How much force is needed to move a planet.

[Debt]

I want to know if, say mother earth, could be moved? How much energy would have to be applied to push a planet closer to it's sun or futher away? Also which force would more likely to move such a mass?

 

[Drakkith]

Any amount of force will move the earth. The rate of change in velocity is inversely proportional to the mass of the object. For example, F=MA. The amount of force applied is equal to the mass of an object times the amount of acceleration. If you keep the force the same, you will have less acceleration as the mass increases.

If you jump off the ground you have effectively pushed the Earth slightly in the opposite direction. However the effect is so small that it is not noticeable.

 

[qraal]

Any amount of force will move the earth. The rate of change in velocity is inversely proportional to the mass of the object. For example, F=MA. The amount of force applied is equal to the mass of an object times the amount of acceleration. If you keep the force the same, you will have less acceleration as the mass increases.

If you jump off the ground you have effectively pushed the Earth slightly in the opposite direction. However the effect is so small that it is not noticeable.

Problem with that Drakkith is that you fall back to Earth and cancel any motion you caused. Only escaping mass will produce a motion permanently. The mass has to escape really rapidly to produce a significant addition to Earth's momentum. If we wanted to drop Earth into the Sun, then the total velocity change is 30 km/s. If we use a photon drive to do that, exhaust velocity 300,000 km/s, then the mass converted to photons has to mass (30/3E+5) Earth's mass, or 1/10,000th, or about 1/100th the Moon's mass. A lot.

 

[qraal]

Problem with that Drakkith is that you fall back to Earth and cancel any motion you caused. Only escaping mass will produce a motion permanently. The mass has to escape really rapidly to produce a significant addition to Earth's momentum. If we wanted to drop Earth into the Sun, then the total velocity change is 30 km/s. If we use a photon drive to do that, exhaust velocity 300,000 km/s, then the mass converted to photons has to mass (30/3E+5) Earth's mass, or 1/10,000th, or about 1/100th the Moon's mass. A lot.

Back to the original question, the amount of force required depends on how long one plans to take accelerating or decelerating. Earth masses ~6E+24 kg and there's roughly ~3E+7 seconds in a year. Braking by 30 km/s over 1 year requires deceleration at 3E+4/3E+7 = 0.001 m/s² which is a force of...

F = m.a = 6E+24 kg * 0.001 m/s² = 6E+21 N

...which is an immense amount of force. Earth is about 1.3E+14 m² in cross-sectional area, so spreading out the force means an average of ~46 GPa pressure applied over the whole surface pointing in that direction. Just a bit high at ~460,000 bars.

To avoid the need to apply such forces directly one can use a so-called "Gravity Tractor", in which a smaller mass is pushed directly and its gravitational attraction of the Earth pulls the Earth along with it. Using the Moon, for example. But the force applied needs to be less than the force that would cause the tractor object to break up.

Of course the usual reason for moving Earth is the need to avoid the Sun's rising luminosity. The Sun has 5.5 billion years left on the Main Sequence and will rise to ~2 times its present output by the end of that phase. This means Earth needs to recede to a distance of sqrt(2) ~1.4 AU from the Sun. To do that requires an impulse amounting to a speed change of ~16 km/s. Spread over 5.5 billion years that's an average acceleration of ~1E-13 m/s² and thus a force of ~5.8E+11 N, which averaged over the whole cross-section of the Earth is ~0.0044 Pa. Much better.

For such a "low" pressure we could use sunlight, which exerts a force of ~1E-5 N per square metre of perfect reflector at the Earth-Sun distance. Thus Earth would need to be towed by a solar-sail that's about ~500 times bigger in area. Alternatively a matter conversion drive annihilating ~2,000 kg/s would supply sufficient force, though finding a suitable place for it could be tricky.

 

[Drakkith]

Problem with that Drakkith is that you fall back to Earth and cancel any motion you caused. Only escaping mass will produce a motion permanently. The mass has to escape really rapidly to produce a significant addition to Earth's momentum. If we wanted to drop Earth into the Sun, then the total velocity change is 30 km/s. If we use a photon drive to do that, exhaust velocity 300,000 km/s, then the mass converted to photons has to mass (30/3E+5) Earth's mass, or 1/10,000th, or about 1/100th the Moon's mass. A lot.

You are correct! And that's a lot of photons needed to move the Earth!

 

[narrator]

A few years ago there were some spectacular photos in the news when a comet or large meteorite hit Saturn or Jupiter. Sorry, I forget the details. Could a strike like that cause orbital problems?

 

[Drakkith]

A few years ago there were some spectacular photos in the news when a comet or large meteorite hit Saturn or Jupiter. Sorry, I forget the details. Could a strike like that cause orbital problems?

