oldaccount1 Posted January 9, 2006 Share Posted January 9, 2006 I have a planet's mass and radius. Mass: 6.5 ? 10^24 Radius: 7250 kilometers How can I calculate things like gravity? How can I calculate orbit velocity? Link to comment Share on other sites More sharing options...
Guest Posted January 9, 2006 Share Posted January 9, 2006 Hi there, Gravitational Field Acceleration = -GM / r^2 (r distance to CENTER of planet, in metres), G - Gravitational Constant, M - Mass of planet (in kg) Orbit Velocity will be to do with the force exerted on the object. The force between the planet and the satellite, moon(?) will be GMm/r^2 Using circular motion, mv^2 / r = GMm/r^2 therefore v^2 = Gm/r therefore v = ROOT (GM/r) (ie. the mass of the orbing object is irrelevant) Dont quotw me on this though - it's been awhile since ive done circular motion :p Link to comment Share on other sites More sharing options...
ventrox Posted January 9, 2006 Share Posted January 9, 2006 Hi there, Gravitational Field Acceleration = -GM / r^2 (r distance to CENTER of planet, in metres), G - Gravitational Constant, M - Mass of planet (in kg) Orbit Velocity will be to do with the force exerted on the object. The force between the planet and the satellite, moon(?) will be GMm/r^2 Using circular motion, mv^2 / r = GMm/r^2 therefore v^2 = Gm/r therefore v = ROOT (GM/r) (ie. the mass of the orbing object is irrelevant) Dont quotw me on this though - it's been awhile since ive done circular motion :p yeah i think you're right (it's been a while since i studied this, too :p) Link to comment Share on other sites More sharing options...
dreamz Veteran Posted January 9, 2006 Veteran Share Posted January 9, 2006 moved here Link to comment Share on other sites More sharing options...
_sphinx_ Posted January 9, 2006 Share Posted January 9, 2006 I have a planet's mass and radius. Mass: 6.5 ? 10^24 Radius: 7250 kilometers How can I calculate things like gravity? How can I calculate orbit velocity? hey there. Let me start you off with a few simple laws: Newton's universal gravitational law: F=(GMm)/(R^2) F: The force by which the 2 masses attract each other (Yes its the same! You pull the earth by the same force as it pulls you but of course since you're much lighter than the earth, you don't attract it efectively) G: The universal gravitational constant....Its ~6.673e-11 (where e means the power of [exponent]) M: Mass of object 1 (in this case, the earth) m: Mass of object 2 (in this case, the object in orbit [satellite]) R:the distance between your two masses So if you have the mass of the earth: 5.98e24 kg The sat.: about 300 kg radius: 7250 km so F=(6.67e-11 x 5.98e24 x 300) / (7250,000^2) =2278 N Now you know for a fact that the weight of anything= mass x accelearation due to velocity Weight=the force of attraction between the satellite and the earth (you know this for a fact) so: mg=(GMm)/(R^2) divde by m g=GM/(R^2) so to calculate the gravity acceleration at any point, you just use this equation....to calculate the gravity acceleration at the orbit of the satellite: g= (6.67e-11 x 5.98e24) / (7250,000^2) = 7.59 ms^-2 To calculate the speed of the satellite craft, you have to know that in the satellite's orbit around the earth, what keeps it moving in a circular path is the centripetal force which = m(v^2)/R This centripetal force is provided by the weight of the satellite which is mg So mg=m(v^2)/R divide by m g=v^2/R so v=square root of gxR substitue the g for the value we just got (7.59) and the R for 7250000 and you'll find that v= 7418 ms^-1 Hope that helps m8 Link to comment Share on other sites More sharing options...
Recommended Posts