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A comet of mass \( m_c = 3.2 \times 10^{14} \) \( \text{kg} \) is orbiting a star with mass \( m_s = 1.8 \times 10^{30} \) \( \text{kg} \). The comet’s orbit is elliptical. At its closest point, the comet is a distance \( r_1 = 8.3 \times 10^{10} \) \( \text{m} \) from the star, and at its farthest point, the comet is a distance \( r_2 = 4.9 \times 10^{11} \) \( \text{m} \) from the star. What is the change in the kinetic energy of the comet as it moves along its orbit from distance \( r_2 \) to distance \( r_1 \) from the star?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the Earth? Which accelerates more?

The Moon does not crash into the Earth because:

Why is more fuel required for a spacecraft to travel from the Earth to the Moon than to return from the Moon to the Earth?

The escape speed of an object of mass \( m \) from a planet of mass \( M \) and radius \( r \) depends on the gravitational constant and

The elliptical orbit of a comet is shown above. Positions 1 and 2 are, respectively, the farthest and nearest positions to the Sun, and at position 1 the distance from the comet to the Sun is 10 times that at position 2. What is the ratio \( F_1 / F_2 \), the force on the comet at position 1 to the force on the comet at position 2?

A [katex] 2.2 \times 10^21 \, \text{kg}[/katex]moon orbits a distant planet in a circular orbit of radius [katex] 1.5 \times 10^8 \, \text{m}[/katex]. It experiences a [katex] 1.1 \times 10^19 \, \text{N}[/katex] gravitational pull from the planet. What is the moon’s orbital period in earth days?

While traveling in its elliptical orbit around the Sun, Mars gains speed during the part of the orbit where it is getting closer to the Sun. Which of the following can be used to explain this gain in speed?

A communications satellite orbits the Earth at an altitude of 35,000km above the Earth’s surface. Mass Earth= [katex]6 \times 10^{24} \text{ kg}[/katex]& Radius Earth= [katex]6.4 \times 10^6 \text{ m}[/katex]. What is the satellite’s velocity?

The magnitude of the gravitational field on the surface of a new planet is 20 N/kg. The planet’s mass half the mass of Earth. The radius of Earth is 6400 km. What is the radius of the new planet?

Consider a neutron star with a mass equal to the sun, a radius of 10 km, and a rotation period of 1.0 s. What is the radius of a geosynchronous orbit about the neutron star?

In 2014, the European Space Agency placed a satellite in orbit around comet 67P/Churyumov-Gerasimenko and then landed a probe on the surface. The actual orbit was elliptical, but well approximate it as a 50 km diameter circular orbit with a period of 11 days.

A child on Earth has a weight of 500N. Determine the weight of the child if the earth was to triple in both mass and radius (3M and 3r).

The exoplanet HD 69830b has a mass 10 times that of the Earth and a radius 5 times that of the Earth. The value of g on HD 69830b is most nearly

Which of the following best explains why astronauts experience weightlessness while orbiting the earth?

A satellite in circular orbit around the Earth moves at constant speed. This orbit is maintained by the force of gravity between the Earth and the satellite, yet no work is done on the satellite. How is this possible?

A spacecraft somewhere in between the earth and the moon experiences 0 net force acting on it. This is because the earth and the moon pull the spacecraft in equal but opposite directions. Find the distance D away from Earth, such that the spacecraft experiences zero net force.

Two satellites are in circular orbits around Earth. Satellite A has speed vA . Satellite B has an orbital radius nine times that of satellite A. What is the speed of satellite B?

Find the net gravitational force on a 2.0 kg sphere midway between a 4.0 kg sphere and a 7.0 kg sphere that are 1.2 m apart.

The distance from earth to sun is \(1 \, \text{AU}\). The distance from Saturn to sun is \(9 \, \text{AU}\). Find the period of Saturn’s orbit in years. You can assume that the orbits are circular.

A satellite circling Earth completes each orbit in 132 minutes. Find the altitude of the satellite. What is the value of g at the location of this satellite?

The Earth’s radius is 6.37 x 10^6 m. What is the radius of a planet that has the same mass as earth but on which the free-fall acceleration is 5.50 m/s2？

A 3300-m-high mountain is located on the equator. How much faster does a climber on top of the mountain move than a surfer at a nearby beach? The earth’s radius is 6400 km.

A 1.5 kg object is located at a distance of 1.7 x105 m fr220m the center of a larger object whose mass is 7.4 x 10 kg. What is the size of the force acting on the smaller object?

Two identical satellites are placed in orbit, one orbits Mars, the second orbits Jupiter. The orbital speeds of each satellite are the same. Which satellite has a greater orbital radius?

The International Space Station has a mass of 4.2 x105 kg and orbits Earth at a distance of 4.0 x102 km above the surface. Earth has a radius of 6.37 x106 m, and mass of 5.97 x104 kg. Calculate…

The gravitational force that the moon exerts on Earth is often cited as the source for the tides we witness. However, the gravitational force the Sun exerts on Earth is over 100 times greater than the force the moon exerts on Earth. Why is the force from the moon credited for the tides, and not the force from the sun?

Imagine a hypothetical planet that has two moons. Moon #1 is in a circular orbit of radius R and has a mass M. Suppose Moon #2 has a mass M, equal to Moon #1 but has an orbital radius twice that of Moon #1, 2R. What is the ratio of the force the planet exerts on Moon #1 compared to the force the planet exerts on Moon #2.