it is theoretically possible to place a satellite at a position between the earth and the sun on the line joining them, where the gravitational forces of the sun and the earth on the satellite combine in such a way that the satellite will execute a circular orbit around the sun that s synchronous with the earth's orbit around the sun. (In other words, the satellite and the earth have the same orbital period about the sun, even though they are at different distances from the sun. the satellite always remains on the line joining the earth and the sun.)
write an expression that relates the appropriate circular orbital speed of v of a satellite in such a situation to its distance r from the sun.
Expressions may also contain quantities such as:
Ms, Me, D, Rs, Re plus the gravitational constant G.
please answer this, cant provide the figure i dont know how to post it here
2007-09-24 17:08:03 · 3 answers · asked by la 1 in Science & Mathematics ➔ Astronomy & Space
water_skipper, that's a very interesting orbit, but not the one la is referring to.
That would be one of the 5 Earth-Sun Lagrange point orbits, specifically L1. Where there are already a few satellites. Notably SOHO and WMAP.
The L1 point in any two-body system is where the gravitational attractions of the two bodies exactly balance. That is, where Ms/Rs^2 = Me/Re^2. For us, that comes out to approximately 0.9 AU from the Sun and 0.1 AU from Earth.
Orbital circumference for L1 would then be 3.1416*1.8 AU, or 8,482,320,000 km. And its orbital velocity would be 96,830 km/hr.
So the formulae are:
Rs = sq rt(Re^2 * Ms/Me)
D = pi * 2Rs
V = D/T
where Rs = distance of L1 from the Sun, Re = distance of L1 from Earth, Rs+Re = 1AU (150 million km), D = orbital circumference of L1 around the Sun, T = orbital period of L1, and V = orbital velocity of L1
G is not necessary in the calculation, nor is the mass of the satellite, since the position is determined by the ratio of two forces, and those factors would cancel out.
***
edited for clarity
2007-09-24 19:36:05 · answer #1 · answered by skeptik 7 · 0⤊ 0⤋
Where is the problem? We have geosynchronous satellites in orbit all they time, they remain in the same spot over the equator and orbit the sun with the Earth.
2007-09-27 21:50:38 · answer #2 · answered by johnandeileen2000 7 · 0⤊ 0⤋
Yes. Not only is it possible, it's true!
2007-09-25 00:32:36 · answer #3 · answered by Anonymous · 0⤊ 0⤋