2006-06-09 14:00:29 · 2 answers · asked by goring 6 in Science & Mathematics ➔ Physics
The radius of gyration is defined in ref. 1 as the length "... obtained by dividing the moment of inertia I by the mass of the object M and taking the square root". In other words, it's the R that satisfies I = M*R^2. The mass of the solar system can be reasonably assumed to be roughly constant in the short term (if we agree on which bodies are planets, asteroids, etc.) but the moment of inertia varies, as does the center of mass about which I is measured, due to orbital motions of the planets.
If numbers related to the sun alone are any help: The sun's mass is 1.99E30 kg (ref. 2) which is 99.8% of the total solar-system mass. The sun's moment of inertia (ref. 3) is 0.059, given as the ratio I/(M*R^2) where R in this context is the radius of the sun. Thus the radius of gyration of the sun is 1/SQRT(0.059) times its actual radius = 0.2429 * 695000 km = 168800 km.
2006-06-14 11:56:09 · answer #1 · answered by kirchwey 7 · 0⤊ 0⤋
it simple take the distance of the last planet from sun(pluto or sedna)then double it and use the formula for ixx from which u can find the radius of gyration
2006-06-09 14:16:23 · answer #2 · answered by sankardivya1 2 · 0⤊ 0⤋