# Mars + 25%

1. Jul 8, 2006

### Thor

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

2. Jul 8, 2006

### Staff: Mentor

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

3. Jul 8, 2006

### Thor

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?

Last edited: Jul 8, 2006
4. Jul 8, 2006

### 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.

5. Jul 8, 2006

### Janus

Staff Emeritus
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.

Last edited: Jul 8, 2006
6. Jul 8, 2006

### Staff: Mentor

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.

7. Jul 9, 2006

### thiotimoline

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.

8. Jul 9, 2006

### Thor

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?

9. Jul 9, 2006

### DaveC426913

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.

10. Jul 9, 2006

### Thor

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.

11. Jul 9, 2006

### DaveC426913

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).

12. Jul 10, 2006

### chroot

Staff Emeritus
...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

13. Jul 10, 2006

### Thor

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

14. Jul 10, 2006

### Thor

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.

15. Jul 10, 2006

### DaveC426913

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???

16. Jul 10, 2006

### DaveC426913

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

17. Jul 10, 2006

### Thor

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 -

600 Km/s is over 1 million MPH

18. Jul 10, 2006

### 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.

19. Jul 11, 2006

### Thor

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.

20. Jul 11, 2006

### DaveC426913

Hope there's oxygen too...