Gravitation Questions and Answers

HINT a Find the magnitude of the gravitational force in N between a planet with mass 7 00 x 1024 between their centers is 2 40 x 108 m N b What is the moon s acceleration in m s2 toward the planet Enter the magnitude m s c What is the planet s acceleration in m s2 toward the moon Enter the magnitude m s kg and its moon with mass 2 50 x 1022 kg if the average distance

7 In the first section you used ac to find the Moon s acceleration is 0 0027099 m s Using this as your measured value what is the percent difference from the acceleration you found in the previous question using Universal Gravitation Hint Percent Difference Predicted Value Measured Value Predicted Value x 100 BANKE r

3 Two small balls A and B attract each other gravitationally with a force of magnitude F If we now double both masses and the separation of the balls what will now be the magnitude of the attractive force on each one in terms of F

What is the gravitational force between the Earth mEarth 5 98 x 1024 kg rEarth 6 378 x 106 m and a 15 000 kg satellite in Earth s orbit 575 km above Earth s surface nswer News

5 Explain why an astronaut orbiting the earth feels weightless

5 Now let s revisit the Moon Use Universal Gravitation to calculate the centripetal acceleration of the Moon Here are some numbers to help The radius of the Moon s orbit is 3 85x10 m The mass of Earth is 5 97x10 kg The mass of the Moon is 7 35x10 2 kg m s

10 Describe the process that formed the planets

Describe the process that formed the plane Singo

Two small balls A and B attract each other gravitationally with a force of magnitude F If we now double both masses and the separation of the balls what will now be the magnitude of the attractive force be each one 4F OF14 OF 16 F O8F

3 Determine the force of gravity between Earth and a 5 500 kg elephant The mass of Earth is 6 0 x 1024 kg and the distance between the elephant and the center of Earth is 6 38 x 105 m

tional Attraction Many physical phenomena obey inverse square laws That is the strength of the quantity is inversely proportional to the square of the distance from the source Isaac Newton was the first to discover that gravity obeys an inverse square law The gravitational force F between objects of masses M and m separated by a distance GMm D is given by F where G is a constant D Suppose that two stars Alpha Major and Beta Minor are separated by a distance of 6 light years Alpha Major has four times the mass of Beta Minor Let M represent the mass of Beta Minor Suppose that an object represented by point P of mass m is placed between the two stars at a distance of D light years from Beta Minor Write an expression for the gravitational force between this object and Beta Minor Write an expression for the gravitational force between this object and Alpha Major What is the distance of a neutral position of the object P with mass m from Beta Minor At neutral position both Beta Minor and Alpha Major exert equal force on point P Beta Minor V 6 light yr Alpha Major A spaceship is stationary between a planet and its moon experiencing an equal ravitational pull from each When measurements are taken it is determined that the aft is 300 000 km from the planet and 100 000 km from the moon What is the ratio of the mass of the planet to the mass of the moon What would be the ratio of their masses if the distance of the spaceship from the

5 Sputnik the first artificial satellite to orbit the Earth had a mass of 83 6 kg and travelled at 7574 m s The radius of the earth is 6371 km and its mass is 5 972 x 1024 kg NOTE You may find different numbers online since there was some uncertainty in the exact orbit These numbers were chosen to keep this question consistent Also this question requires a subtraction which can cause difficulty with the numerical tolerance Keep about 5 figures as you go through the calculation I have increased the tolerance to 10 5a 1 point possible graded

2 An astronaut of mass 63 kg climbs a set of stairs with a total vertical rise of 3 4 m a What is the astronaut s gravitational potential energy relative to the bottom of the stairs If the stairs are located on Earth 2142 J b Repeat a if the stairs are located on the Moon where g 1 6 N kg 343 J

An artificial satellite circles the Earth in a circular orbit at a location where the acceleration due to gravity is 8 82 m s2 Determine the orbital period of the satellite X

