Acceleration Due to Gravity Practice Problems

The radius of Jupiter is 11.2 times the radius of the Earth and its mass is 317 times that of the Earth. Determine the density of Jupiter. Assume that Jupiter is a sphere and that the average density of the Earth is 5500 kg/m³.

An exoplanet has a mean radius equal to 0.09 times the radius of Earth and a mass equal to 0.00023 times the mass of Earth. What would be the gravitational acceleration at the exoplanet's surface?

Uranus's mass is 14.5 times that of the Earth, and its radius is 4 times the radius of the Earth. What would you weigh at Uranus' surface if you weighed 800 N on Earth's surface? 

The mass of an exoplanet beyond our solar system is triple that of Earth, and its radius is half of Earth's radius. Using the previous information, calculate the gravitational acceleration at the exoplanet's surface.

The acceleration due to Earth's gravity at a given point in Earth's atmosphere is 8.70 m/s² instead of 9.80 m/s² at the Earth's surface. What is the altitude of this point above the Earth's surface?

At the south pole, a metallic sphere is suspended from a string. The measured tension in the string is 50.00 N. If you use the same device at the equator, what would be the tension in the string? Remember that the Earth rotates on an axis that passes through its north and south poles. Take g = 9.81 m/s².

Assume the radius of the earth is increased keeping its mass constant. Determine the ratio of its new radius to the old one if the acceleration due to gravity at the surface is half its original value.

A satellite is orbiting a planet at an altitude where free-fall acceleration is one-third of its value at the planet's surface. What is the distance of the satellite from the planet's surface? Express your answer as a multiple of the planet's radius.

The moon of Jupiter has a radius of 3270 km and a free-fall acceleration at its surface of 1.79 m/s². What is the mass of the moon?

Suppose there is a planet with a mass that is 4 times the mass of the Earth. If a spaceship lands on the planet's surface, it measures the free-fall acceleration to be 1/8 of that of the Earth's acceleration due to gravity. Determine the radius of the planet.

A dog is in space in a space suit. Given that the total mass of the dog with the space suit is 42 kg, determine the weight that is apparent to itself if it travels with a constant velocity.

A 32-kg monkey is sent on a mission to Mars as a test in a spaceship. At a distance of 3600 km from the center of the mars it is moving toward the planet at an acceleration of 4.2 m/s². What is the weight that is apparent to itself? In which direction the monkey feels its weight? (Assume that the mass of Mars is 6.42 × 10²³ kg, and the gravitational constant G = 6.674 × 10^-11 Nm²/kg².)

Two identical planets, each with mass M, are positioned along the x-axis at coordinates x = +d and x = -d. Calculate the gravitational field at points along the +y-axis due to these two planets. Express the gravitational field g as a function of y, M, d, and the gravitational constant G.

Two spheres, each with a mass of m, are positioned on the x-axis at x = +d and x = -d. The gravitational field at any point on the y-axis is given by the expression

$g=\frac{2Gmy}{\left(d^2+y^2\right)^{\frac{3}{2}}}$

where G is the gravitational constant. Identify the points on the y-axis where the magnitude of $g$ is maximized, and determine the maximum value.

Astronauts are finally on Mars. The planet has two different moons. Deimos, which is at a distance of 23000 km from Mars, and Phobos, which is at a distance of 9400 km from Mars. Given that Mars rotates about itself once every 24 hours and 39 minutes, for the astronauts, would the moons appear to revolve around Mars faster than the sun? Assume that the mass of Mars is 6.4 x 10²³ kg.

A science fiction author is considering the possibility of sending a monkey off to another planet. Considering centripetal acceleration, determine how many g's would the monkey experience at the equator of the planet given that the mass of the planet = 2.9 $\times$ 10²⁷ kg, the radius of the planet at the equator = 4.5 $\times$ 10⁴ km, the length of a day on the planet = 7 hr 33 mins.

A space probe is initially hovering at 2r_m above Mars' surface. Suddenly it's thrusters dysfunction, and it starts to fall freely toward the Mars' surface. Given that r_m is Mars's radius and M is the mass of Mars, calculate the probe's velocity just before it touches the surface. Assume that, there is no air on Mars, and take the outward direction from the center of Mars along its radius as positive.

[Hint: Apply Newton's second law, the law of universal gravitation, and then utilizing the chain rule, integrate to find the result.]

A space agency is preparing to send a mission crew to visit a planetoid on a spaceship. The spaceship is planned to travel to the planetoid that is located 7.9 billion km away and orbit it at an altitude of 15 km above its surface. Given the dimensions of the planetoid as 25 km × 31 km × 35 km and its density as 2.3 × 10³ kg/m³, estimate what the value of the gravitational force "g" is at the planetoid’s surface. To simplify our calculations, let us treat the planetoid like a sphere which has the same density and volume. Note that the gravitational constant is G = 6.67 × 10⁻¹¹ N⋅m²/kg².