Undergrad Which object will hit the surface of a planet first?

[James Briggs]

If we have two objects A and B appear on the opposite sides of the equator of a planet like Earth with the same mass as Earth. Object A is a neutron star with the mass of the sun and object B is a iron cube with the mass of one gram. Will A or B hit the Earth at the same time or will one hit first and if one hits first which one will it be.

 

[jedishrfu]

Which do you think it is and why?

 

[James Briggs]

I do not know. I was taught that the combination of the two masses determine the acceleration due to gravity. However since I have started reading this forum I have gotten the impression that only the mass of the Earth counts. I hope my question will result in an answer not an attack.

 

[jedishrfu]

I'm not attacking as it stands your question looks like a homework assignment from your teacher and so my question reflects that stance.

To start then consider the masses:

iron cube = 1 gram
earth = 5.972 × 10^27 g
sun = 1.989 × 10^33 g

so we have a mass ratio of 1 : 10^27 : 10^33

It's like a dust speck vs a pumpkin vs the Earth.

What would happen?

 

[FactChecker]

The two masses determine the force between them. When you use that force to calculate the acceleration of a body of mass $m_1$, then you will find out that the force has a factor of $m_1$ and then it is divided by $m_1$ to get the acceleration. So the factor of $m_1$ is canceled out.

This makes great sense when one studies General Relativity. You learn that one body distorts space-time so that the other body, which seems to be accelerating, is actually following a "straight line" (more exactly, a geodesic) in space-time. Since all bodies, regardless of mass, will follow the same straight line, their "acceleration" is the same.

 

[Locke79]

The short and simple answer is more gravity means more inertia, this inertia cancels out any additional gravitational force by basically being resistance to movement.

In this example stars and planets from stationary points won't accelerate very quickly due to the inertial resistance so the idea of a neutron stars extra mass influencing gravitational pull is canceled out. An iron cube has much less resistance and moves readily due to having much less mass.

 

[James Briggs]

I'm not attacking as it stands your question looks like a homework assignment from your teacher and so my question reflects that stance.

Looks like a homework to you? I am 70 years old and have an advanced degree in psychology. You can answer the question anyway you want but you are answering it as if it were a homework assignment. I only asked which one hit first.

To start then consider the masses:

iron cube = 1 gram
earth = 5.972 × 10^27 g
sun = 1.989 × 10^33 g

so we have a mass ratio of 1 : 10^27 : 10^33

It's like a dust speck vs a pumpkin vs the Earth.

What would happen?

 

[James Briggs]

People with degrees in physics will ask me questions about their son who is using drugs or about their grandmother who seems confused. I don't accuse them of taking a class in psychology and looking for an answer to a homework assignment. I don't give them a lecture on stimulus response or ask them to figure it out themselves. I give them a practical answer and talk about general principles of psychology. I have been asking simple questions about physics on the net for around twenty years and physicists tend to act like they are omniscient and anyone who questions them is a fool worthy of ridicule. No wonder you guys have so many problems dealing with people.

 

[davenn]

I have been asking simple questions about physics on the net for around twenty years and physicists tend to act like they are omniscient and anyone who questions them is a fool worthy of ridicule. No wonder you guys have so many problems dealing with people.

I hope my question will result in an answer not an attack.

it was far from being an attack

Sorry, but that is a really poor attitude and it shows that you totally misunderstand one of the big purposes of PF

That being …..
We try and avoid spoon feeding people the answers, you learn nothing and you are likely to forget what you were told by the end of the day
Rather we try and get people to do some thinking and research for themselves and when they show an effort to do that, it helps us gauge your level of understanding of whatever topic is being discussed.
when this happens, what you read and learn is more likely to remain with you
When you do some thinking and reading up about the problem and then come back to answer questions like …..

Which do you think it is and why?

you can then give an intelligent response, instead of insults.
Then you can be guided through the problem to a solution

I too looked at your initial question and thought it looked like homework and was close to getting it moved to that section of the forumDave

 

[jbriggs444]

If we have two objects A and B appear on the opposite sides of the equator of a planet like Earth with the same mass as Earth. Object A is a neutron star with the mass of the sun and object B is a iron cube with the mass of one gram. Will A or B hit the Earth at the same time or will one hit first and if one hits first which one will it be.

