1. The vector R2 is 150 million kilometers j. The vector Ri is as in problem (3)
ID: 1879529 • Letter: 1
Question
1. The vector R2 is 150 million kilometers j. The vector Ri is as in problem (3). R # 0.7 R1 + 0.7 Rz . Find the components of the vector R in SI units and express them in Find the magnitude of the vector R scientific notation. 2. Given F in problem (2) of Quiz 1 is the magnitude of the gravitational force of Mi on M2, if Mi is the mass of the Sun 2.0X10 g, and Mz is the mass of the Earth 6.0x1027 g and Newton's universal gravitational constant G 6.7X10-11 kg1 m3 s2, and the displacement from the Sun to the Earth is R as above at some time t, find the magnitude of the gravitational force of the Sun on the Earth at that time. 3. Suppose that the displacement from the Earth to Mars at the time t above is 85 gigameters in the +x direction, find the magnitude and the direction of the displacement from the Sun to Mars at time t. 4. The period of a circular orbit of an object bound by gravity around a spherically symmetric distribution of matter depends only on Newtons universal gravitational constant G and the average density of the matter inside a sphere whose center is the center of the orbit. Mars is bound by gravity. Approximate the orbit of Mars by a circle and the Sun to be au its center. The sum of the masses of Venus and Mercury and the smalle objects orbiting closer to the Sun than Mars is less than the mass of the Earth. Find the time in Earth years that it takes Mars to orbit the Sun. Hints: use dimensional analysis to find a relation between density and period and translate this into a relation between distance and period f planets orbiting the Sun.]Explanation / Answer
Given that,
R2 = 150*10^6 (j) km
R1 (from problem 3) = 85*10^6 (i) km
R = 0.7R1 + 0.7R2
R = 0.7* 85*10^6 i + 0.7*150*10^6 j
R = (59.5 i + 105 j) million kms
x - component of vector R = 59.5 i million kms
y - components of vector R = 105 j million kms
magnitude of vector R,
|R| = sqrt [(59.5)^2 + (105)^2]
|R| = 120.68 million kms
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