Question

# MATINS BETERE 1) If an object is in Earth's orbit (a=1.000 A.U., e=0.0167) and suddenly increases its energy by 10 per cent without increasing its angular momentum [perhaps it fires a

rocket engine towards the Sun, accelerating it directly outwards]: what is the final semi-major axis and eccentricity of the object's orbit? Note: E<0. Therefore increasing E by 10% means less negative or 90% of the original value. (Marks: 4) 2) The Earth was last at perihelion on January 3, 2022. The period of the Earth's orbit is 365.25 days. (a) If the Earth's orbit was a perfect circle when (give the actual calendar date in your answer!) would it reach a True Anomaly (angle with respect to perihelion) of 160 degrees? (b) But given that the Earth's orbit is slightly elliptical (e-0.0167), when (calendar date) will the Earth actually be at True Anomaly of 160 degrees? (c) How far will the Earth be from the Sun at that time? (d) How fast will the Earth be moving in its orbit on that day? (e) (for comparison to (c) and (d)) what is the distance (from the Sun) and speed of the Earth when it is at perihelion? (Marks 10) 3) How bright will Pluto appear in reflected or scattered sun-light (total Flux received in W/m²) at the Earth when Pluto is at Opposition and a distance from the Sun of 40.0 A.U.? Assume that Pluto has an albedo of 0.60 and a radius of 1.2 x 10³ km. (Marks: 6) DELL

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