Solar Sailing 201 - Revision history

Ben: /* Gravity */

2007-12-14T19:53:11Z

‎Gravity

Ben at 19:30, 14 December 2007

2007-12-14T19:30:36Z

Ben at 18:53, 14 December 2007

2007-12-14T18:53:44Z

Ben at 19:54, 17 February 2006

2006-02-17T19:54:31Z

New page

==Introduction==

[[Solar Sailing 101]] is a qualitative introduction to solar sailing. That is, there was almost no math involved. This document will introduce the basic mathematics behind solar sails. Upon completion, the reader should be able to:
* Calculate the acceleration of a solar sail in orbit around a star.
* Plot the orbit of a solar sail that is pointed straight at the sun.
* Using a computer, calculate the trajectory of a sail held at a constant angle with respect to the sun.

==Gravity==

Solar sails, like other objects, are subject to gravity when travelling through space. This discussion will be limited to gravity from the sun and not the planets or other bodies. This is simpler, because both sunlight (which pushes outward) and gravity (which pulls inward) come from the same nearly fixed source.

The acceleration <math>a_g</math> of a solar sail due to the sun's gravity

← Older revision		Revision as of 19:53, 14 December 2007
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	Solar sails, like other objects, are subject to gravity when travelling through space. This discussion will be limited to gravity from the sun and not the planets or other bodies. This is simpler, because both sunlight (which pushes outward) and gravity (which pulls inward) come from the same source.		Solar sails, like other objects, are subject to gravity when travelling through space. This discussion will be limited to gravity from the sun and not the planets or other bodies. This is simpler, because both sunlight (which pushes outward) and gravity (which pulls inward) come from the same source.

−	The acceleration <tex>a_g</tex> of a solar sail due to the sun's gravity is <tex>{\mu \over r^2}</tex>, where <tex>\mu</tex> is the ''gravitational parameter'' of the sun.	+	The acceleration <tex>a_g</tex> of a solar sail due to the sun's gravity is <tex>{\mu \over r^2}</tex>, where <tex>\mu</tex> is the [[wikipedia:gravitational parameter\|gravitational parameter]] of the sun.

@@ Line 2: / Line 2: @@
 [[Solar Sailing 101]] is a qualitative introduction to solar sailing. That is, there was almost no math involved. This document will introduce the basic mathematics behind solar sails. Upon completion, the reader should be able to:
 * Calculate the acceleration of a solar sail in orbit around a star.
 * Plot the orbit of a solar sail that is pointed straight at the sun.
@@ Line 10: / Line 11: @@
 Solar pressure and gravity both decrease as you travel farther from the sun which approximates an ''inverse square law'', which will be explained here. The photons leaving the surface of the sun expand in a continually growing sphere. These larger spheres have the same original amount of sunlight, and hence momentum, but it is spread out over a larger area, so the solar pressure is lower. Gravity works similarly, but with different principles <TBD>.
-The area of the sun, with radius <tex>r_s = 6.960\times 10^8 </tex>
+The area of the sun, with radius <tex>r_s = 6.960\times 10^8 m</tex>, is <tex>4 \pi r_s^2</tex>. Farther from the sun, the area is <tex>4 \pi r^2</tex>. The ratio of the two is <tex>{r_s^2 \over r^2}</tex>. Thus, the area of the sphere has decreased by a factor of <tex>{1 \over r^2}</tex>, the ''inverse square'' of the distance ''r'' from the sun.
 ==Gravity==
@@ Line 16: / Line 17: @@
 Solar sails, like other objects, are subject to gravity when travelling through space. This discussion will be limited to gravity from the sun and not the planets or other bodies. This is simpler, because both sunlight (which pushes outward) and gravity (which pulls inward) come from the same source.
-The acceleration <tex>a_g</tex> of a solar sail due to the sun's gravity
+The acceleration <tex>a_g</tex> of a solar sail due to the sun's gravity is <tex>{\mu \over r^2}</tex>, where <tex>\mu</tex> is the ''gravitational parameter'' of the sun.