Question

2. Suppose you and some aliens decide to plot the solar system. The only natural point in the solar system might be the sun as the center. So both you and the aliens decide to put the origin there. The Aliens decided to use the basis given in green and you are using the basis given in blue (See below). The aliens sent you their coordinates for the planets Mercury, Venus, Earth, and Mars, in their coordinate system. You also happen to know how to express the alien's coordinates through your coordinates. That is fı = ei tea and f2 = -21 +€2. You need to convert the information they gave you to your basis to be able to provide the United Nations the information you and the aliens have been sharing. What are the coordinates of the planets in your system? Here are the coordinates for the planets in the alien coordinate system: (Stercury: (-12 Views: 13 Earth: Mars: 12 e2 e 1 f1 Figure 1: Solar system

Answer 1

21 fa between own The relation 7 co-ordinate system (ee) and 0 f 0 the alien's co-ordinate system (fi, f₂) is given by Zhe system of equis - f = etę f2 = - 3ete W gives, fo-f₂ = 7 sae= (fi-f2) 2 / 3 x + ① gives, (a fit f2) = 7 3 2 ₃ E 3/2 ( 12 f1 + f2) So be will own im for Mercury (f., f₂) = (1,- £) co-ordinate (4,2)-((1+1), 14.-))) - 62). Similarly, for Venus, (41,42)=(2,0). So, (4,2)-($(2-0), 3(3.2+0) -() For Furth, (frotz) = (-3,-1). So, (4, 5)-((2+1), 3(442-1) --»-) For Mars, (fi, f2) = (3, 1). So, (9,3)=((3-1), $(13.3 +1)) = (2,5)