If you reduce your attention to the interaction between the Earth and the neutron star, would you characterize this as the neutron star falling onto the Earth or as the Earth falling onto the neutron star?

We can agree to ignore the tidal shredding of the Earth that is likely to ensue.

Edit: Our mutual J Briggs-ness seems to be pure coincidence.

 

[sophiecentaur]

I have been asking simple questions about physics on the net for around twenty years and physicists tend to act like they are omniscient and anyone who questions them is a fool worthy of ridicule.

The problem is often due to the undervaluing of Physics that you get in the popular media. People ask questions which imply there must be a simple answer when there is not. Remember that this is not a 'free advice service" and that you are the one who wants the help. It's really important not to take offence at responses you may get. It makes you and others feel bad about the situation and it doesn't help. Fact is that many PF members actually do know a lot about some of the topics and can get tetchy with demands for oversimplification. They are (almost) human, you know.

It is common for people to use PF as their first convenient stop for information and not to read around first. I wonder how many people with questions ever bother to search PF first. This thread was started only a few weeks ago and has all the answers in it. Try reading through it.

 

[Janus]

I do not know. I was taught that the combination of the two masses determine the acceleration due to gravity. However since I have started reading this forum I have gotten the impression that only the mass of the Earth counts. I hope my question will result in an answer not an attack.

In this situation, both the mass of the Earth and 1 gram object are, for all practical purposes, insignificant compared to the 1 solar mass neutron star. So the easiest way to examine the scenario is to treat it as the Earth being a given distance from the neutron star and the 1 gram object being twice as far away and then working out how the Earth and 1 gram object would each fall towards the neutron star. Keep in mind that the acceleration due to gravity falls off by the square of the distance from the neutron star.

Or you can consider the tidal force acting on the 1 gram and Earth over the distance separating them, which is due to the differential of the neutron star's gravity, as compared to the gravitational attraction between the 1 gram and the Earth.

 

[berkeman]

Looks like a homework to you? I am 70 years old and have an advanced degree in psychology. You can answer the question anyway you want but you are answering it as if it were a homework assignment. I only asked which one hit first.

This thread may help to explain our approach to schoolwork-type questions here at the PF. Hope it helps.

https://www.physicsforums.com/threads/homework-coursework-questions.373889/

 

[Dale]

People with degrees in physics will ask me questions about their son who is using drugs or about their grandmother who seems confused. I don't accuse them of taking a class in psychology and looking for an answer to a homework assignment. I don't give them a lecture on stimulus response or ask them to figure it out themselves.

What if they did not have a son or grandmother in trouble, but they were specifically trying to learn about stimulus response. Wouldn’t a lecture and requiring them to think be more effective?

We are not here to help your son or your grandmother. If they need help of the sort that might come from here our usual policy is to recommend hiring a professional engineer/electrician/forensic investigator/physician.

That is not our mission. Our mission is education, and that requires a certain level of effort from the questioner.

Regarding your question. The acceleration of the iron and the neutron star can be calculated as $a=Gm/r^2$ where m is the mass of the Earth and r is the distance from the center. To fully answer this question you will also need to calculate the acceleration of the Earth which uses the same formula except using the mass of the star.

 

[sophiecentaur]

I do not know. I was taught that the combination of the two masses determine the acceleration due to gravity. However since I have started reading this forum I have gotten the impression that only the mass of the Earth counts. I hope my question will result in an answer not an attack.

The only thing missing from that is to include that the acceleration is relative to the Centre of Mass. Clearly the two objects have the same magnitudes of velocities relative to each other but the big one's acceleration depends only on the other one's mass. There is no paradox, not problem as long as the real situation is described and not some half way idea that may be 'intuitive'.
This works for a neutron star and a grain of sand or even for three masses.

 

[jedishrfu]

I think it’s time to close this thread as we have truly answered this question to many degrees of precision.

Thanks to all who contributed here and to the OP (original poster) for asking the question.