Gravitation Questions and Answers

Imagine you put a cannon on the top of a very tall mountain. You start firing cannonballs horizontally. Each time you add more gunpowder to the cannon, which makes the next cannonball travel further before hitting the ground. Is it possible that at some point the cannonball will miss the ground? What does this have to do with the orbit of the moon?

Recently there has been a lot of hue and cry over the possibility of an asteroid hitting the earth. NASA reports that it has spotted an asteroid Bennu which may possibly hit the earth somewhere in 22th century. The probability of its hitting the earth's surface is only one in 2000, yet social media sites are expert in spreading rumour about its possible impact Assume that it was at rest at a large distance from earth and it is moving only under the influence of earth's gravitational field. Neglect the influence of any other celestial body like sun, moon etc. on the asteroid or the earth. The size of Bennu is much smaller than earth. (Take: escape speed from earth's surface as 11 km/s.) If the asteroid were to hit the surface of the earth normally at the equator and gets embedded in the earth just below the surface, the duration of the day would become 30 hrs. What is the mass of the asteroid/mass of earth?

If I weigh 741 N on Earth at a place where g = 9.80 m/s² and 5320 N on the surface of another planet, what is the acceleration due to gravity on that planet? A. 81.0 m/s² B. 70.4 m/s² C. 51.4 m/s² D. 61.2 m/s²

What is the gravitational force of attraction between two asteroids in space, each with a mass of 50,000 kg, separated by a distance of 3800 m?

19. A spacecraft which is moving with a speed u relative to the earth in the x-direction, enters the gravitational field of a much more massive planet which is moving with a speed 3u in the negative x-direction. The spacecraft exits following the trajectory as shown below. The speed of the spacecraft with respect to the earth a long a time after it has escaped the planet's gravity is given by (a) u (b) 4u (c) 2u (d) 7u

As represented in the diagram below, an object of mass m, located on the surface of the Moon, is attracted to the Moon with a gravitational force, F. (Not drawn to scale) An object of mass 2m, at an altitude equal to the Moon's radius, r, above the surface of the Moon, is attracted to the Moon with a gravitational force of F 2F F/2 F/4

Why do you have different weights on different planets?

Sally and Sam are in a spaceship that comes to within 18,000 km of the asteroid Ceres. Determine the force Sally experiences, in N, due to the presence of the asteroid. The mass of the asteroid is 8.7 x 1020 kg and the mass of Sally is 71 kg. For calculation purposes, assume the two objects to be point masses. N MY NOTES ASK YOUR TEACHER

A 70.7-kilogram astronaut weighs 694 newtons at the surface of Earth. What is the mass of the astronaut at the surface of the Moon, where the acceleration due to gravity is 1.62 meters per second squared? * O 70.7 kg O 65.0 kg O 105 kg 43.6 kg

The function h = -16t² + 1700 gives an object's height h, in feet, at t seconds. a. What does the constant 1700 tell you about the height of the object? b. What does the coefficient of t2 tell you about the direction the object is moving? c. When will the object be 1000 ft above the ground? d. When will the object be 940 ft above the ground? e. What are a reasonable domain and range for the function h?

An infinitely long wire having uniform mass density is placed along z-axis. If W is the work done by an external agent to move a point mass m very slowly from point P(3,-4, -1) to Q(-4, 3, 2) then choose the correct answer. (A) W> 0 (B) W <0 (C) W = 0 (D) Magnitude of W does not depends on path

Two stones A and B are thrown in upward direction with speed 60 m/s on north pole and equator respectively. Third stone C is thrown on the surface of moon with same speed as A and B. If A, B and C reach to maximum height hĄ, h₂ and he respectively, then which of the following relation is correct?

part 1 of 3 During a solar eclipse, the moon (of mass 7.36 x 1022 kg). Earth (of mass 5.98 x 1024 and Sun (of mass 1.99 x 100 kg) lie on the same line, with the moon between Earth and the Sun. kg), What gravitational force is exerted on the moon by the Sun? The universal gravitational constant is 6.673 x 10-11 N-m²/kg², the Earth-moon distance is 3.84 x 108 m, and the Earth-Sun distance is 1.496 × 10¹1 m. Answer in units of N. Answer in units of N part 2 of 3 What gravitational force is exerted on the moon by Earth? Answer in units of N. Answer in units of N part 3 of 3 What gravitational force is exerted on Earth by the Sun? Answer in units of N. Answer in units of N.

The nucleus of the deuterium atom (heavy water) consists of a proton and a neutron at a distance of about 2x10^-15 m. The mass of the proton and neutron is 1.7x10^-27 kg each. Compare the magnitude of the gravitational force between the two particles to the magnitude of the nuclear force, which is about 200 N. (The nuclear force is a different force of nature.)

