3) An asteroid (with negligible escape speed) is discovered in a circular orbit 0.26 AU from the Sun. If you launched a rocket from Earth to it on a minimum energy orbit, how long would it take to get there (in years), what would be the relative speed be at close encounter and what would the Earth-asteroid distance be when the spacecraft arrived (in AU)? What was the launch speed from Earth (in km/s)?
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- When a falling meteoroid is at a distance above the Earth's surface of 2.4 times the Earth's radius, what is its acceleration due to the Earth's gravitation? (Units: m/s2)Refer to this table to determine the average distance between the Earth and the Sun. Then calculate the average speed of the Earth in its orbit in kilometers per second and meters per second?6. Consider a planet of mass m in orbit about a star of mass M. Since M >> m, we can assume the star is at rest. a) Show that the energy of the planet can be written as GMm E = 2mr? b) Now assume the planet is in a perfectly circular orbit. What is the energy in this case? c) Represent the energy obtained in part (b) on an energy diagram. (Draw and label very carefully.)
- We would like to be able to make meaningful interpretations of variations in the acceleration due to gravity, g, as small as 0.1 mgal. How accurate must our knowledge of the latitude of our gravity stations be? (A “gravity station" is just a location at which you make a gravity measurement.) You can assume your latitude is 45°.Black holes are difficult to observewith telescopes because they, bydefinition, don’t emit or reflect any light. They can be found by look-ing for other nearby objects orbit-ing them, however. Here is a dia-gram of a star in a circular orbit around a black hole. a. The period of the star’s orbit is 90 days, and its orbital radius around the black hole isobserved to be 3.6 : ×10^11 m. Find the orbital velocity of the star in units of m/s. (You need to convert 90 days to seconds, first). The circumference of a circle is 2πr. b. The mass of the star is known to be 4 × 10^30 kg. Find the centripetal acceleration of thestar and the strength of the gravitational force on the star. c. Find the mass of the black hole.3 From Wikipedia: "Various sources state the first Death Star has a diameter of approximately 140 kilometers." A) In order to stand on the surface of the Death Star and experience the familiar gravitational acceleration of g = 9.8 m/s², what is the required mass of the Death Star? Calculate the density as well (yikes!) B) An escape pod is now launched from the surface of the Death Star at speed v₁ = 760 m/s. How fast is the pod moving when it reaches a distance of 130 km from the center of the Death Star? Star
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- Suppose astronomers found evidence of an earth-like planet 20 lightyears away. a) what may be two ethical considerations that one may consider when deciding if humans should travel to this planet? b) how fast would a spaceship need to travel if the roundtrip can no take longer than 40 years for the astronauts? c) how much time will the trip take according to the people on earth?The energy to mové a rocket (mass m) nfinitely far from the Earth (Radius R and mass M) E = jGMma 1 E = x? 2 is What escape velocity at liftoff gives an energy that equals E. RA spacecraft traveling at a velocity of (-20, -90, 40) m/s is observed to be at a location (200, 300, -500) m relative to an origin located on a nearby asteroid. At a later time, the spacecraft is at location (-380, −2310, 660) m. (a) How long did it take the spacecraft to travel between these locations? (b) How far did the spacecraft travel? (c) What is the speed of the spacecraft (d) What is the unit vector in the direction of the spacecraft's velocity?