(a) Find the magnitude of the gravitational force (in N) between a planet with mass 7.00 ✕ 1024 kg and its moon, with mass 2.75 ✕ 1022 kg, if the average distance between their centers is 2.50 ✕ 108 m.  N (b) What is the moon's acceleration (in m/s2) toward the planet? (Enter the magnitude.)  m/s2 (c) What is the planet's acceleration (in m/s2) toward the moon? (Enter the magnitude.)  m/s2

The acceleration due to gravity of a particle falling toward the earth is a=-gR2/r2, where r is the distance from the center of the earth to the particle, R is the radius of the earth, and g is the acceleration due to gravity at the surface of the earth. If R = 3960 mi, calculate the escape velocity, that is, the minimum velocity with which a particle must be projected vertically upward from the surface of the earth if it is not to return to the earth. (Hint: v = 0 for r= ∞.)

You go where no one has gone before and discover an interesting planet of radius r. When you arrive, you clearly want to do some experiments to learn more about this world. You begin with some simple kinematics and measure the time t for an object thrown directly up with velocity vi to return to your hand. With this information, you find that the acceleration due to gravity gi s much lower than on Earth. a) You decide to orbit the planet in your spacecraft at a distance Rabove the surface of the planet. Find the time required to complete one orbit in terms of R, r, vi, t, and any necessary constants. b) FInd the escape velocity ve–the initial velocity necessary for an object to barely escape the gravitational pull of the planet. Express your answer in terms of vi, r, t,and any necessary constants. c) Find the distance from the planet’s center at which an object launched from the surface with velocity vwill have lost 90% of its initial kinetic energy at the surface in terms of v,vi, r,…

The NEXT morning, you wake up in a strange room yet again, and this time you drop a ball from a height of 2.20 m above the floor. The ball hits the floor 0.335 s after your drop it. You guess that you must have been taken to an alien planet with gravity different from Earth s. What is this planet s g (that is, the magnitude of the acceleration due to gravity on this planet)?     39.2 m/s^2     19.6 m/s^2     29.4 m/s^2     62.7 m/s^2

The NEXT morning, you wake up in a strange room yet again, and this time you drop a ball from a height of 1.33 m above the floor. The ball hits the floor 0.365 s after your drop it. You guess that you must have been taken to an alien planet with gravity different from Earth s. What is this planet s g (that is, the magnitude of the acceleration due to gravity on this planet)?     40.0 m/s^2     20.0 m/s^2     10.0 m/s^2     15.0 m/s^2

Problem 10: On the moon the acceleration due to gravity is 1/6 of Earth's. A ball is thrown straight up on the moon and it takes t = 26 s to return to the surface. Part (a) What is the numeric value for the magnitude of the free fall acceleration on the moon, Ameen in m/s²? Part (b) Write an expression for the maximum height achieved by the ball on the moon, hm, in terms of the gravitational acceleration on earth, g, and the time, t. Part (c) What is the numeric value for this height in meters? Part (d) What is the difference in the maximum height of the ball when it is thrown on the Moon (hm) and the ball being thrown on the Earth (hE), assuming the same time of flight?

Compute the Moon's centripetal acceleration in its orbit around the Earth. Recall that the Moon orbits the Earth every 28.0 days and that it is about 240000 miles from the Earth. What force causes this acceleration? Please first report the answer using symbolic algebra and then the numerical value. Be sure to convert to SI units.

The acceleration of an object due to air resistance is a = -bư/m, where v is the %3D speed of the object and m is its mass. What are the SI units of b? O kg/s O kg/s? O kg/m kg/m? O kg - m/s? none of these

Kepler's third law states that for any object in a gravitational orbit,  P2∝a3P2∝a3  where PP  is the orbital period of the object and aa  is the average distance between the object and what it is orbiting. In our Solar System, the natural units are distances measured in astronomical units (A.U.) and orbital periods measured in years. This can be seen for the Earth-Sun system which has an orbital period P=1P=1  year and an average distance  a=1a=1  AU. Using these natural units in the Solar System, the proportionality becomes an equality, so for our Solar System:  (Pyears)2=(aA.U.)3(Pyears)2=(aA.U.)3 . Using your mathematical prowess, determine what the orbital period in years would be for an asteroid that was discovered orbiting the Sun with an average distance of 25 astronomical units.

but your architects use the units You have negotiated with the Omicronians for a base on the planet Omicron Persei 7. The architects working with you to plan the base need to know the acceleration of a freely falling object at the surface of the planet in order to adequately design the structures. The Omicronians have told you flurg meter that the value is goP7 = = 7.29 and from your previous experience you know that both the Omicronians and your architects are terrible at unit conversion. Thus, it's up to you to do the unit conversion. Fortunately, you know the unit equality grom²¹ second² meter relationships: 5.24 flurg : 1 meter and 1 grom = 0.493 second. What is the value of gop7 in the units your architects will use, in second² VE ΑΣΦ SOP7 = ? meter second² " ?