Throwing stones on the asteroid Ryugu
Finally, we get here. After mentioning the amazing footage of the probe landing on the asteroid Ryugu, I can now work out what it would be like to throw a stone on such a tiny body. I’m doing my own What If? (well worth the read, BTW)
It is tiny. And the strength of its gravity depends on that mass. Time to re-do the gravity calculation for little Ryugu
We are after rough values, so we’ll assume it’s a sphere. It’s about 800m in diameter and has a mass of about 450 billion kg (450,000,000,000).
Drop them into the spreadsheet:
0.000162 About 1/60,000th of Earth’s value. I think my ‘how far can I throw a stone’ values are going to be huge. But, I’ve come this far.
How Far and How High?
The formulae for these calculations are quite easy.
- h is the maximum height
- R is the maximum distance (range)
- u is initial velocity
- θ is the angle
- g is… (you should know by now)
For maximum distance, we’ll set the angle as 45 degrees. Some research shows 25 m/s is more than achievable for the average adult. It should do a nice curve, called a parabola, like this (y is the height as a function of x, the distance) :
Ok, time to drop everything in. Then mix it all up, bake for 30 minutes…and:
Ok, that’s mathematically correct but getting silly. With so little gravity I can throw the stone to a height of 962 km and distance 3,848 km. Somewhat further than Melbourne to Darwin. In fact nearly all the way to Timor.
But a rough calculation shows that velocity of just 25 m/s would be much greater than the escape velocity of the asteroid. So I’m pretty sure the stone would neither return back (how could it, given how far away it is goes compared to the size of the asteroid?) nor go into any form of orbit. I think it would just sail off into space.
I also think if I did throw it when standing on the asteroid – thanks to Newtons’ Laws – I may accelerate (a bit?) in the opposite direction and so may even tumble backwards (?). Mmm, it looks like another physics problem just appeared.
