Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10The “New” AstronomyWhat is the force of gravity on a satellite that is one Earth radius above the surface of the Earth? The weight of the satellite on Earth is 10,000 N?The “New” AstronomyWhat is the force of gravity on a satellite that is one Earth radius above the surface of the Earth? The weight of the satellite on Earth is 10,000 N?At one Earth radius above the surface of the Earth, h = RE. Thereforeg = G Mp / (Rp + h)2 g = G Mp / (Rp + RE )2 g = G Mp / (2 Rp )2 g = (¼) G Mp / ( Rp )2 = (¼) 9.8 m/sec2Therefore W = m (1/4) g = ¼ m g = ¼ (10,000 N) = 2,500 NThe “New” AstronomyA comet has an orbit that just touches the Earth’s orbit at perihelion and just touches the orbit of Neptune at aphelion. What is the period of the comet’s orbit? Assume the orbit of the earth and Neptune are circular.Table 2.1 Some Solar System DimensionsTable 2.1 Some Solar System DimensionsPlanetPlanetSemimajor Axis (au)Semimajor Axis (au)Period (Earth Years)Period (Earth Years)EccentricityEccentricityMercuryMercury0.3870.3870.2410.2410.2060.206VenusVenus0.7230.7230.6150.6150.0070.007EarthEarth1.0001.0001.0001.0000.0170.017MarsMars1.5241.5241.8811.8810.0930.093JupiterJupiter5.2035.20311.8611.860.0480.048SaturnSaturn9.5379.53729.4229.420.0540.054UranusUranus19.1919.1983.7583.750.0470.047NeptuneNeptune30.0730.07163.7163.70.0090.009PutoPuto39.4839.48248.0248.00.2490.249The “New” AstronomyA comet has an orbit that just touches the Earth’s orbit at perihelion and just touches the orbit of Neptune at aphelion. What is the period (approximately) of the comet’s orbit? Assume the orbit of the earth and Neptune are circular.If the orbits are considered to be circular, then the distance to perihelion is approximately 1 au, and the distance to aphelion is approximately 30.07 au. Therefore, the length of the major axis is 31.07, and the length of the semimajor axis is 15.535 au. From Kepler’s Third Law15.5353 ≈ 3749 = P2Therefore, the Period = 61.2 yearsThe “New” AstronomyWhat is the eccentricity of the comet’s orbit in the previous question?Distance to perihelion = 1 au = a (1 – e)Where a is the length of the semimajor axis and e is the eccentricity.Therefore, 1 = 15.535 (1 – e) → e = 0.936The “New” AstronomyA satellite is to be placed in orbit 2 Earth radii above the surface of the Earth. At what speed will the satellite have to move in order to establish a circular orbit at the height?F = F = G {MEarth msatellite / r2 } = msatellite v2 / r (circular orbit)Therefore, with some algebra,V2 = G MEarth / r = G MEarth / 3REarth The values of G, MEarth, and REarth can be found in tables in the book.The “New” AstronomyWhere is the center of mass of the Sun and Jupiter when Jupiter is at aphelion?Table 2.1 Some Solar System DimensionsTable 2.1 Some Solar System DimensionsPlanetPlanetSemimajor Axis (au)Semimajor Axis (au)Period (Earth Years)Period (Earth Years)EccentricityEccentricityMercuryMercury0.3870.3870.2410.2410.2060.206VenusVenus0.7230.7230.6150.6150.0070.007EarthEarth1.0001.0001.0001.0000.0170.017MarsMars1.5241.5241.8811.8810.0930.093JupiterJupiter5.2035.20311.8611.860.0480.048SaturnSaturn9.5379.53729.4229.420.0540.054UranusUranus19.1919.1983.7583.750.0470.047NeptuneNeptune30.0730.07163.7163.70.0090.009PutoPuto39.4839.48248.0248.00.2490.249The “New” AstronomyWhere is the center of mass of the Sun and Jupiter when Jupiter is at aphelion?At aphelion, the distance between the Sun and Jupiter is a (1 + e) = 5.203 (1+0.048) = 5.453 auUsing the center of the sun as a reference, Xcm = (MSun xSun + MJupiter xJupiter)/(MSun + MJupiter) = (317.8 MEarth 5.453 au)/(330000 MEarth + 317.8 MEarth = (1732.96/330317.8)= .00525 auThe “New” AstronomyWhere is the center of mass of the Sun and Jupiter when Jupiter is at aphelion?At aphelion, the distance between the Sun and Jupiter is a (1 + e) = 5.203 (1+0.048) = 5.453 auUsing the center of the sun as a reference, Xcm = (MSun xSun + MJupiter xJupiter)/(MSun + MJupiter) = (317.8 MEarth 5.453 au)/(330000 MEarth + 317.8 MEarth = (1732.96/330317.8)= .00525 auThe “New” AstronomyWhere is the center of mass of the Sun and Jupiter when Jupiter is at aphelion?The center of mass of the Sun-Jupiter system is shifted 0.00525 au from the center of the sun.The radius of the sun is 0.00465
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