darkdave3000 said:
So what if I moved an ice rock from the asteroid belt say a 20km diameter one and crashed it into Mars as slow as possible say 2km/s? The Asteroid Belt does not have as much potential difference in gravitational energy as compared to kuiper belt objects as you know so we should be able to manage a lower delta V in this case.
You are correct. Let's look as some numbers.
Let's first assume the icy object is in a near-circular orbit at 3.0 AU. Orbital velocity at this distance from the Sun is 17.2 km/s. To bring the periapsis down to intersect Mars' orbit, 1.66 AU or less, requires slowing the object down from 17.2 km/s to 14.5 km/s, for a delta V of 2700 m/s. Upon reaching Mar's orbit the object's velocity has increased to 26.1 km/s, compared to Mars' 22 km/s, a difference of about 4 km/s. Now, upon reaching Mars' sphere of influence the object will begin accelerating towards Mars, increasing its speed relative to Mars even more.
A slow moving object falling from the edge of Mars' sphere of influence gains about 4 km/s delta V. But our object is already moving at 4 km/s, so we wouldn't gain quite that much. Let's say 3 km/s. So now you have to slow your impactor down from 7 km/s to 2 km/s, a delta V of 5 km/s.
Added together, we need a total delta V of 2.7 + 7 - 2 = 7.7 km/s.
Now let's grab a comet from way out in the outer solar system. If you grab one whose periapsis is already within 1.66 AU, then you're in luck. You don't need to spend the delta V to slow it to bring its orbit down to meet Mars'. But let's look at that anyways. For an object in a near-circular orbit at 30 AU (Right around Neptune's orbit):
Speed: 5.44 km/s
Once we slow it down so the periapsis is at 1.66 AU:
Speed at apoapsis: 1.76 km/s
Speed at periapsis: 31.8 km/s
Mars' speed at apoapsis (where we want to intercept it): 22 km/s
So we need to spend about 3.68 km/s delta V to slow it down and our intercept velocity is much higher. Assuming our object is whipping around and catching up to Mars from behind, that's a difference in velocity of almost 10 km/s. Add in another 2 km/s at least to account for when the object 'falls' to Mars inside the sphere of influence, and we're looking at 3.68+10+2 - 2 = 13.68 km/s of delta V if you want to crash a 20 km diameter icy object into Mars at only 2 km/s.
How much fuel would we need? Let's assume a 'perfect' rocket of negligible mass compared to the mass of the fuel and payload.
Case 1
Object from asteroid belt, mass 4x10
15 kg:
Required delta V: 7.7 km/s.
Engine ISP: 450 (liquid hydrogen-oxygen engine)
Fuel mass: 19x10
15 kg (19 petatons, or 19 million gigatons)
Engine ISP: 20,000 (DS4G ion engine)
Fuel mass: 160x10
12 kg (160 gigatons)
Case 2
Object from 30 AU, same mass as above:
Required delta V: 13.68 km/s
Engine ISP: 450
Fuel Mass: 84x10
15 kg (84 petatons, 84 million gigatons)
Engine ISP: 20,000
Fuel Mass: 290x10
12 kg (290 gigatons)
Well, on the plus side, an ion engine cuts your fuel usage from 18x the mass of the object to about 0.05x the mass of the object.
*Note: I used apoapsis and periapsis instead of aphelion and perihelion because that's what I'm used to seeing, as I've played a lot of Kerbal Space Program and that's what they use. The -apsis words are generic and apply no matter what body you're orbiting.
I used this
Delta-V calculator for all the delta V calculations and Universe Sandbox for the object's various velocities.