Nano Posted June 29, 2009 Share Posted June 29, 2009 Hello. Can someone help me with how to calculate how much energy (in joules) it would take to lift an object with a given mass and radius out of the earths gravitational field? I get the answer in m\s (escape velocity), but I need to know what correspond to that in energy. And I also wonder how to calculate how much fuel is needed to make an object escape the earth. Thanks. Link to comment Share on other sites More sharing options...
Sisyphus Posted June 29, 2009 Share Posted June 29, 2009 Well, it's simple enough if you disregard air resistance. Kinetic energy is equal to (1/2)mv^2, with energy in joules, mass in kilograms, and velocity in meters per second. Including air resistance makes it a lot more complicated, since it's dependent on the shape of the object. Link to comment Share on other sites More sharing options...
insane_alien Posted June 29, 2009 Share Posted June 29, 2009 just find out your gravitational potential energy (not the mgh stuff) and there you go. that is the minimum energy needed to remove you from the earth. Link to comment Share on other sites More sharing options...
Nano Posted June 30, 2009 Author Share Posted June 30, 2009 Thanks for answers. Is this right then? If I want to send an object of 1 kg to Mars, when the planet is the closest to the earth as possible: Ug = mgh 1kg x 9.8^2 m\s x 54,6 x 10^9 m = 5,2*10^12 Joules But this formula does not take into account that the gravitational field gets weaker the further away from the earth you go? Do I also have to think about that the sun is pulling this object (If I choose to send it toward Mars AWAY from the sun) What is the corresponding amount of Joules stored in 1 liter of jet-engine-fuel? And how much does 1 liter of fuel weigh? Link to comment Share on other sites More sharing options...
insane_alien Posted June 30, 2009 Share Posted June 30, 2009 i said not the mgh one. U=-Gm1m2/r that one. Link to comment Share on other sites More sharing options...
Janus Posted July 1, 2009 Share Posted July 1, 2009 Thanks for answers. Is this right then? If I want to send an object of 1 kg to Mars, when the planet is the closest to the earth as possible: Ug = mgh 1kg x 9.8^2 m\s x 54,6 x 10^9 m = 5,2*10^12 Joules But this formula does not take into account that the gravitational field gets weaker the further away from the earth you go? Right, which is why you use the formula given by insane_alien instead. Do I also have to think about that the sun is pulling this object (If I choose to send it toward Mars AWAY from the sun) Yes, you do. However, to use the minimum amount of energy to get to Mars you do not launch when Mars is at its closest. Instead you use a Hohmann transfer orbit. This type of orbit intersects the orbit of Mar's 180° from where it leaves Earth. The velocity needed to enter this orbit is found by: [math] \Delta V = V_e \left ( \sqrt{\frac{2Rm}{Re+Rm}}+1 \right )[/math] Where Ve = the orbital velocity of the Earth Re the orbital radius of the Earth Rm the orbital radius of Mars The energy can then be found by [math]E = \frac{\Delta V^2 M}{2}[/math] What is the corresponding amount of Joules stored in 1 liter of About 3.4 million Joulesjet-engine-fuel? And how much does 1 liter of fuel weigh? 787 grams. Link to comment Share on other sites More sharing options...
Nano Posted July 1, 2009 Author Share Posted July 1, 2009 Great, thanks. Lots of help. Link to comment Share on other sites More sharing options...
swaha Posted July 21, 2009 Share Posted July 21, 2009 what is hoghmann transfer orbit? can anybody give me the deduction for minimum energy? or tell me where to find it pls. i am a 1st yr stdnt of physics only. Link to comment Share on other sites More sharing options...
marketsmarkets Posted July 21, 2009 Share Posted July 21, 2009 By finding gravitational PE. We can get ans. Link to comment Share on other sites More sharing options...
swansont Posted July 21, 2009 Share Posted July 21, 2009 what is hoghmann transfer orbit? can anybody give me the deduction for minimum energy? or tell me where to find it pls. i am a 1st yr stdnt of physics only. Google leads me to Wikipedia. These two sites are your friends for this kind of question. http://en.wikipedia.org/wiki/Hohmann_transfer_orbit Link to comment Share on other sites More sharing options...
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