If Mars had 25% more mass would its orbit be further or closer to the sun?

[Thor]

If Mars had 25% more mass would its orbit be further or closer to the sun?

 

[Astronuc]

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]

At the same orbital velocity, yes. One has to consider the angular momentum and kinetic energy (in relation to the gravitational potential energy).

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?

 

[DaveC426913]

Hang on.

The orbit of an orbiting body is independent of its mass.

Consider the space station and the shuttle. If each of their orbits were dependent on their mass, they'd never be able to hook up. Likewise, a lost wrench from an astronaut does not immediately take off into a wildly different orbit due to its tiny mass.

There are plenty of asteroids in the same orbit as Earth. They are quite happy to maintain the same distance from the Sun as Earth and the same
orbital velocity.


So, your initial question could be considered ambiguous.

If Mars just happened to be larger than it is, there is no reason why it would not be in the orbit it is. Now, if you STARTED with Mars the size it is and ADDED mass, that's a different story, which I believe is what Astronuc is getting at.

 

[Janus]

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 total energy of a planet can be expressed as either

$$Et = \frac{mv^2}{2}- \frac{GMm}{r}$$

or

$$Et = - \frac{GMm}{2a}$$

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'.

$$- \frac{GMm}{2a} = \frac{mv^2}{2}- \frac{GMm}{r}$$

$$- \frac{GMm}{2 \left (\frac{mv^2}{2}- \frac{GMm}{r} \right )} = a$$

simplifing:

$$-m \frac{GM}{2m \left (\frac{v^2}{2}- \frac{GM}{r} \right )} = a$$

$$-\frac{m}{m} \frac{GM}{2 \left (\frac{v^2}{2}- \frac{GM}{r} \right )} = a$$

m is in both the top and bottom of the fraction so it cancels out:

$$- \frac{GM}{2 \left (\frac{v^2}{2}- \frac{GM}{r} \right )} = a$$

Which means a change in 'm', the mass of the planet, would have no effect on the distance from the sun.

 

[Astronuc]

At the same orbital velocity, yes. One has to consider the angular momentum and kinetic energy (in relation to the gravitational potential energy).

The way this is stated, I am wrong.

If mass was added, but angular momentum the same, then orbital velocity would be less and the orbital distance less.

Janus shows that the orbit is dependent on orbital velocity.

 

[thiotimoline]

The total energy of a planet can be expressed as either

$$Et = \frac{mv^2}{2}- \frac{GMm}{r}$$

or

$$Et = - \frac{GMm}{2a}$$

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'.

$$- \frac{GMm}{2a} = \frac{mv^2}{2}- \frac{GMm}{r}$$

$$- \frac{GMm}{2 \left (\frac{mv^2}{2}- \frac{GMm}{r} \right )} = a$$

simplifing:

$$-m \frac{GM}{2m \left (\frac{v^2}{2}- \frac{GM}{r} \right )} = a$$

$$-\frac{m}{m} \frac{GM}{2 \left (\frac{v^2}{2}- \frac{GM}{r} \right )} = a$$

m is in both the top and bottom of the fraction so it cancels out:

$$- \frac{GM}{2 \left (\frac{v^2}{2}- \frac{GM}{r} \right )} = a$$

Which means a change in 'm', the mass of the planet, would have no effect on the distance from the sun.

FYI, Kepler's 3rd law of planetary motion states that regardless of mass of secondary body orbiting a stationary massive primary body, square of period T^2 is directly proportional to the cube of the distance of separation R^3 between the two bodies. In short, change in mass of Mars does no change its orbit. A change in orbital velocity, which in turn change its period T, will change its R.

 

[Thor]

The total energy of a planet can be expressed as

$$-m \frac{GM}{2m \left (\frac{v^2}{2}- \frac{GM}{r} \right )} = a$$

$$-\frac{m}{m} \frac{GM}{2 \left (\frac{v^2}{2}- \frac{GM}{r} \right )} = a$$

m is in both the top and bottom of the fraction so it cancels out:

$$- \frac{GM}{2 \left (\frac{v^2}{2}- \frac{GM}{r} \right )} = a$$

Which means a change in 'm', the mass of the planet, would have no effect on the distance from the sun.

