Exam 7: Gravity

A satellite of mass m₁ circles a planet of mass m₂ and radius r in an orbit at a height 2r above the surface of the planet. What minimum energy is required to change the orbit to one for which the height of the satellite is 3r above the surface of the planet?

In an isolated system of two bodies that exert gravitational forces on one another, the quantity (quantities) that remain(s) constant is(are)

The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

Knowing that at sea level and that R⊕ = 6.37 × 106 m, we find that the value of g in at a distance RE from the surface of the Earth is

A satellite circles planet Roton every 2.8 h in an orbit having a radius of 1.2 × 107 m. If the radius of Roton is 5.0 × 106 m, what is the magnitude of the free-fall acceleration on the surface of Roton?

Planet Zero has a mass of 5.0 × 1023 kg and a radius of 2.0 × 106 m. A space probe is launched vertically from the surface of Zero with an initial speed of 4.0 km/s. What is the speed of the probe when it is 3.0 × 106 m from Zero's center?

Two stars of masses M and 6M are separated by a distance D. Determine the distance (measured from M) to a point at which the net gravitational force on a third mass would be zero.

Two identical planets orbit a star in concentric circular orbits in the star's equatorial plane. Of the two, the planet that is farther from the star must have

Three 5.0-kg masses are located at points in the xy plane as shown in the figure. ​ ​ Use this exhibit to answer the following question(s). -What is the magnitude of the resultant force (caused by the other two masses) on the mass at x = 0.40 m, y = 0?

A spacecraft (mass = m₁) orbits a planet (mass = m₂) in a circular orbit (radius = r). What is the minimum energy required to send this spacecraft to a distant point in space where the gravitational force on the spacecraft by the planet is negligible?

When two solid spheres of the same material and same radius r are in contact, the magnitude of the gravitational force each exerts on the other is directly proportional to

What is the magnitude of the free-fall acceleration at a point that is a distance 2R above the surface of the Earth, where R is the radius of the Earth?

The period of a satellite circling planet Nutron is observed to be 84 s when it is in a circular orbit with a radius of 8.0 × 106 m. What is the mass of planet Nutron?

The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

A spaceship of mass m1 circles a planet (mass = m²) in an orbit of radius r. How much energy is required to transfer the spaceship to a circular orbit of radius 3R?

Which of the following quantities is conserved for a planet orbiting a star in a circular orbit? Only the planet itself is to be taken as the system; the star is not included.

Three 5.0-kg masses are located at points in the xy plane, as shown. What is the magnitude of the resultant force (caused by the other two masses) on the mass at x = 0, y = 0.30 m?

What is the period of revolution of a planet in circular orbit around a star of 4.0 solar masses if it is at a distance from the star equal to that of the Earth from the Sun?

Calculate the Earth's angular momentum in the approximation that treats the Earth's orbit around the Sun as a circle. (MSun = 1.99 × 1030 kg; T = 3.156 × 107 s; ME = 5.98 × 1024 kg.)

The figure below shows a planet traveling in a clockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,