Force of Gravity

Acceleration Due to Gravity

Kepler's Third Law

Conceptual Questions

Conceptual questions - 2

A planet has a mass of 2.6 x 10^{24 }kg and another has a mass of 9.17 x 10^{22 }kg. Calculate the force of gravity if the distance between the planets is 6.35 x 10^{8} m.

3.94 x 10^{19 }N

Calculate the acceleration due to gravity on the surface of a planet with radius 6.9 x 10^{6} m and a mass of 9.21 x 10^{24} kg.

12.90 m/s^{2}

The orbital period of a planet is 2.7 Earth years and its orbital radius is 7.45 x 10^{8} m. What is the orbital period of a planet with an orbital radius 9.73 x 10^{7}m.

.127 Earth years

Increasing this value will *increase *force of gravity.

Mass.

Name two ways to increase acceleration due to gravity on the surface of a planet.

Decrease radius/distance to center or increase mass of the planet.

Two planets are 2.41 x 10^{9 }m apart and have identical masses of 8.41 x 10^{25}^{ }kg. What is the force of gravity between the two planets?

8.12 x 10^{22 }N

The acceleration due to gravity on a planet is 4.2 m/s^{2} and the radius of the planet is 8.42 x 10^{6 }m. Calculate the mass of the planet.

4.64 x 10^{24} kg

The orbital period of a planet is 8.4 Earth years and its orbital radius is 8.91 x 10^{6} m. Calculate the orbital radius of a planet in the same system with an orbital period of 6.15 Earth years.

7.237 x 10^{6} m = 7237827 m

Increasing this variable will *decrease* force of gravity.

Distance

Two moons orbiting a planet have the same mass, but one is twice as far as the other. Which moon experiences a greater force of gravity from the planet?

The moon that is closer to the planet.

The force of gravity from a planet acting on an asteroid is 4.79 x 10^{12} N. If the asteroid has a mass of 8.21 x 10^{12} kg and the planet has a mass of 9.34 x 10^{20} kg, calculate the distance between the asteroid and the planet.

3.268 x 10^{5} m = 326786 m

The acceleration due to gravity is 7.52 m/s^{2} on a planet with mass 2.54 x 10^{26} kg. Calculate the radius of the planet.

4.746 x 10^{7} m

A planet orbiting a star has an orbital radius of 7.91 x 10^{7} m and an orbital period of 13.1 Earth years. Another planet orbiting the same star has an orbital period that is twice as long as the first planet. What is the orbital radius of the second planet?

1.255 x 10^{8 }m

Solve the F_{g }equation for r. (get r by itself)

r = sqrt(G*m_{1}*m_{2}/F_{g})

A planet orbits a star and travels from point A to point B, which takes twice as long as it does to travel from point C to point D. Which segment will have a greater area?

Segment A to B.

The force of gravity on a brick on Earth is 14 N. The mass of the Earth doubles. What is the new force of gravity on the brick if the radius of the Earth does not change?

28 N

The acceleration due to gravity on the surface of a planet is 14.96 m/s^{2}. What will be the new acceleration due to gravity if the mass of the planet suddenly doubled, but the radius stayed the same?

29.92 m/s^{2}

What information would we need to calculate the orbital radius of a satellite if it has an orbital period of 90 minutes?

The orbital radius and orbital period of another satellite or the moon.

Solve the F_{g} equation for m, if the planets have the same mass.

m = sqrt(F_{g}*r^{2}/G)

The Earth has an orbital period of 52 weeks and an orbital radius of 1 AU. Earth's moon has an orbital period of about 4 weeks. Can we solve for the orbital radius of the moon with this information?

No. The moon is not orbiting the same object as the Earth.

The force of gravity on a dog is 40 Newtons when it is on the surface of the Earth. What would the new force of gravity be if the radius of the Earth shrunk by one half? (r is divided by two)

160 N

A newly discovered planet has the same acceleration due to gravity as the Earth, but the radius of the planet is twice as big as Earth's. How much bigger should the mass of this new planet be?

Four times bigger

The orbital period of Mars is 1.88 Earth years. What is the orbital radius of Mars?

1.523 AU

Solve the force of gravity equation for m_{1} if both planets have different masses.

m_{1}=F_{g}*r^{2}/(G*m_{2})

One planet orbits a star. Another planet with the same mass orbits the same star, but has twice orbital radius. If the planets are the same size, which has the greatest acceleration due to gravity on the surface.

They have the same acceleration due to gravity on the surface.

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