Assume the Earth is in a circular orbit around the sun. With the further assumpt
ID: 2077588 • Letter: A
Question
Assume the Earth is in a circular orbit around the sun. With the further assumption that gravitational potential energy = 0 at infinite distance, what is the gravitational potential energy of Earth in its orbit around the Sun? (B) What is the kinetic Earth as it moves in its orbit around the Sun? (C) What is the escape velocity from the Sun of an object at 1 AU from the Sun? (This is, of course, the escape velocity of Earth from the solar system.) What is the dot product of A = -2 i + 8 j + 10 k and B = -5i + 3 j - 3 k?Explanation / Answer
5(A) PE = - G M m / r
= - (6.67 x 10^-11) (1.99 x 10^30) (5.972 x 10^24)/ (149.6 x 10^9)
= - 5.30 x 10^33 J
(B) KE = - PE/2 = 2.65 x 10^33 J
(C) total energy = PE + KE = - 2.65 x 10^33 J
initial total energy = final total energy (final PE + KE)
- 2.65 x 10^33 + (5.972 x 10^24 v^2 / 2) = 0
v = 29786 m/s Or 29.8 km/s
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dot product: A.B = ( -2i + 8j + 10k). (-5i + 3j - 3k)
= (-2 x -5) + (8 x 3) + (10 x -3)
= 10 + 24 - 30
= 4