Question

Problem Solving: LightSail 2
LightSail 2 was a satellite that was designed to use solar radiation to change its altitude as it circled Earth. The spacecraft had a mass of 5.0kg. It was originally launched by a rocket with its sail closed, and established an orbit at an altitude of 720 km above Earth’s surface. Then it deployed its sail, which had an area of 32m2. Assume the sail is completely reflective.   
1) After a full month of “½ time exposure” (you don’t want the sail turned towards the sun during the part of the orbit in which the change in momentum would slow the craft), what would be the expected change in the craft’s speed? Assume a 30 day month. Also assume all the force goes into a change in speed. 2) What would be its change in orbital altitude (assuming circular orbits)?

Hints:
o You will need to look up a number of constants about the Sun and Earth. o One thing a sophisticated solution should consider is that the gravitational force from Earth at the satellite’s location is NOT “mg” with “g” as 9.8m/s2. If you go to this level of sophistication then you will need to use the equation for gravitational force between two spherical masses, i.e. the one with “G,” the universal gravitational constant. Also, if you go to this level of sophistication, your result will probably surprise you. It may be useful to then look at a chart of planetary speeds versus planetary orbits. And discuss. Also note: this would really cause the spacecraft to develop orbits with eccentricity (elliptical characteristics). It had limited success. A lot of “tumbling” occurred but some altitude deviations were observed with enough consistency to be presented in publication.   

Answer 1

Sol- I] Light sail=2 The Sun Poce at earth is 2 I= 13 70 W/m2 an O8bit at an altitude = 720 km surface curea - 32m2. menoglu The radiation Pressure is ... 218 P= 21 - 2(1370) e 3x108 eltaart si =9.13*1ö Paolo 1 The Presswre. F-PACE A Bornesto =19.138165) (32) = 2.92*10-4 M M The change in linear momentum is.exual to The impulse. J = FAL=A PEMAND S solling for the change in Velocity: Av - Fiat m. The giving data: Av = (2.92810-4 (30 x 24*60*60 CS$canned with CamScanner 5.0 nner

Av = 151.4 m/s For a circular orbit: v=V Gm V=V htR M= is the mass of earth h = The altitude above the Earth's furtace R = is The Yadius of earth The speed = f Gm HAR Avv=V=Van Cinta VAR) Then Av=N-V=VGm C HUR The given values. 151.4 = 6.67x16"(5.97X iš 5.97X10 6720x10+6371x103 W H +6371*103 Hz The value o H = 1.015*10cm = 1015km CS$canned with CamScanner