The Oort Cloud extends out to (possibly) one light-year from the sun. Objects in the Oort Cloud are still gravitationally bound to the sun. Suppose one such iceball orbits the sun in a circle. I'm going to alter some numbers, such as the mass of the sun and even G. The gravitational force is directed toward the sun and has the following magnitude: GMm p2 Calculate the force on the object if these are the numbers: G = 6.1*10-11 N*m?/kg² • M = 2.7*1030 kg • m = 1.5*108 kg = 19*1015 m %D Calculate your answer in microNewtons (10-6 N).

B4

Somewhere far, far away on the other side of our galaxy, there is a new protoplanetary disk where two baby planetesimals are growing. Planetesimal A is currently 5x10° kg, and Planetesimal B is 2x105 kg. If these two planetesimals are 100 meters apart, what is the gravitational force between them? (Hint: the Universal Gravitational Constant (G) is 6.67x10-11 Nm²/kg²) Gm,m2 FG r2 Planetesimal A Planetesimal B 5 x 10°kg 2 x 105kg 100 meters

Neptune has a mass of 1.0 × 1026 kg and is 4.5 × 10⁹ km from the Sun with an orbital period of 177.5 years. Planetesimals in the outer primordial solar system 4.5 billion years ago coalesced into Neptune over hundreds of millions of years. If the primordial disk that evolved into our present day solar system had a radius of 10¹1 km and if the matter that made up these planetesimals that later became Neptune was spread out evenly on the edges of it, what was the orbital period of the outer edges of the primordial disk? Express your answer rounded to the nearest year, and be sure not to do any rounding before expressing your final answer. P = years

The mass of an electron is 9.11 x 10 ^-31 kg. The mass of a proton is 1.67 x 10 ^-27 kg. They are about 5.3×10^ −11 m apart in a hydrogen atom. What is the gravitational force between these two particles in the hydrogenatom?

On February​ 15, 2013, Asteroid 2012 DA14 passed within​ 17,200 miles​ [mi] of the surface of the Earth at a relative speed of 7.8 kilometers per second​ [km/s]. This is considerably closer than the orbit of geosynchronous satellites​ (26,200 miles). This is the closest recorded approach of an object this large. The asteroid 2012 DA14 was estimated to have a diameter of 30 meters​ [m] and a specific gravity of 3. If 2012 DA14 had hit the​ Earth, what is the total amount of energy that would have been released​ (i.e., what was the kinetic energy of the​ asteroid)? Express your answer in megatons​ [Mton]. One megaton is the energy released by one million metric tons of TNT explosive. A metric ton equals​ 1,000 kilograms​ [kg], and the explosive energy of TNT is 4,184 joules per gram​ [J/g].

Problem 6. (Palen, et. al., 2nd ed., Problem 49) Sirius and its companion orbit around a common center of mass with a period of 50 years. The mass of Sirius is 2.02 times the mass of the Sun. a) If the orbital velocity of the companion is 2.07 times greater than that of                   Sirius, what is the mass of the companion? b) What is the semimajor axis of the orbit?

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.

In 1999, scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun that occupy less space than our moon. Suppose that one of these black holes has a mass of 1x10^3 suns and a radius equal to one-half the radius of our moon. What is the density of the black hole in g/cm^3? The radius of our sun is 7.0x10^5 km, and it has an average density of 1.4x10^3 kg/m^3. The diameter of the moon is 2.16x10^3 miles.

You're designing a mission with a special type of rocket, a nuclear thermal rocket (NTR). Since it uses a nuclear reactor to heat the propellant, it can achieve an exhaust velocity of vex = 5.65 km/s. The crew's habitat space, the rocket itself, the shadow shield to protect from radiation, and the instrument payload for scientific research all have a combined mass of 607 x 103 kg, and the propellant is 3,638 x 103 kg. What is the total delta-V of the rocket in km/s?