4 Now let s look at how everything you ve seen so far fits together to make the standard equation Using data for individual exoplanets you found a xwhere r is the distance from the star to a planet Another way to say this A where AR is the slope of the graph and what we called the acceleration ratio is a In this section you saw AR x m where my is the mass of the star Since the slope of the graph you made is also called G we can also say AR Gm When we combine that with what you found using individual exoplanets we get ac The equation is usually written in terms of force rather than acceleration Since the centripetal acceleration of an exoplanet is caused by the force of gravity on the exoplanet by the star then F m a where me is the mass of the exoplanet This becomes the standard equation mym This equation is often called the Universal Gravitation equation and works to find the force of gravity between any two objects not just a star and a planet 5 Let s try applying this equation to predict the acceleration due to gravity near Earth s surface The mass of Earth is 5 972 x 10 0 kg and the radius of Earth is 6 371 x 10 m According to the universal gravitation equation what should be the acceleration due to gravity near Earth s surface m s

6 The radius of the earth is R At what distance above the earth s surface will the acceleration of gravity be 4 9 m s2 A 0 41 R B 0 50 R C 1 00 R D 1 41 R E 0 25 R

5 Satellite A has twice the mass of satellite B and moves at the same orbital distance from Earth as satellite B Compare the speeds of the two satellites A The speed of B is twice the speed of A B The speed of B is one half the speed of A C The speed of B is one fourth the speed of A D The speed of B is equal to the speed of A E The speed of B is four times the speed of A Explanation

Assuming a circular orbit what is the orbital velocity of Mars in kilometers per hour Express the answer in scientific notation and rounded to three significant figures V x 10 km

1 07 What are the units for little g Ometers second OOO Newtons O Newtons kg Newton meters meters second 2

A 54kg student travels to the moon You may enter answers in scientific notation as shown 1 23 x 105 1 23e5 What is her weight on earth N Fill out each quantity for the interaction between the student and the moon F N G M m r 6 67e 11 7 35e 22 54 1740000 m kg s kg kg m What is her weight on the moon unit V earth data mass 5 97 x 1024kg radius 6 37 x 106m moon data mass 7 35 x 102 radius 1 74 x 10

6 28 If we are standing at the top of Everest what is true about us in relation to earth s gravitational field O We are experiencing the same acceleration of gravity as on the surface because we are close to the surface of the planet O Force of gravity and gravitational field strength are independent of each other so we cannot tell 1 point O Force of gravity mgh and because Everest is taller than the surface it has more gravitational energy The gravitational field might be weaker but acceleration of gravity remains constant O Because distance and gravitational field are inversely proportional field strength decreases as distance increases The force of gravity and acceleration of gravity are less

How many times has Uranus rotated on its axis in the last 56 Earth hours rotations

Express the answer in scientific notation A particular star is 2 4 x 10 7 m away from Earth with a luminosity L of 1 8 1028 W Ignoring the effects of the atmosphere what is the brightness B of the star in W m as observed from Earth B x 10 W

All changes saved 6 In the 1960s the Soviet Union launched a satellite into a nearly circular orbit around Earth One commentator expressed concern that such a satellite could drop a nuclear bomb on the United States If in fact an orbiting satellite should release a bomb how would the bomb travel O It would move in a straight line into deep space O It would remain in orbit with the rocket O It would follow a parabolic trajectory and strike Earth some distance forward of the satellite s position O It would follow a straight line trajectory and strike Earth directly below the satellite s position

After calculating the Moon s acceleration one student makes the following claim I think the Moon s acceleration is so small because it is far away from the surface of Earth The acceleration due to gravity must get smaller as you get farther from Earth s surface In this section you will test this claim using data for several different exoplanets Exoplanets are planets that orbit stars besides our sun Earth only has one moon so it would be very difficult to construct a model for how increasing the radius of an orbit affects the acceleration due to gravity However since a planet orbiting a star behaves very similarly to a moon orbiting a planet we can use data for exoplanet systems where astronomers have found the orbital period and orbital radius for several different planets around the same star You will use this data to construct a model for how increasing the radius of an orbit affects the acceleration due to gravity then test your model in the next section by revisiting the acceleration of the Moon 1 This table has data for planets orbiting a star named Kepler 186 The star was named for the Kepler space telescope which is used to study exoplanets including the ones in this table beb 2 3 A In the previous section you found the centripetal accelleration of the Moon from it s orbital radius and period with the following steps Use the orbital radius to find the circumference of the orbit Use the circumference of the orbit and the period to find the velocity Use the velocity and radius to find the centripetal acceleration In the data table set up column formulas to go through the same calculations for each planet Since the student made a claim about how acceleration is related to orbital radius you will need to make a graph with acceleration on the vertical axis and orbital radius on the horizontal axis www www Orbital Radius m 5 65458249 8 53704e 9 r 1 288056e 10 1 619136e 10 Orbital Period 3 358102 5 6 278952 5 T 1 152835e 1 906030e 6 www Orbit Circumference m C 3 55126c 10 5 387e 10 8 08099148e 10 1 14211710BL 10 Velocity m s 10575e 5 0856745 70164c 4 IM 09501264 5 Acceleration mys 1 Saved PHIN