Mars has a mass of about 6.39 × 10^23 kg, and its moon Phobos has a mass of about 1 x 10^16 kg. If the magnitude of the gravitational force between the two bodies is 4.37 x 10^15 N, how far apart are Mars and Phobos? The value of the universal gravitational constant is 6.673 x 10-¹¹ N.m²/kg2 Answer in units of m

The radius of the earth is 6.371 x 10^6 m and its mass is about 5.972 x 10^24 kg. Calculate the gravitational force on a satellite of mass 650 kg in a geosynchronous orbit above the earth. Hint: Geosynchronous satellites are in circular orbits with speeds such that they rotate around the earth in 24 hours. Use uniform circular motion to determine the centripetal acceleration.

Calculate the radius of the orbit of an exoplanet in a circular orbit around a star whose mass is 1.54 times that of the sun with a period of 2.2 days. Such a planet would be extremely hot, but we have found such planets. Hint: the mass of the sun is 1.99 x 10³⁰ kg. Use uniform circular motion to determine the centripetal acceleration.

In the distant future, when humans have mastered space travel, we find ourselves on a new planet. We have determined that the radius of the planet is 6.7x10^6 m. In addition, the amount of time for a 9.0 kg ball to fall 86.4 m from rest is measured to be 3.9 s. Use this information to determine the mass of this new planet. Hint: You can consider the acceleration due to gravity to be constant because the ball remains near the surface of the new planet. Use kinematics to start.

Given: G = 6.67259 x 10-¹¹ Nm²/kg². A 1220 kg geosynchronous satellite orbits a planet similar to Earth at a radius 1.94 x 10^5 km from the planet's center. Its angular speed at this radius is the same as the rotational speed of the Earth, and so they appear stationary in the sky. That is, the period of the satellite is 24 h. What is the force acting on this satellite? Answer in units of N.

The period of the earth around the sun is 1 year and its distance is 150 million km from the sun. An asteroid in a circular orbit around the sun is at a distance 207 million km from the sun. What is the period of the asteroid's orbit? Answer in units of year.

Jupiter has a mass of 1.898x1027 kg and radius of 69,912 km. If we were to treat Jupiter as if it was a sphere of uniform density, what would be the magnitude of the acceleration due to gravity of the 340 kg Galileo space probe when it was 140 km below the "surface." This probe was shot into the atmosphere of Jupiter to learn more about how it varies with depth. The probe's signal was lost when it was about 140 km deep.

In this problem, you will calculate the location of the center of mass for the Earth-Moon system, and then you will calculate the center of mass of the Earth-Moon-Sun system. The mass of the Moon is 7.35×10^22 kg, the mass of the Earth is 6.00×10^24 kg, and the mass of the sun is 2.00×10^30 kg. The distance between the Moon and the Earth is 3.80×10^5 km. The distance between the Earth and the Sun is 1.50×10^8 km Calculate the locationem of the center of mass of the Earth-Moon system. Use a coordinate system in which the center of the Earth is at x = 0 and the Moon is located in the positive x direction. Express your answer in kilometers to three significant figures.

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.

The mass of a moon is MM and the mass of the planet it orbits is Mp. The distance between the center of the moon and the center of the planet is R. What would happen to the gravitational force between the moon and the planet if the moon's mass was doubled and the distance between their centers was halved?

A satellite is orbiting Earth at a distance of 2 km from the Earth's surface. The radius of the Earth is 6.37x10^6 m, the mass of the Earth is 6x10^24 kg, and the force of gravity between the satellite and the Earth is 19,713.13 N. What is the mass of the satellite?

A satellite is orbiting Earth at a distance D from the surface of the Earth. The radius of the Earth is RE, the mass of the Earth is ME and the mass of the satellite is Ms. Write an equation representing the magnitude of the gravitational force acting between the satellite and the Earth.

How much would a 51.8 kg person weigh on the surface of Venus? Remember, weight is a force! And if you are standing on the surface of a planet, the distance between your centers will be equal to the planet's radius. m₂ (mass of Venus) = 4.89 x 10^24 kg d = 6.05 x 10^6 m Round your answer to the nearest whole number - do not add units!

How much would a 69.3 kg person weigh on the surface of Jupiter? Remember, weight is a force! And if you are standing on the surface of a planet, the distance between your centers will be equal to the planet's radius. m₂ (mass of Jupiter) = 1.91 x 10^27 kg d = 7.14 x 10^7 m Round your answer to the nearest whole number - do not add units!

Event A occurs before event B in a certain frame of reference. How could event B occur before event A in some other frame of reference? 1. It's a matter of relative velocity. 2. The spaces are distorted. 3. Its a matter of relative distance. 4. It's impossible.

How much would a 84 kg person weigh on the surface of Mars? Remember, weight is a force! And if you are standing on the surface of a planet, the distance between your centers will be equal to the planet's radius. m₂ (mass of Mars) = 6.43 x 10^23 kg d = 3.40 x 10^6 m Round your answer to the nearest whole number - do not add units!

How much would a 46.6 kg person weigh on the surface of Mars? Remember, weight is a force! And if you are standing on the surface of a planet, the distance between your centers will be equal to the planet's radius. m₂ (mass of Mars) = 6.43 x 10^23 kg d = 3.40 x 10^6 m