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I did the mistake of watching an episode of the Science Fiction series "For All Mankind". There they are trying to catch an asteroid in order to bring it back to Mars. I know this series is not realistic at all. However I got curious what would be needed in order to achieve this.

The setting is this: An asteroid of around 100m in all dimensions - I calculated that might be a mass of around 3 million metric tons - is caught. They attached a rocket to it trying to move it with their ion thrusters. The rocket has 24 ion thrusters and since the series is happening in the early 2000s I assume their efficiency similar to currently used ones.

The story implies they are moving it from the asteroid belt to Mars with a human crew so they have maybe 6 months of time for a distance from Asteroid belt to Mars. I assumed for simplicity 50 million km.

In short:

  • Asteroid: 3,000,000 tons (ignore the attached rocket)
  • 24 ion thrusters (wikipedia states maybe a specific impulse 10000s)
  • Distance: 50,000,000 km
  • 6 months time

My question would be: Would that be even possible? And if not (which I assume):

If something like that would be tried in reality:

  • how much fuel would be needed and
  • how long would it take to bring that asteroid to Mars?

Bonus question:

  • How would I calculate the flight duration/acceleration for a given mass and a thruster?

Thanks for every bit of help. I'm not terribly bad at math but I can't wrap my mind around impulse and acceleration/speed of an object of a given mass.

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    $\begingroup$ Actually, on the spectrum of sci-fi series, For All Mankind is on the "impressively realistic" end of the scale. $\endgroup$
    – phil1008
    Commented May 17 at 17:01
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    $\begingroup$ "since the series is happening in the early 2000s I assume their efficiency similar to currently used ones" – That's a strange assumption since the whole idea of the series is to explore what could have happened if the Space Race never ended, funding for space technology had stayed on Apollo levels, nuclear propulsion had not been abandoned, etc. $\endgroup$ Commented May 17 at 19:13
  • $\begingroup$ Sure but then again going to wild with the assumptions doesn't really help finding a solution. After all the "future tech" argument just makes it hard to estimate. Furthermore I was curious for a real world scenario anyway. $\endgroup$ Commented May 17 at 19:42

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If we assume that the asteroid's orbit is similar to the kind of orbit one would take when traveling from Earth to Mars, then we can get a rough idea of the delta-v needed to capture the asteroid from a delta-v map of the solar system. Keep in mind that the numbers in these maps assume that burns are done at orbital perigees - in this case, the perigee of the asteroid's hyperbolic trajectory past Mars. That is, the asteroid needs to be deep in Mars's gravity well when the burn is done so that we can take advantage of the Oberth Effect to get a low number for capture delta-v.

enter image description here

From the map, the Mars capture delta-v is about 0.67 km/s. Then you can use the rocket equation to determine the amount of propellant you will need.

$$m_0/m_f=exp({\Delta}V/v_e)$$

${\Delta}V$ is the 0.67km/s we need to capture the asteroid. $v_e$ is the exhaust velocity (10000s * 9.8 m/s2 = 98000 m/s). $m_f$ is the mass of your asteroid and the engines (~3 million tons). $m_0$ is the mass of your asteroid, the engines, and the propellant.

$$m_{propellant}=m_0-m_f$$

Doing the math...

$$m_{propellant}=m_f*exp({\Delta}V/v_e) - m_f=3000000(1.000007)-3000000=20.5 tons$$

So, given the "lucky find" assumption in the show, and assuming advanced fusion-powered engine technology that, not only has high ISP but also produces lots of thrust, it is entirely possible.

As for how long it would take, in the show the asteroid was a "lucky find" because it was already headed for Mars. They probably had to change its course only slightly to arrange for it to swing close by. It's not possible to say how long it would take to get an arbitrary asteroid on the right trajectory for capture. It depends on the asteroid's original orbit.

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    $\begingroup$ Nice. So the estimation for the fuel would be 20 tons? Is there any way of estimating how long that flight might last (with a "common" ion thruster)? $\endgroup$ Commented May 17 at 19:50
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    $\begingroup$ It depends on the total thrust of that thruster. They normally don't impart a lot of thrust, but no law says you can make a really big one. But you'll want to complete the burn while you're still deep in Mars's gravity well. $\endgroup$
    – phil1008
    Commented May 17 at 20:08
  • $\begingroup$ What is shown in the series is bigger than the "normal" one from NASA / ESA etc. But since I'm curious for a real world scenario I would ask for something currently used. So if I would take a "normal" small thing we use for let's say a Starlink satellite how about that? The scaling (e.g. assume they are 10 times as powerful or so) is something I can do in my head. But I'm not sure how to calculate their thrust into an acceleration. $\endgroup$ Commented May 17 at 20:21
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    $\begingroup$ That's just F=ma. F is your thrust. m is the asteroid's mass. Perhaps stating the obvious here, but a Starlink thruster times ten will be insufficient for capturing an asteroid. But at=v, and, if I recall, they burned for about half an episode, so let's say 20 minutes, or 1200 seconds. 0.67/1200=5.6E-4 m/s2. Multiply by 3 billion kg, and you get 1.675 MN of thrust. To put that in perspective, Superheavy's thrust is 74.4 MN. $\endgroup$
    – phil1008
    Commented May 17 at 21:39
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    $\begingroup$ The ion thrusters on the Dawn space probe produce 92 mN, so you'd need 18 million such thrusters. Or 300,000 of the record-setting X3 thruster, at 5N, and a 30 GW power source. space.com/38444-mars-thruster-design-breaks-records.html $\endgroup$ Commented May 17 at 22:01

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