A rocket orbits a planet in a circular orbit at a constant speed as shown in the drawing Note these arrows 4 2 3 4 At the instant shown in the drawing For each quantity listed in the first column choose an arrow that describes its direction The centripetal force on the rocket 5 The gravitational forre 1 Arrow 1 2 Arrow 21

7 What is the length of a simple pendulum oscillating on Earth with a period of 2 5 s

11 Come up with at least one idea to explain the difference you saw between the Moon s acceleration and the acceleration of objects near Earth s surface Hint Your task here is to come up with some plausible explanations not the right one

3 Johannes Kepler was a German mathematician and astronomer who lived from 1571 1630 He discovered the mathematical relationship between the orbital radius and orbital period T x 7 This says The orbital period squared is proportional to the radius cubed Another way to write this is T kx r where k is the slope of a graph of T 2 vs 73 Let s see how well your data matches Kepler s prediction make a calculated column that cubes the radius make another that squares the period change the graph axes so the radius cubed is on the horizontal axis make period squared on the vertical axis add a linear fit What is the slope from the equation of the line on your graph Hint For scientific notation you can use e notation where the number before the exponent goes before the e and the power of 10 follows the e For example 1e3 is 1 000 and 1e13 is 1 x 1013 and 1e 3 is 0 001

8c5p80 Imagine a landing craft approaching the surface of Callisto one of Jupiter s moons If the engine provides an upward force thrust of 2808 N the craft descends at con speed if the engine provides only 1895 N the craft accelerates downward at 0 39 m s2 What is the weight of the landing craft in the vicinity of Callisto s surface Submit Answer Tries 0 8 What is the mass of the craft Submit Answer Tries 0 8 c What is the free fall acceleration near the surface of Callisto

hrw8c13p27 A solid sphere of uniform density has a mass of 4 5x104 kg and a radius of 2 0 m What is the gravitational force due to the sphere on a particle of mass 1 0 kg located at a distance of 2 50 m from the center of the sphere Submit Answer Tries 0 8 What is the gravitational force due to the sphere on a particle of mass 1 0 kg located at a distance of 1 00 m from the center of the sphere

hrw8c13p45 Our Sun with mass 2 00 1030 kg revolves about the center of the Milky Way galaxy which is 2 20 1020 m away once every 2 50 108 years Assuming that each of the stars in the galaxy has a mass equal to that of our Sun that the stars are distributed uniformly in a sphere about the galactic center and that our Sun is essentially at the edge of that sphere estimate roughly the number of stars in the galaxy

3 What is the difference between gravitational forces and electrostatic forces 10 points

Cellite in Earth orbit has a mass of 105 kg and is at an altitude of 1 97 x 106 m Assume that U 0 as r a What is the potential energy of the satellite Earth system b What is the magnitude of the gravitational force exerted by the Earth on the satellite N c What force if any does the satellite exert on the Earth Enter the magnitude of the force if there is no force enter N

A satellite of mass m is in a circular orbit of radius r about a planet of mass M The total energy of the satellite E r is given by a GMm r b GMm r O c GMm r O d GMm 2r e GMm 2r

The nearest neighboring star to the Sun is about 4 light years away If a planet happened to be orbiting this star at an orbital radius equal to that of the Earth Sun distance what minimum diameter would an Earth based telescope s aperture have to be in order to obtain an image that resolved this star planet system Assume the light emitted by the star and planet has a wavelength of 550 nm

