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Thor
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If Mars had 25% more mass would its orbit be further or closer to the sun?
At the same orbital velocity, yes. One has to consider the angular momentum and kinetic energy (in relation to the gravitational potential energy).Thor said:If Mars had 25% more mass would its orbit be further or closer to the sun?
Astronuc said:At the same orbital velocity, yes. One has to consider the angular momentum and kinetic energy (in relation to the gravitational potential energy).
Thor said:I presume with more mass Mars would have to orbit faster to escape the pull of Sol. With a higher orbital velocity wouldn't it also have seek an orbit further from the sun or would the effect of its increased mass keep it in the same position?
I'm sure there is some simple equation to describe this - any suggestions?
The way this is stated, I am wrong.Astronuc said:At the same orbital velocity, yes. One has to consider the angular momentum and kinetic energy (in relation to the gravitational potential energy).
Janus said:The total energy of a planet can be expressed as either
[tex]Et = \frac{mv^2}{2}- \frac{GMm}{r}[/tex]
or
[tex]Et = - \frac{GMm}{2a}[/tex]
Where:
G is the gravtational constant
M is the mass of the sun
m is the mass of the planet
v is the orbital velocity at a given point of its orbit.
r is the distance from the sun at that given point.
a is the semi major axis of the orbit (the average distance of r over the orbit. for circular orbits r=a at all points)
So if we want to find out what a change of mass of the planet will due to the average distance of the orbit to the Sun we just can equate these two expressions solve for "a" and note what changes in 'm" cause in 'a'.
[tex]- \frac{GMm}{2a} = \frac{mv^2}{2}- \frac{GMm}{r}[/tex]
[tex]- \frac{GMm}{2 \left (\frac{mv^2}{2}- \frac{GMm}{r} \right )} = a [/tex]
simplifing:
[tex]-m \frac{GM}{2m \left (\frac{v^2}{2}- \frac{GM}{r} \right )} = a [/tex]
[tex]-\frac{m}{m} \frac{GM}{2 \left (\frac{v^2}{2}- \frac{GM}{r} \right )} = a [/tex]
m is in both the top and bottom of the fraction so it cancels out:
[tex]- \frac{GM}{2 \left (\frac{v^2}{2}- \frac{GM}{r} \right )} = a [/tex]
Which means a change in 'm', the mass of the planet, would have no effect on the distance from the sun.
Janus said:The total energy of a planet can be expressed as
[tex]-m \frac{GM}{2m \left (\frac{v^2}{2}- \frac{GM}{r} \right )} = a [/tex]
[tex]-\frac{m}{m} \frac{GM}{2 \left (\frac{v^2}{2}- \frac{GM}{r} \right )} = a [/tex]
m is in both the top and bottom of the fraction so it cancels out:
[tex]- \frac{GM}{2 \left (\frac{v^2}{2}- \frac{GM}{r} \right )} = a [/tex]
Which means a change in 'm', the mass of the planet, would have no effect on the distance from the sun.
Hm. You may have bigger fish to fry. A comet 25% of the mass of Mars is not a comet, it's a planetoid. You just don't get comets that size.Thor said:Thanx. REALLY good information.
I'm writing a futuristic sci-fi where a comet about 25% the mass of Mars is captured and becomes its moon. Anyone care to project how long it would take before the heat of the sun dissolves it?
Yeah, granted, and they don't travel at a million miles an hour, either - UNLESS they are not from our solar system, but debris from deep space cast off when one of two companion stars went supernova.DaveC426913 said:Hm. You may have bigger fish to fry. A comet 25% of the mass of Mars is not a comet, it's a planetoid. You just don't get comets that size.
Yeah, I was going to comment on that. Have you done the math on how long it'll take your comet to do its thing? Is it obeying all the laws of physics? If you're going to write a sci-fi story you have to ensure that your physics is consistent. (that doesn't mean you can't have stardrives, but it does mean your orbits & stuff have to work).Thor said:Yeah, granted, and they don't travel at a million miles an hour, either - UNLESS they are not from our solar system, but debris from deep space cast off when one of two companion stars went supernova.
chroot said:...and why would a supernova cast off an enormous ball of ice of roughly the size of a planet?
There's a difference between science fiction and fantasy.
