by henk21cm » Wed Jul 02, 2008 1:10 pm
apodman wrote:I wonder how much mass moving it would take to change our orbit?
Ahh, a chalenge!
Using Earth units: Keplers third law says:
1 = a³/T² or T² = a³
when a is in Astronomical units and T is in years. The earth orbits in a circular orbit (almost), the circumference is 2πa, so the speed, v, is
v = 2πa/T = 2π/√a
Now lets move the earth to 1.2 AU, 180 E6 km form the sun, in order to diminish the effects of the greenhouse gasses. This is an example, not even an assumption, which originates from a very blunt thumb.
The speed of the earth has to be reduced by √1.2 and that is approximatedly 1.1. So in stead of 30 km/s it has to be just 10% lower, 3 km/s less. To reduce the speed of the earth, we must eject a mass m in the direction of the movement of the earth. Using conservation of moment, the speed of the earth will reduce. Furthermore we do not want to see this mass m ever back on earth, so it has to have the escape velocity at least. This is a little more than 11 km/s. To make the calculation without a calculator a little easier, i use 12 km/s. Now we build a huge spring, place the mass m on it, load the spring and release it. The mass on the spring is launched with a velocity of 12 km/s, relative of the remaining earth, and thus the remaining part of the earth recoils with -3 km/s. Applying conservation of moment:
(M - m) * 3 - m * 12 = 0 ⇒ 3M - 15m = 0 or
m = 1/5 M.
We loose
one fifth of the earth mass in this scheme.
Unfortunately this method will not move the remaining earth further away from the sun, since it is at a position (1 AU) and its speed is too low. It will fall towards the sun, in an orbit closer to the sun. It is a rather cumbersome method to reduce the effects of greenhouse warming. It is much easier to use common sense and apply energy sources which are greenhouse gas neutral.
Accidentally hit the wrong button, so a half message must have appeared on this board.
[quote="apodman"]I wonder how much mass moving it would take to change our orbit?[/quote]
Ahh, a chalenge!
Using Earth units: Keplers third law says:
1 = a³/T² or T² = a³
when a is in Astronomical units and T is in years. The earth orbits in a circular orbit (almost), the circumference is 2πa, so the speed, v, is
v = 2πa/T = 2π/√a
Now lets move the earth to 1.2 AU, 180 E6 km form the sun, in order to diminish the effects of the greenhouse gasses. This is an example, not even an assumption, which originates from a very blunt thumb.
The speed of the earth has to be reduced by √1.2 and that is approximatedly 1.1. So in stead of 30 km/s it has to be just 10% lower, 3 km/s less. To reduce the speed of the earth, we must eject a mass m in the direction of the movement of the earth. Using conservation of moment, the speed of the earth will reduce. Furthermore we do not want to see this mass m ever back on earth, so it has to have the escape velocity at least. This is a little more than 11 km/s. To make the calculation without a calculator a little easier, i use 12 km/s. Now we build a huge spring, place the mass m on it, load the spring and release it. The mass on the spring is launched with a velocity of 12 km/s, relative of the remaining earth, and thus the remaining part of the earth recoils with -3 km/s. Applying conservation of moment:
(M - m) * 3 - m * 12 = 0 ⇒ 3M - 15m = 0 or
m = 1/5 M.
We loose [b]one fifth[/b] of the earth mass in this scheme.
Unfortunately this method will not move the remaining earth further away from the sun, since it is at a position (1 AU) and its speed is too low. It will fall towards the sun, in an orbit closer to the sun. It is a rather cumbersome method to reduce the effects of greenhouse warming. It is much easier to use common sense and apply energy sources which are greenhouse gas neutral.
Accidentally hit the wrong button, so a half message must have appeared on this board.