Comet Shoemaker-Levy in 1994? http://en.wikipedia.org/wiki/Shoemaker-Levy
Also there was this in 2009: http://en.wikipedia.org/wiki/2009_Jupiter_impact_event

Any orbital problems are the least of our concerns. Anything with enough impact energy to actually but a serious shift in the Earths orbit would obliterate pretty much most if not all life on Earth.

 

[qraal]

A few years ago there were some spectacular photos in the news when a comet or large meteorite hit Saturn or Jupiter. Sorry, I forget the details. Could a strike like that cause orbital problems?

The short answer is: No.

The slightly longer answer is that there will be a slight change depending on the details of the collision. But the collision is more likely to spread the remains of the colliding masses in a wide splash rather than change the orbit significantly. Off-centre collisions spray significant amounts into new orbits only if the two masses are similar, else it's more of a merger event, with the larger absorbing the smaller. A direct collision perfectly centered and of equal masses will change the orbit significantly but the odds are very low. Comets and asteroids are unlikely to significantly change a planet's orbit in an individual collision.

However collectively a disk of asteroids/planetesimals can cause large planets to migrate towards, and away from, the central star. This requires a very heavy disk, which is long gone from our solar system, but probably caused the inwards and outwards motions of all the giant planets as they formed.

 

[jslo5203]

I am not interested in changing Earth's orbit, I see no practical benefit; however it would be beneficial to move the orbit of Venus somewhere outside Earth's orbit and let it cool for a while, until it was cool enough to visit, since Venus has similar mass to Earth all of our existing life support systems probably will function there with little or no change, so Venus would be easy to colonize. My first question would be: if a comet swung by Venus with enough mass and in the appropriate path, could its gravity pull nudge Venus to an orbit outside Earth's own? My second question is: assuming Venus moved to an outer orbit, how long would it take to cool down to temperatures similar to earth's?

 

[thebiggerbang]

Problem with that Drakkith is that you fall back to Earth and cancel any motion you caused.

Can you please explain how? :)

 

[qraal]

Can you please explain how? :)

You jump, which pushes Earth away from you, but then gravity pulls you back together with the Earth which cancels the first impulse. For every action there is an equal and opposite reaction. QED

 

[qraal]

I am not interested in changing Earth's orbit, I see no practical benefit; however it would be beneficial to move the orbit of Venus somewhere outside Earth's orbit and let it cool for a while, until it was cool enough to visit, since Venus has similar mass to Earth all of our existing life support systems probably will function there with little or no change, so Venus would be easy to colonize. My first question would be: if a comet swung by Venus with enough mass and in the appropriate path, could its gravity pull nudge Venus to an orbit outside Earth's own? My second question is: assuming Venus moved to an outer orbit, how long would it take to cool down to temperatures similar to earth's?

First question involves a lot of tricky orbital maneuvering. One impulse event would not be enough. A bunch of asteroids, carefully timed, could allow Venus to migrate out from the Sun, but the amount of energy required is mind-bogglingly large. Venus masses 0.815 Earth's mass of 5.9722E+24 kg. If we drag it out to Mars's orbit, which should be enough to chill it down. To move a planet from one orbit to another very slowly requires a velocity change equal to the difference in orbital speeds between the two. In this case that's ~11 km/s and so 60.5 MJ/kg of kinetic energy has to be added to Venus by all those asteroids. Total energy = (0.815 x 5.9722E+24 kg x 60.5E+6 J/kg) = 2.945E+32 J. Surprisingly that's just 8.86 days worth of the Sun's energy output, so the whole process could be solar-powered at relatively low efficiency if we take a leisurely ~500 years to do the job.

Once there we can estimate how long the atmosphere will take to chill down and rain-out - the bottom part of Venus's atmosphere is super-critical CO2 which should liquefy once the atmosphere drops to ~304 K below the 75 bar level. For the first stage of cooling, the temperature can drop from the whole atmosphere average of about ~630 K to just 304 K in about a decade if it radiates at roughly the average. Chilling the bottom ~20 bars worth to liquid will take a couple more decades, then it's a slow chill-out as the rest of the atmosphere drops to CO2's triple point (216 K, 5.2 bar) because the effective temperature is so low. In about ~200 years, most of it should be liquid or snow. If it can sink into the crust, then most of the disposal job is done. If we import a hundred metres (over the whole surface, which is ~4.6E+14 m^2, so ~4.6E+19 kg - a pure ice asteroid ~470 km across) or so of water, then the ocean pressure should be enough to keep it liquid on the bottom, where it can slowly percolate into the crust and form carbonates for longer term storage.

In theory Mars and Venus could become co-orbital planets and remain fairly stable, requiring the occasional nudges via our planet moving system to keep them from perturbing each other into collision or orbital excursions.

All the asteroids being used for the orbit-moving system will need some kind of propulsion system to do the job, probably fusion drives. Very big fusion drives. But if we're sun-powering the whole lot, then some kind of particle exchange network would be better, accelerating streams of mass electromagnetically. This will require some hefty engineering, but then no job worth doing was ever easy.