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?

 

[DaveC426913]

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?

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]

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, 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]

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.

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).

 

[chroot]

...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

 

[Thor]

...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

TO GET TO THE OTHER SIDE - LOL :rofl:

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

 

[Thor]

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).

Been batting this around other astronomy sites and got the companion star supernova as a suggestion from a fairly reliable source. It was the ONLY way he thought a body could reach that velocity.

 

[DaveC426913]

TO GET TO THE OTHER SIDE - LOL :rofl:

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

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?

 

[DaveC426913]

...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

Hey. Science doesn't attempt to answer why. Merely how.

 

[Thor]

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?

The comet is a cryogenic 'arc' designed to keep alien creatures from extinction. The length of time is inconsequential.

As for the size and speed of the comet -
From http://www.madsci.org/posts/archives/dec96/830267930.As.r.html"

Area: Astronomy
Posted By: Philip Plait, Astronomer/Programmer
Date: Tue Apr 23 14:49:46 1996

--------------------------------------------------------------------------------

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.

600 Km/s is over 1 million MPH

 

[DaveC426913]

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.

 

[Thor]

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.

Took me almost a month to research the configuration of the solar system in 2091-2094. Dipthda is the star they were observing and it coincides with the trajectory of the comet. On D-Day the moon will be shielded behind the earth. I'm trying to be as astronomically correct as possible.

1M MPH and moon sized comet are extremes, but not impossible and since they are from another galaxy it leaves a lot of poetic license...especially when the comet is actually a cryogenic alien escape vehicle. Wanna ask me how they got to 1M MPH ... it's WONDERFUL that comets have lots of volatile methane.

 

[DaveC426913]

Wanna ask me how they got to 1M MPH ... it's WONDERFUL that comets have lots of volatile methane.

Hope there's oxygen too...

 

[chroot]

it's WONDERFUL that comets have lots of volatile methane.

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? :rofl:

- Warren

 

[DaveC426913]

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? :rofl:
- Warren

Beatcha2it.:tongue2:

 

[franznietzsche]

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?

Is it relevant how long it takes? I mean I agree that the scenario is far fetched at best, but I don't see how this one matters. More to the point, something larger than Mars is not going to become its moon(not in the normal sense that we use the term anyway). When the two masses become appreciably close, one body does not orbit the other, they orbit the common center of mass (technically they do this when the masses are not appreciably similar but the approximation of one body orbiting the other is close enough in that limiting case). I highy doubt something coming in that fast could be captured by something smaller than it and form a stable system. Not in a 2 body interaction anyway. 3 or more, maybe. But not likely.

 

[DaveC426913]

...something larger than mars is not going to become its moon ...

What part of 25% of Mars' mass is escaping you?

I highy doubt something coming in that fast could be captured by...

What part of alien space vehicle is escaping you?

 

[higheriration]

Why would it matter how long it takes?

 

[DaveC426913]

Why would it matter how long it takes?

Agreed, provided the author has taken that into consideration. I wasn't sure if he realized the implications of an extragalactic journey.

It is a journey that will be at least 1 billion years.

When this arc set out on its journey, Earth life was just barely getting the hang of multicellular life! The most advanced form of life on the planet was algae!

This may or may not have an effect on the plot. But it sure makes me wonder what they liked when they saw our little Solar System from 2 million light years away...

 

[Soul Surfer]

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]

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.

Or...

the driver could just hit the brakes.

 

[franznietzsche]

What part of 25% of Mars' mass is escaping you?

The part where it says Mars +25%.

Ok, I see I'm mixing different subjects from th same thread now on that one. This is why its bad to only skim a thread every other day.

What part of alien space vehicle is escaping you?

The part where its a comet?