Question

Think the Sun to be at the origin of a xy-coordinate system. A telescope spots an asteroid in the xy-plane at a position given by (x, y) with a velocity given by (vx, vy). 

[DATA: (x, y) = (3.3, 5.5) ×10^11 m; 

(vx, vy) = (-6.1, -4.0) ×103^ m/s.] 

(A) What will asteroid's speed be at closest approach (perihelion)? 

(B) What will asteroid's distance from the Sun be at closest approach?

2. The perihelion distance from the sun for planet Uranus is 2.750 ×10^9 km; the aphelion distance is 3.000 ×10^9 km. 

(A) compute period of revolution around the sun, for the planet Uranus. [Hint: 1 AU = 1.496 ×10^8 km.] 

(B) Determine the eccentricity of the orbit of Uranus. 

3. NASA sends satellites to Mars by placing the satellite in a Keplerian orbit (around the sun) such that the perihelion is at radius of the Earth's orbit (1 AU) and the aphelion is at the radius of Mars's orbit (1.52 AU). Most of the trip to Mars is just free fall in the sun's gravitational field. The small gravitational effects of Earth and Mars, which only affect satellite at the very beginning and end of the trip, may be neglected. Calculate the time it takes the satellite to travel from Earth to Mars. State the result in days. 

4. A) the perihelion distance of Halley's Comet is 0.587 AU, and the period is 76.1 years. Calculate the aphelion distance, expressed in AU. [Hint: 1 AU is mean radius of Earth's orbit.] 

B) Using the result of the first part, calculate the speed of Halley's Comet at perihelion and aphelion. Express results in km/s. [The speed of Earth is 30 km/s.] 

First, what is speed at perihelion (in km/s)? 

Second, what is speed at aphelion (in km/s)?