Which of the following best describes how astronomers have deduced the existence of dark matter within the Milky Way a stars near the center of the Milky Way are moving too quickly b stars near the center of the Milky Way are moving too slowly c stars near the edge of the Milky Way are moving too quickly d stars near the edge of the Milky Way are moving too slowly

Two small objects, with masses mand M, are originally a distance rapart, and the gravitational force on each one has magnitude F. The second object has its mass changed to M/4. What is the magnitude of the new gravitational force? F/4 16F 4F F/16

The Earth has a mass of 5.98 x 1024 kg, the Moon has a mass of 7.34 x 1022 kg, and the distance from the center of the Earth to the center of the Moon is 3.8 x 105 km. Calculate the gravitational attractive force between the Earth and the Moon. A. 2.027 x 10^+20 N C. 0.2027 x 10^-11 N B. 2.027 x 10^+11 N C. 0.2027 x 10^-11 N D. None of the above

Venus, like other planets, circles the Sun in a round manner while spinning about its axis. A year is defined by the time it takes to complete one complete orbit (i.e., the period of orbit), just as it is on Earth. A day is defined by the time it takes to complete one complete turn about its axis (i.e., the period of rotation). The Earth's orbital period is 365.25 days, while its rotational period is 24 hours (1.00 day). When these identical figures for Venus are stated relative to Earth, it is discovered that Venus has an orbital period of 225 days and a rotational period of 243 days. A day would last longer than a year for Venus residents! Determine the frequency of orbit on Venus. Blank 1 x 10^Blank 2 Hz Blank 1 Blank 2

The gravitational field strength between two objects is the sum of two vectors pointing in opposite directions. Somewhere between the objects, the vectors will cancel, and the total force will be zero. Determine the location of zero force as a fraction of the distance r between the centres of two objects of mass m, and m₂.

An alien spacecraft is out in space leaving an unknown planet. It detects the pull of gravity due to his unknown planet to be 100.0 N. Later the alien rechecks the pull on their spacecraft and detects it to be 33 N. By what factor has their distance changed as they left the unknown planet? Show proof!

An object has a mass of 35 kg. The acceleration of gravity is 9.8 m/s². What is its weight on the earth? Answer in units of N. What is its mass on the moon where the force of gravity is that of the earth? 6 Answer in units of kg. What is the weight of that object on the moon? Answer in units of N.

A 300.0 kg asteroid is 8.0*105 meters away from the center of Earth. What is the gravitational force between the asteroid and the Earth? (HINT: You will need to look up the mass of the Earth). 4. The center of a 100.0 kg rock is located 2.0 km away from a .001 kg marble. What is the gravitational force between the rock and the marble?

The moon has a mass of 1 x 10^22 kg, and the gravitational field strength at a distance R from the planet is 0.001 N/kg. What is the gravitational force exerted on the moon while it is in orbit around the planet?

To derive the 3rd law of Keppler. Use the the 2nd Newtons law, the law of gravity, centripetal acceleration, and the speed for the rotation of the complete circumference in the orbital period T Substitute and solve for.

Infinite number of bodies, each of mass 2kg are situated on x-axis at distance 1m, 2m, 4m, 8m, . respectively, from the origin. The resulting gravitational potential due to this system at the origin will be

A particle of mass M is situated at the centre of spherical shell of same mass and radius a. The magnitude of the gravitational potential at a point situated at a/2 distance from the centre, will be

Two solid spherical planets of equal radii R having masses 4 M and 9 M their centre are separated by a distance 6 R. A projectile of mass m is sent from the planet of mass 4 M towards the havier planet. what is the distance r of the point from the lighter planet where the gravitational force on the projectile is zero?

At closest approach, the 722 kg Voyager 2 probe flew by Neptune at an altitude of 29,240 km. - watch your units!!! A) What was the probe's weight at that moment if Neptune has a radius of 24,900 km and a mass of 9.99 x 10²5 kg? B) Use the information from part A to calculate the acceleration due to gravity at that altitude above Neptune.