Science: tell me about...escape velocity

Everyone knows what happens when you throw a stone upwards. Gravity eventually makes it fall back to the ground, accelerating it at 9.8 metres per second per second (so one second after it stops rising, its downward speed is 9.8 m/s, one second after that it is 19.6 m/s, and so on).

But imagine if you threw that stone hard enough, and in the right direction - just off-vertical. It would reach a point where it stopped rising; but because you had thrown it so hard, the surface of our spherical world would curve away under it as fast as gravity made it fall. The object would be in orbit, and remain circling the Earth for eternity unless something slowed it down.

Now imagine throwing another object, a bit faster. It will not enter orbit. Instead it will break free from the Earth's gravity and shoot off into space. It has achieved escape velocity, defined as the minimum velocity that will enable a small object to escape from the gravitational attraction of a larger one.

Escape velocity is calculated by the formula 2Gm/r, where G is the gravitational constant, m is the mass in kilograms of the planet from which you want to escape, and r is the distance in metres from the planet's centre. For the Earth, escape velocity at the surface works out as 11.2km per second, or about 25,000mph in old money.

But accelerating a spaceship to 25,000mph needs a lot of heavy fuel, and huge engines. Earth's inconveniently high escape velocity is why the Apollo moon rockets were the size of skyscrapers. If you want to send people to Mars from Earth, and bring them home again, you would need even bigger rockets.

If you could build and launch your spaceship from a place with a much lower escape velocity, the problem would be much simpler. The Moon has only one-sixth of the gravity of its parent planet, and hence a much lower escape velocity - a mere 5,300 mph. Until recently though this was thought to be of little use. Even if you built your spaceships on the Moon, you would still need to cart the fuel for them from the Earth, thus defeating the point of the exercise.

But earlier this month, Nasa scientists excited the world by announcing that they had detected millions of tonnes of rocket fuel on the Moon - in the form of water ice. Water can be separated by solar power into hydrogen and oxygen. Mixed together and ignited, they produce a lot of energy. That means a Mars rocket could be built and launched on the Moon.

- Michael Hanlon

Suggested Topics
News
scienceExcitement from alien hunters at 'evidence' of extraterrestrial life
Life and Style
Customers can get their caffeine fix on the move
food + drink
News
newsRyan Crighton goes in search of the capo dei capi
Extras
indybest

PROMOTED VIDEO
Have you tried new the Independent Digital Edition apps?
Life and Style
ebooksA superb mix of recipes serving up the freshest of local produce in a delicious range of styles
Life and Style
ebooksFrom the lifespan of a slug to the distance to the Sun: answers to 500 questions from readers
Arts and Entertainment
Actors front row from left, Jared Leto, Jennifer Lawrence, Meryl Streep, Ellen DeGeneres, Bradley Cooper, Peter Nyongío Jr., and, second row, from left, Channing Tatum, Julia Roberts, Kevin Spacey, Brad Pitt, Lupita Nyongío and Angelina Jolie as they pose for a
film
Sport
sport
Life and Style
techCould new invention save millions in healthcare bills?
Sport
David Moyes gets soaked
sport Moyes becomes latest manager to take part in the ALS challenge
Voices
A meteor streaks across the sky during the Perseid Meteor Shower at a wind farm near Bogdanci, south of Skopje, Macedonia, in the early hours of 13 August
voicesHagel and Dempsey were pure Hollywood. They only needed Tom Cruise, says Robert Fisk
News
peopleEnglishman managed quintessential Hollywood restaurant Chasen's
Life and Style
food + drinkHarrods launches gourmet food qualification for staff
Arts and Entertainment
Michael Flatley prepares to bid farewell to the West End stage
danceMichael Flatley hits West End for last time alongside Team GB World champion Alice Upcott
Life and Style
Horst P Horst mid-fashion shoot in New York, 1949
fashionFar-reaching retrospective to celebrate Horst P Horst's six decades of creativity
News
Members and supporters of the lesbian, gay, bisexual, transgender (LGBT) community walk with a rainbow flag during a rally in July
i100
Life and Style
Black Ivory Coffee is made using beans plucked from elephants' waste after ingested by the animals
food + drinkFirm says it has created the "rarest" coffee in the world
Life and Style
news

As Voltaire once said, “Ice cream is exquisite. What a pity it isn’t illegal”

Life and Style
food + drinkThese simple recipes will have you refreshed within minutes
Independent
Travel Shop
the manor
Up to 70% off luxury travel
on city breaks Find out more
santorini
Up to 70% off luxury travel
on chic beach resorts Find out more
sardina foodie
Up to 70% off luxury travel
on country retreats Find out more
Latest stories from i100
Have you tried new the Independent Digital Edition apps?
Independent Dating
and  

By clicking 'Search' you
are agreeing to our
Terms of Use.

