adjust its orbit according to the new mass?"

Hypothetically speaking, if you had a satellite in orbit around a massive object and you somehow were able to make half of the mass of the satellite disappear instantaneously after it had established an orbit, the satellite will all of a sudden leave the established orbit. If you were to simply set force due to gravity equal to the centripetal acceleration on the satellite, you will find that the gravitational mass of the satellite will cancel out the inertial mass of the satellite on the two sides of the equation. Mass of the satellite actually will not affect the equation on either side. It is easy, then, to conclude that the satellite will remain in exactly the same orbit if you somehow managed to change its mass. However, this analysis is not complete. This neglects conservation of momentum. The satellite traveling in an orbit has a fixed momentum that equals its mass times its linear velocity. When you suddenly make half the mass disappear, it will at the same time double its velocity. At the moment the velocity of the satellite is doubled, it will no longer stay in the orbit that it had because centripetal acceleration due to gravity is no longer sufficient to keep it in circular motion at the increased velocity. So the satellite will leave its orbit.

"How does this effect orbiting bodies that spin while in orbit such as Earth?"

If the mass of the satellite is negligible compared to that of the planet, changes to the mass of the satellite will not have any noticeable effect on the path of the planet. If the mass of the satellite is large, however, the planet and the moon will actually orbit each other around the center of mass of the two bodies. Changing the mass of one in this case will significantly affect the orbits of both bodies.

"If it were to be taken by a great impact, would it be possible to "knock" it out of orbit?"

Yes. When it is struck by another object, there is a change in the momentum of the satellite. When momentum of the satellite changes, it will leave its established orbit. In reality, if the body coming near the satellite were massive enough, it does not need to actually strike the satellite to affect a change in the satellite's momentum. Effect of gravity between the satellite and the passing body can be significant enough that it alters the satellite's orbit around Earth. It will take a rather significant size object, though, passing near the satellite.

Answer 2

The orbit of an object is dependent on the mass of the primary, not the mass of the object. Changing an orbiting body's mass by even 100% will not appreciably affect its orbit.

F = ma = - GmM/R^2
a = - GM/R^2

Impact by another object is a different story. The collision will change the object's velocity according to the conservation of momentum and conservation of energy. The new velocity will result in a new orbit. Still, the impact would have to be really massive at a really high relative velocity to appreciably affect Earth's orbit.

Answer 3

If the object is much less massive than the body it orbits (as is the case with the Earth relative to the sun), changes in mass by themselves will have a negligible effect on the orbit, as the centripetal acceleration will remain constant. If the impacting object is large enough and fast enough, it could change the energy and momentum of the planet. That would change the orbit.

Answer 4

The acceleration due to the Earth's gravity is 32 feet per second per second. If gravity is the only force, then everything falls at this speed. However, there are usually other forces than gravity, most often the resistance of the air. The resistance of the air, often called wind resistance, depends on the shape of the object and also its weight, thus a falling object does depend on its mass, since mass would be a factor in determing wind resistance. The speed of a satellite in orbit depends on two things, the height of the orbit and the attraction of gravity. The mass of the object has no effect on speed.

Answer 5

An object of a given mass only orbits at a very specific "altitude" at a very specific speed. If any of these three factors change, the orbit is disturbed. As I recall from way back in physics class, theoretical experiments we conducted showed that an object in a circular orbit moved into an elliptical orbit if we changed either the object's mass, speed, or altitude while keeping the other two factors constant. Unfortunately, I don't remember the proofs for these experiments. =(

Likewise, if one of these factors suddenly changed for the Earth, then it would likely move into an elliptical orbit. (Even more elliptical than it already is.)

Hope this helps somewhat.

Answer 6

if a event occurred large enough the orbital patterns could be effected for all the planets in a system. as far as what planets would be effected would be determined by how close to the star they are orbiting to use our solar system for example the planet earth would be more effected if Venus was highly impacted, but not as much as if Jupiter was assaulted. what is being said is that the closer that the body is to what it is orbiting the main gravitational pull will effect those other bodies that radiate around it.

Answer 7

So since energy (mass) is conserved the way the mass of a body could "change" is if some of it was converted to energy or vice versa. Another way a "body" could change mass would be if it collided with another body.
Anyway. Yes the orbit would change. My guess is that there would be NO change in the orbits eccentricity. (eliptical nature)