Camille Flammarion 1888. Freedman and Madore (2010)

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Presentation transcript:

Camille Flammarion 1888

Freedman and Madore (2010)

S S’ E E’ O R ES R EM rSrS rErE rsrs rMrM Aristoteles Eudoxus terminator D. HaworthNASA/JHUAPL

Cons. Momentum Center of Mass Collisions Superball - basketballGravity assisted spaceflight

Mayor and Queloz (1995) Rubin and Ford (1970)

Cons. Momentum Center of Mass Mahy et al (2010) HD48099 Exoplanets Binary stars Mayor and Queloz (1995) Rocket propulsion and Multi-stage rockets Apollo 11 Pluto & Charon ( NASA/JHU)

Problem: Exoplanet Kepler 5b: circular orbit about a star M star = 1.37 M Sun orbital speed = 230 m/s, orbital period = 3.55 days. (a)Find the radius of the planet’s orbit (in AU). (b)Find the orbital speed of the planet. (c)Find the planet’s mass (in units of M jup ). When the planet transits the star, the star’s measured intensity decreases by a factor of The transit takes roughly 4.4 hours from start to finish. (d)Find the star’s radius (R Sun = 7 x 10 8 m). (e)Find the radius of the planet. Compare this to the R Jup. Koch et al (2010)

Mars Earth rprp rara Catling & Zahnle (2009 )

Problem : Sagittarius A is a black hole at the center of MW galaxy. The star labeled S0-2 has been tracked for more than half of its elliptical orbit about the galactic center: T (period) = 15.8 ±.4 yr, ε (eccentricity) =.89 ±.01, a (semi-major axis) = 1040 ± 20 AU. In 2012, star S0-102 was successfully tracked, with T = 11.5 ±.3 yr and ε = (a)Calculate the mass of Sagittarius A in terms of solar masses. (b) Find the semi-major axis of S (c) What is the speed of S0-102 at its periapsis? Express this as a fraction of the speed of light.

θ RERE

Problem: Tidal effects are slowing Earth’s rotation. Far in the future, the planet’s rotation will be phase-locked to the orbit of the Moon. At that time, the Moon’s orbital angular momentum will be nearly equal to the total angular momentum of the Earth and Moon. ( L orb ≈ 0.8 L tot at the present time.) Use this approximation to answer the following questions. (a)How far away will the Moon be at that time? Express your answer in Earth radii. (b)What will be the length of an Earth day? What will be the period of the Moon’s orbit? Express your answers in terms of a present Earth-day. (c)Approximately when will this occur? Ans: (a) 89.3 R E (b) 49.6 d (c) 4.9 Gyr NASA

Exercise: One-dimensional “collision”: space probe executing a close fly- by of Jupiter. (a)What is the probe’s initial velocity relative to the CM? (b) What is its final relative velocity ? (c)What is its final speed relative to the Sun? Ans: (a) 23 i km/s (b) - 23 i km/s (c) 36 km/s 10 km/s 13 km/s Problem: 3-dimensional fly-by: Galileo and Venus. (a) If Venus deflects Galileo by 150° (in the CM reference frame), what is the final velocity of the spacecraft relative to the Sun? (c) Suppose instead that the two bodies are moving in the same direction, and the spacecraft’s deflection is 90° (in the CM frame). What is the final speed of the craft relative to the Sun? 35 km/s 40 km/s