On BBC Radio 4, Drs Adam Rutherford and Hannah Fry have been answering intriguing scientific questions from listeners and the BBC Future audience.

One vexing query the pair have been exploring rocketed in from Elisabeth Hill, via BBC Future’s Facebook page, who asked: “Could we shoot garbage into the Sun?”

Fair question. After all, if we can detect gravitational waves, or send a probe to land on a comet, surely we can send some rubbish to our nearest star?

Though as Rutherford and Fry discovered in the radio episode below, it’s not so simple:

The Curious Cases of Rutherford and Fry: The Stellar Dustbin

The primary problem is weight. The average person in the UK produces 1.85kg (4lb) of waste per day; in the US, it’s 2.3kg (5lb).

It works out at around £29,000 per kilogram. A hefty price to pay for a few plastic wrappers and a bottle or two

As Andrew Pontzen of University College London points out, it costs $200m (£143m) to get the Ariane V rocket into an orbit ready to travel further into space. With a payload of approximately 7,000kg, that works out at around $41,000 (£29,000) per kilogram. A hefty price to pay for a few plastic wrappers and a bottle or two.

In the coming decade, commercial operations like SpaceX hope to make cheaper rockets – closer to $90m per launch – and in the far future, space elevators might be an option too.

But even then, the Sun is 93 million miles away, and you’d still need an enormous amount of (expensive) fuel to get the rocket to plummet into the Sun if you took the direct route. Pontzen reckons that, unless you plan the mission very carefully, you’d need about 10 times more energy for the trip between Earth and the Sun’s surface than you’d already spent getting into orbit.

So, theoretically possible? Yes. But realistically desirable? Probably not.

Visit Radio 4 to download the full episode and hear more in the Curious Cases of Rutherford and Fry series.

If you have any scientific cases you would like the team to investigate please email: curiouscases@bbc.co.uk