ES Rentals

    iJobs Job Widget
    iJobs General

    Network Engineer - CCNP, Hedge Fund, London

    £50000 - £60000 per annum: Harrington Starr: Network Engineer - CCNP, Hedge Fu...

    Senior Network Engineer-CCIE, Multicast, Low Latency

    £60000 - £70000 per annum: Harrington Starr: Senior Network Engineer-CCIE, Mul...

    Network Infrastructure Engineer

    £30000 - £50000 per annum: Harrington Starr: Network Infrastructure Engineer (...

    Network Engineer (CCNP, BGP, Multicast)

    £35000 - £45000 per annum: Harrington Starr: Network Engineer (CCNP, BGP, Mult...

    Day In a Page

    All this talk of an ‘apocalyptic’ threat is simply childish

    Robert Fisk: All this talk of an ‘apocalyptic’ threat is simply childish

    Chuck Hagel and Martin Dempsey were pure Hollywood. They only needed Tom Cruise
    Mafia Dons: is the Camorra in control of the Granite City?

    Mafia Dons: is the Camorra in control of the Granite City?

    So claims an EU report which points to the Italian Mob’s alleged grip on everything from public works to property
    Emmys look set to overhaul the Oscars as Hollywood’s prize draw

    Emmys look set to overhaul the Oscars as Hollywood’s prize draw

    Once the poor relation, the awards show now has the top stars and boasts the best drama
    What happens to African migrants once they land in Italy during the summer?

    What happens to migrants once they land in Italy?

    Memphis Barker follows their trail through southern Europe
    French connection: After 1,300 years, there’s a bridge to Mont Saint-Michel

    French connection: After 1,300 years, there’s a bridge to Mont Saint-Michel

    The ugly causeway is being dismantled, an elegant connection erected in its place. So everyone’s happy, right?
    Frank Mugisha: Uganda's most outspoken gay rights activist on changing people's attitudes, coming out, and the threat of being attacked

    Frank Mugisha: 'Coming out was a gradual process '

    Uganda's most outspoken gay rights activist on changing people's attitudes, coming out, and the threat of being attacked
    Radio 1 to hire 'YouTube-famous' vloggers to broadcast online

    Radio 1’s new top ten

    The ‘vloggers’ signed up to find twentysomething audience
    David Abraham: Big ideas for the small screen

    David Abraham: Big ideas for the small screen

    A blistering attack on US influence on British television has lifted the savvy head of Channel 4 out of the shadows
    Florence Knight's perfect picnic: Make the most of summer's last Bank Holiday weekend

    Florence Knight's perfect picnic

    Polpetto's head chef shares her favourite recipes from Iced Earl Grey tea to baked peaches, mascarpone & brown sugar meringues...
    Horst P Horst: The fashion photography genius who inspired Madonna comes to the V&A

    Horst P Horst comes to the V&A

    The London's museum has delved into its archives to stage a far-reaching retrospective celebrating the photographer's six decades of creativity
    Mark Hix recipes: Try our chef's summery soups for a real seasonal refresher

    Mark Hix's summery soups

    Soup isn’t just about comforting broths and steaming hot bowls...
    Tim Sherwood column: 'It started as a three-horse race but turned into the Grand National'

    Tim Sherwood column

    I would have taken the Crystal Palace job if I’d been offered it soon after my interview... but the whole process dragged on so I had to pull out
    Eden Hazard: Young, gifted... not yet perfect

    Eden Hazard: Young, gifted... not yet perfect

    Eden Hazard admits he is still below the level of Ronaldo and Messi but, after a breakthrough season, is ready to thrill Chelsea’s fans
    Tim Howard: I’m an old dog. I don’t get too excited

    Tim Howard: I’m an old dog. I don’t get too excited

    The Everton and US goalkeeper was such a star at the World Cup that the President phoned to congratulate him... not that he knows what the fuss is all about
    Match of the Day at 50: Show reminds us that even the most revered BBC institution may have a finite lifespan – thanks to the opposition

    Tom Peck on Match of the Day at 50

    The show reminds us that even the most revered BBC institution may have a finite lifespan – thanks to the opposition