The scientific satellite ISEE 1 had its perigee is at 1.2 Re, apogee at 23 Re. About how much slower do you think its motion was at apogee, compared to its perigee pass?

How many AU is  it from the Sun to its apogee

 

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Kepler’s Law

1.Tycho’s nova had right ascension RA = 0, 22 m, declination d = 63 degress 53′. Look up at a star chart– in which constellation did it occur?

Tycho’s nova occured in the constellation Cassiopeia

 

2.Section #8b about using a total lunar eclipse to measure the distance to the moon , includes a map of the eclipse of August 11, 1999. The path of totality across the Black Sea is shown, as are samples of the region of totality at selected times. You will notice that region is nearly circular

However, on a map of the complete path of totality (which by the way is available at the web site cited there), you will find that as you follow that path, the patch of totality becomes more and more elliptical and elongated. By the time the eclipse ends, at sunset in India, the patch is a rather lengthy ellipse. Why? And why do you suppose the duration of the eclipse is shorter there?

When the moon’s umbral shadow strikes the earth is is in the shape of a cone. By the time the eclipse ends, at sunset in India, the patch is a rather lengthy ellipse because when the moon’s shadow first moves across the Earth at sunrise it is more elongated. As it moves across the Earth through the day, it becomes more circular and then around sunset elongates again. Since the moon’s shadow that is touching the Earth is more elongated at sunset and at the narrower end of the shadow’s cone the duration of the eclipse is shorter.

 

3.The mean distance of Neptune from the Sun is 30.07 AU (=astronomical unit, means Earth-Sun distance), that of Pluto 39.4 AU. Are these two numbers connected? (Hint: Derive the ratio of the orbital periods!)

Neptune has an orbital period of approximately 165 earth years. Pluto has a orbital period 248 earth years. Together they share a 3:2 ratio meaning that for every 3 orbits of the Sun completed by Neptune, Pluto completes 2 orbits. The higher the orbital period the lower the AU.

 

4. The period of Comet Halley is approximately 75 years. Assume its perigee is at 0.5 AU from the Sun (1 AU or “astronomical unit” is the mean Earth-Sun distance). How many AU is  it from the Sun to its apogee? Does it get further from the Sun than the mean distance of Pluto, about 39 AU?

Equation used:

(Aphelion + Perihelion)/2=a=(75^2)

Aphelion = 2[(75^2)] – Perihelion

Aphelion = 2 [(75^2)] – 0.5

The apogee is 11249.5 AU and does not get further than the mean distance of Pluto.

 

5.A satellite in a circular orbit just above the surface of the Earth (r = 1 Re) would need 8 km/sec to stay in orbit. If a missile is sent at that same speed straight up, how high will it get?

Hints: (1) The semimajor axis of an orbit depends only on the launch energy.(2) The trajectory of an object tossed straight up may be viewed as an ellipse of zero width.

 

6.The scientific satellite ISEE 1 had its perigee is at 1.2 Re, apogee at 23 Re. About how much slower do you think its motion was at apogee, compared to its perigee pass?

 

7.Meteorites tend to fall more frequently in the afternoon, suggesting they overtake the Earth in its orbital motion. What can this tell about their origin?

The meteorites orbit is beyond that of the Earth’s orbital motion.

 

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