- Warren
DaveC426913 said:Yeah, I was going to comment on that. Have you done the math on how long it'll take your comet to do its thing? Is it obeying all the laws of physics? If you're going to write a sci-fi story you have to ensure that your physics is consistent. (that doesn't mean you can't have stardrives, but it does mean your orbits & stuff have to work).
Galaxy? It's extragalactic? Have you calced how long it would take to get here at a million mph from a minimum of 2 million light years away?Thor said:TO GET TO THE OTHER SIDE - LOL
No, seriously - that's only 25X the normal velocity of a comet.
If our galaxy and another were approaching each other at a liesurely 500K MPH, relative to the other galaxy the comet would be traveling at customary speed
Hey. Science doesn't attempt to answer why. Merely how.chroot said:...and why would a supernova cast off an enormous ball of ice of roughly the size of a planet?
There's a difference between science fiction and fantasy.
- Warren
DaveC426913 said:Galaxy? It's extragalactic? Have you calced how long it would take to get here at a million mph from a minimum of 2 million light years away?
Area: Astronomy
Posted By: Philip Plait, Astronomer/Programmer
Date: Tue Apr 23 14:49:46 1996
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1) How big can a comet be in size?
Questions like "How big can something get..." usually run into trouble simply because of definitions. The latest thoughts about comets are that they are chunks of ice and rock something like a snowball with gravel in them. The most famous comet of all, Halley's , is about 16 x 8 x 8 kilometers in size. Hyakutake, the bright comet that swung by the Earth in March 1996 is probably somewhat bigger then that. Hale-Bopp, which promises to be extremely bright by the end of 1996 may be even bigger still.
But how big can they get? Just last year, the Hubble Space Telescope may have captured pictures of truly giant iceballs, that may be as big as 1000 kilometers across or more! Some people even think the planet Pluto is more like a comet than a planet. So comets may get pretty big, but our definition of just what is a comet may break down before then!
2) How fast can a comet go?
Some comets fall towards the Sun from very far away, even way beyond the orbit of Pluto. It is possible for those to pass the Sun at speeds of about 600 kilometers per second! For comparison, the speed of sound on the Earth is about 1/3 kilometers per second.
DaveC426913 said:Well OK.
Just one thing though:
"It is possible for those to pass the Sun at speeds of about 600 kilometers per second!"
This is doable at perihelion, but this kind of speed coming into the Solar System at high speed is something very different.
Not that any of this means your story can't happen, but what it does mean is that all the scientists in your story will be EXTREMELY suspicious of the origin of this thing if it doesn't behave naturally.
Hope there's oxygen too...Thor said:Wanna ask me how they got to 1M MPH ... it's WONDERFUL that comets have lots of volatile methane.
Thor said:it's WONDERFUL that comets have lots of volatile methane.
Beatcha2it.chroot said:Let's hope they also have lots of volatile oxidizer, or they're be no way for the aliens to use all that methane... that sure would be a shame, wouldn't it?
- Warren
DaveC426913 said:Galaxy? It's extragalactic? Have you calced how long it would take to get here at a million mph from a minimum of 2 million light years away?
What part of 25% of Mars' mass is escaping you?franznietzsche said:...something larger than mars is not going to become its moon ...
What part of alien space vehicle is escaping you?franznietzsche said:I highy doubt something coming in that fast could be captured by...
Agreed, provided the author has taken that into consideration. I wasn't sure if he realized the implications of an extragalactic journey.higheriration said:Why would it matter how long it takes?
Or...Soul Surfer said:For the object to be captured by Mars in its current orbit its approach velocity and direction will have to be defined quite accurately or it will just shoot by. it will also disturb the orbit of Mars by quite a lot depending on the direction that it comes in. It is also quite possible that the required approach velocity and orbit are not compatible with a conventional solar system orbit and the object entering the solar system will have to have been strongly deflected by a giant planet on its way in.
DaveC426913 said:What part of 25% of Mars' mass is escaping you?
What part of alien space vehicle is escaping you?
Yes, an increase in Mars' mass would affect its orbit around the sun.
An increase in Mars' mass would result in a closer orbit to the sun.
The orbit of a planet is determined by its mass, velocity, and the force of gravity between the planet and the sun.
Yes, an increase in Mars' mass would have a slight impact on the orbits of other planets in the solar system due to the gravitational pull of Mars.
An increase in Mars' mass would not have a significant impact on the length of its year, as it is primarily determined by the planet's distance from the sun.