Astro-1010 Chapter 4 Homework

Compare the gravity between these pairs, each consisting of an Earth-like planet and its star. You are given the mass of the planet in Earth masses, the mass of the star in Sun masses, and the distance in AUs.

1 Mearth/2 Msolar/2AU 4Mearth/2 Msolar/3AU 1 Mearth/1 Msolar/1AU 2 Mearth/1 Msolar/ 1AU

In the diagram shown, m2 is in a circular orbit around m1. Label m2 with the arrow that shows the direction of the gravitational force acting on it from m1.

Arrow Up and to the Left

Sort the positions marked on the diagram of Earth into categories based on whether they are experiencing high or low ocean tides when the Moon is in the location shown. You may neglect the effects of Earth's rotation.

High Tide 0, 180 Low tide 90,270

Weight refers to the force of gravity acting on a mass. We often calculate the weight of an object by multiplying its mass by the local acceleration due to gravity. The value of gravitational acceleration on the surface of Mars is 0.38 times that on Earth.Assume your mass is 85.00 kg. Then your weight on Earth is 833.00 newtons (833.00 N = m × g = 85.00 kg × 9.8 m/s2).

Mass= 85 Weight=316.54

The connection between gravity and orbits enables astronomers to measure the __________ of stars and planets.

Masses

Which of the selected orbits have the greatest and the lowest closest-approach speed?

Orange is the slowest speed at closest approach Blue is the Fastest speed at closest approach

In the following diagram, label the gravitational force and velocity vector on the corresponding force vector.

Part 1 Velocity going up Gravity going sown Part 2 Gravity on right Velocity on Left

Sort each of the following pictures according to whether the Earth would be experiencing a spring or neap tide.

Spring tide -Full Moon -New Moon Neap tide - 3rd quarter -1st quarter

The force of gravity depends on the distance between objects, and this fact has some interesting implications for objects of substantial size. The force of gravity from the Moon, for instance, is different on each piece of the Earth, depending on how far that piece is from the Moon at that moment. Rank the parts of the Earth on the figure in order of decreasing gravitational force felt from the Moon.

Starting from top 4 2 Straight line (left to right) 5 3 1

If Earth shrank to a smaller radius but kept the same mass, the gravitational force between Earth and the Moon would

Stay the same

Given the sense of rotation in the figure, and the location of the Earth's bulge with respect to the Moon, what effect would you expect to come from this reaction force?

The Earth's day will become longer with time

Newton determined that the force of gravity on an object is proportional to its mass, causing its mass to be canceled out (Newton's second law) and resulting in a constant acceleration. If the laws of physics are universal, then Newton should be able to apply his discoveries about gravity on Earth to the motion of the planets in our Solar System. Newton's third law says that for every force there is an equal reaction force in the opposite direction. What does this imply about the force of gravity associated with a person standing on the Earth?

The Earth's gravity pulls downward on the person, and the person's gravity pulls upward on the Earth.

The gravity of this off-center bulge has an effect on the Moon. Study the above figure, and choose the statement below that follows from it.

The Moon used to be closer to Earth than it is now.

Newton's second law says that the acceleration (a) of an object depends on its mass (m) by the equation: a=F/m F​ is the force that is causing the object to accelerate. In the case of dropping objects from a height, the force that causes them to accelerate toward the Earth is gravity. If the acceleration of objects dropped from a height does not depend on the object's mass (as shown by Galileo's experiment), what does this imply about the force of gravity?

The force of gravity increases with increased mass.

Newton developed a universal law of gravitation that can be used under most circumstances, not just for objects on the surface of the Earth. Here is the law:F=Gm1m2r2F=Gm1m2r2 where G is a constant.Think about what happens when you increase and decrease each of the variables in Newton's equation for the gravitational force between two objects of mass m1 and m2, a distance r from one another. Given your results, what is the likely cause of Kepler's observation that planets travel faster when they are closer to the Sun?

The force of gravity is stronger closer to the Sun.

Astronauts in a space shuttle can float while orbiting Earth. Why are these astronauts weightless?

They are falling around Earth at the same rate as the shuttle.

According to the object orbits shown on the vertical axis at left of the graph, identify each orbit as either unbound, circular, or elliptical.

Unbound -Orbit 3 -Orbit 4 Circular -Orbit 1 Elliptical -Orbit 2

For a pair of objects, the center of mass is located

along the line between the two objects, closer to the more massive object.

An object in a(n) __________ orbit in the Solar System will remain in its orbit forever. An object in a(n) __________ orbit will escape from the Solar System.

bound; unbound

If the distance between Earth and the Sun were cut in half, the gravitational force between these two objects would

increase by a factor of 4.

Suppose you are transported to a planet with twice the mass of Earth, but the same radius of Earth. Your weight would __________ by a factor of __________.

increase; 2

If you went to Mars, your weight would be

lower because Mars has lower mass and a smaller radius that together produce a lower gravitational force.

Rank the following pairs of masses by the strength of their gravitational force. Note: The captions under the images give the relative masses of each object and their distance from one another (M1, M2, d).

m,m,1.5r (smallest) m,m,r m,2m,r(greatest)

Weight refers to the force of gravity acting on a mass. We often calculate the weight of an object by multiplying its mass by the local acceleration due to gravity. The value of gravitational acceleration on the surface of Mars is 0.377 times that on Earth. If your mass is 85 kg, your weight on Earth is 830 N (m × g = 85 kg × 9.8 m/s2 = 830 N). What would be your approximate mass and weight on Mars?

mass 85 kg; weight 310 N

If an object crosses from farther to closer than the Roche limit, it

may be torn apart.

Spring tides occur only when

the Moon is in new or full phase

Spring tides occur only when:

the Moon is in new or full phase.

The primary factor in Earth's tides is

the Moon's gravity.

Subsequent semi-diurnal (twice daily) tides happen precisely once every 12 hours and 25 minutes. Given what you know of the motions of the Earth and Moon, where is this extra 25 minutes likely coming from?

the orbit of the Moon around the Earth

Compared to your mass on Earth, on the Moon your mass would be

the same; mass doesn't change.

What causes the Moon to always keep the same face toward Earth?

tidal locking

The "second" high tide is caused by

weaker gravity pulling on Earth on the side opposite the Moon

If the Moon had twice the mass that it does, how would the strength of the lunar tides change?

The highs would be higher and the lows would be lower.