The Hubble Space Telescope (HST) travels in a circular orbit above the Earth’s atmosphere, allowing astronomers to conduct aberration-free measurement. The HST has a mass of 11,110 kg. (a) The HST completes one circular orbit around Earth in 5725 s. How high is its orbit above the surface of the Earth? (b) The HST is estimated to have a lifetime of about 15 more years before crashing into the earth due to atmospheric drag. Estimate how much work the atmosphere does per circular orbit on the HST.Assume the work done and the period are the same for each revolution (realistically both of these quantities would change as the orbital radius decreased).

Wonder Woman and Superman fly to an altitude of 1630 km, carrying between them a chest full of jewels that they intend to put into orbit around Earth. They want to make this tempting treasure inaccessible to their evil enemies who are trying to gain possession of it, yet keep it available for themselves for future use when they retire and settle down. But perhaps the time to retire is now! They accidentally drop the chest, which leaves their weary hands at rest, and discover that they are no longer capable of catching it as it falls into the Pacific Ocean. At what speed does the chest impact the surface of the water? Ignore air resistance, although in the real world it would make a world of difference. The radius and mass of Earth are 6370 km and 5.98×10^24 kg, respectively.

Helpful information: (1) An alpha particle is a helium nucleus, (2) e = 1.6 × 10-¹⁹ C, (3) k₂ = 9.0 × 10⁹ Nm² C-2, (4) 1nm = 1 × 10-⁹ m 1-An alpha particle lies on the x-axis, a distance of 1.0 nanometer from a proton (in this set-up, the alpha particle is at the origin while the proton is in the positive direction). Which of the following choices below represents the magnitude of the electric force on the alpha particle? (a) 2.3 × 10-10 N (b) 4.6 × 10-10 N (c) 2.3 x 10-19 N (d) 4.6 x 10-19 N cing the voltage so following insta choices below at a time! 1.00 s?

Orbital plane change: A satellite is launched due east from the Kennedy Space Center (latitude 28.6º). Following orbit insertion and a circularizing second burn with no plane change, the satellite is in a circular orbit at an altitude of 540 km. Its final destination is a circular orbit at 15,000 km with an inclination of 0 degrees.   a. Using two Hohmann transfers, what total Δv is required to move the satellite from the initial orbit to the higher circular at the same inclination? Include a sketch showing the initial orbit, the transfer orbit and the final orbit. Include the location(s) of the burn(s). b. Calculate the Δv required to change the orbital inclination from its initial value to zero degrees in both the initial circular orbit and the higher circular orbit. Where would you want to make the change to the orbital inclination?

How much energy is required to move a satellite of mass 1000 kg from the surface of the Earth to an altitude 3 times the radius of the Earth? Compute the energy in joules.

While passing between Earth and the Moon, a spacecraft is momentarily located on the line connecting the centers of the two bodies and is at a distance of d = 166 km from a radio antenna on the surface of Earth. The distance from the antenna to the moon is denoted by dm.   (b)  Scientists on Earth send a command to the spacecraft, which immediately sends back a receipt confirmation signal. How long, in seconds, after the scientists send the command does it take before they learn it was received?   (c)  Scientists bounce a laser beam off the Moon and measure the two-way travel time to be 2.42 s. How far away is the Moon in meters?

Consider an electron orbiting around a proton with an orbital radius of R=8.48⋅10−10R=8.48⋅10-10 m. What is the orbital frequency of the electron motion? Use me=9.11×10−31me=9.11×10-31 kg, e=1.6×10−19e=1.6×10-19 C, and k=9×109k=9×109 Nm2/C2. The frequency, f0 =  Units           . By how much would this frequency increase (assume the same orbital radius) if an external magnetic field of B = 0.5 T is applied to the system along the the electron axis of rotation? The increase in the frequency , Δf =  Units           .

The escape velocity from a massive object is the speed needed to reach an infinite distance from it and have just slowed to a stop, that is, to have just enough kinetic energy to climb out of the gravitational potential well and have none left. You can find the escape velocity by equating the total kinetic and gravitational potential energy to zero   E=12mv2esc−GmM/r=0E=12mvesc2−GmM/r=0 vesc=2GM/r−−−−−−√vesc=2GM/r   where GG is Newton's constant of gravitation, MM is the mass of the object from which the escape is happening, and rr is its radius. This is physics you have seen in the first part of the course, and you should be able to use it to find an escape velocity from any planet or satellite.  For the Earth, for example the escape velocity is about 11.2 km/s, and for the Moon it is 2.38 km/s.  A very important point about escape velocity: it does not depend on what is escaping.  A spaceship or a molecule must have this velocity or more away from the center of the planet to be free…

It takes light from the Sun 6.00 minutes to reach Venus. How far away is the planet from the Sun (in km)? The speed of light, c, is 3 ✕ 105 km/s.

A spaceship is at a distance of 1.1 × 10¹⁰ m from a blackhole of mass 8.26×10³6 kg. How long will an hour be inside the ship?