1 Elliptical Orbits [30%] Consider three different orbits of a satellite around the Moon (Mmoon = 7.35 × 10^22kg), each with the eccentricity vector pointing in the î direction and periapsis distance rp = 2000km, but with three different eccentricities: e = 0.25, 0.5, 0.75. Provide a computer-generated sketch of the orbits overlayed on one plot, and for each determine: the apoapsis distance, ra; the semi-major axis, a; the orbital energy, ℰ; and the orbital period, τ.

1 Elliptical Orbits [30%] Consider three different orbits of a satellite around the Moon ($M_{moon} = 7.35 \times 10^{22}kg$), each with the eccentricity vector pointing in the $\hat{i}$ direction and periapsis distance $r_p = 2000km$, but with three different eccentricities: $e = 0.25, 0.5, 0.75$. Provide a computer-generated sketch of the orbits overlayed on one plot, and for each determine: the apoapsis distance, $r_a$; the semi-major axis, $a$; the orbital energy, $\mathcal{E}$; and the orbital period, $\tau$.

Problem 2: Elliptical orbit (12 pts.) Around the same time that astronomers downgraded Pluto to a dwarf planet, they began to find evidence that could suggest another large planet far outside the orbits of the rest (planet 9). If this is correct, the mass would be around that of Neptune, or 1.02 1026 kg. Its perihelion distance would be Rp = 200 AU from the Sun, and aphelion distance Ra = 1,200 AU. A. For this elliptical orbit, find the following quantities: 1. The semi-major axis a. 2.The distance from the center of the orbit to the Sun, c 3.The eccentricity e. B. The mass of the Sun is 1.99 1030 kg,and 1 AU = 1.5 1011 m.What would the orbital period of this planet be, in years? C. What is the total energy of the planet in this orbit?

Timothy J.

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