My homework says-
explain why weight would be different on different planets by talking about gravity.

And I gather that instead of trying it on your own, you want me to do it for you.

The force of gravity between two objects always involves the product of
both of their masses.

"Weight" is the force of gravity between a planet and an object on its surface,
so it depends on both masses.

When a rock, a space probe, or an astronaut goes to a different planet, its/his
mass doesn't change, but the mass of the body they're standing on is different. 
So the weight of the rock or the astronaut is different from what it is on Earth.

Gravitational forces on different planets and natural satellites are different. Let's take an example of Moon and the Earth. The gravitational force on Moon is  of that on Earth. And we know that -

 

So, this formula clearly depicts that Weight of any object depends on mass of that object as well as on the gravitational acceleration. So, the lesser gravitational acceleration on Moon makes an object weigh lighter on Moon than on Earth. Similarly it is true for different planets also.

10 is the . . .