19. A laser beam takes 0.024s to travel from a rocket to the reflective surface of a planet and back to the rocket. How far is the rocket from this planet's surface? a) 2400 km b) 1200 km c) 1800 km d) 3600 km e) 4800 km Sign out V1 9:08
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- 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.)a. Find the acceleration due to gravity at the surface of a neutron star of mass 1.5 solar masses and having a radius of R = 10.0 km. b. Find the weight of a 0.120-kg baseball on the surface of this star. c. Assume the equation U = mgh applies, and calculate the energy that a 70.0-kg person would expend climbing a 1.00-cm-tall mountain on the neutron star. d. Find the speed needed by a small satellite to maintain a circular orbit with a radius of 2R around the neutron star.1. Consider our Sun - it is in orbit around the center of our Milky Way Galaxy. The velocity of the Sun in its orbit is about 250 km/s. The distance to the center of the galaxy is about 9.1 kpc (kiloparsecs). We can use Kepler's third law to calculate the mass of the galaxy interior to the Sun's orbit. We assume that the orbit is circular so that the semimajor axis is just the radius of the circular orbit = 9.1 kpc. First we need to calculate the number of AU's in 9.1 kpc. (Note that 1 Крс - 1000 рс - 3260 1t yrs and 1 pc - 206,265 AU.) %3D a =r =9.1kpc = (9.1kpc) 1000 pc 206,265AU] 1kpc AU Sun 1pc
- 1. Let’s say we have a black hole with a mass 10 times that of the Sun (the Sun’s mass is 2 x 1030kg so the mass of the black hole is then 2 x1031 kg) Using the definitions for G and c what Schwarzschild radius of this black hole be? g=6.67 x 10-11 m3 kg-1 s-2 c=3 x 108 m s-1Consider a US Air Force launch of its latest GPS satellite from Cape Canaveral. Radar tracking shows the following J2000 state vector (X,Y,Z and Vx,Vy,Vz) at burnout. 26 Feb 2022 17:10:00.000 (X,Y,Z): 5210.345121 -549.481941 4300.883291 (Vx,Vy,Vz): -1.451280 7.391098 2.690198 Calculate the minimum total delta V required to maneuver this spacecraft into a circular orbit with a 12-hour period and an inclination of 61 degrees, assuming impulsive maneuvers and two-body dynamics. Please solve using equations from Howard Curtis's Orbital Mechanics for Engineering Students, 4th Edition. Or if not possible name the equations you use. If you could solve with specific angular momentum "h", earth gravitational parameter "mu", semimajor axis "a", and the target velocity for orbit "v_target". Also please use matlab syntax for solving or write the equations out clearly. Thanks!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
- Consider a US Air Force launch of its latest GPS satellite from Cape Canaveral. Radar tracking shows the following J2000 state vector (X,Y,Z and Vx,Vy,Vz) at burnout. 26 Feb 2022 17:10:00.000 (X,Y,Z): 5210.345121 -549.481941 4300.883291 (Vx,Vy,Vz): -1.451280 7.391098 2.690198 Calculate the minimum total delta V required to maneuver this spacecraft into a circular orbit with a 12-hour period and an inclination of 61 degrees, assuming impulsive maneuvers and two-body dynamics. Please solve using equations from Howard Curtis's Orbital Mechanics for Engineering Students, 4th Edition. Or if not possible name the equations you use. Also please use matlab syntax for solving or write the equations out clearly. Thanks!3. Explain the concept of Sommerfeld Elliptical orbits. Also discuss the quantization of elliptical orbits and the value of eccentricity. What is the relativistic correction to Sommerfeld elliptical orbits?While working with part of a research team you discover a set of exoplanets in a nearby star system. One of the planets is much closer to its mother star than the other and because of this you are able to determine the average radius of the closer planets orbit to be 37.26 x 10 to the 6 kilometers the Planet complete one orbit every 53.4 days. a) what is the mass of the star in this system?
- GMm F, r2 F(r = R) The surface gravity g of a body is. The acceleration due to gravity that an object m would feel on the surface of the body. A. Show that the surface gravity of Earth is ge = 9.8 m/s². B. Determine the surface gravity of the Sun. C. Determine the surface gravity of the Sun when it becomes a red giant star, assuming RG 1 AU. Use this answer to explain the significant mass loss rates observed in these objects.A space probe with a diameter of 2.50m is moving past Saturn's moon Enceladus. An observational platform on Enceladus measures the shortest length of the ellipsoidal probe to be 1.25m. How fast is the probe moving relative to the moon? a) .999c b) .995c c) .957c d) .883c e) .866cSuppose 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?