BRAIN DUMP

What if Earth was twice its mass?

Felipe Jacobs

■ The surface gravity of a planet depends on its mass and its radius. You calculate it using the formula g = GM/r² , where G is the gravitational constant, M is the mass and r is the radius. Increasing Earth’s mass would make surface gravity go up, but increasing its radius would make surface gravity go down. The effect of doubling Earth’s mass would depend on how you did it. If the mass of Earth doubled but the radius didn’t increase, surface gravity would double. But if Earth’s radius did increase, the effect on surface gravity wouldn’t be so extreme. If the radius increased far enough, surface gravity would actually decrease. LM

What powers the world’s trains?

Clara Harrison

■ Many of the world’s trains run on electricity from cables that run above the tracks. However, less than 50 per cent of rail lines have these cables,