Gravitational Field

Guiding Questions

How do two masses interact? Do they need to be in physical contact to do so?
What do field lines represent? Do field lines represent similar things for gravitational fields and electric fields?
How can we understand the motion of planets and satellites? Are we at the centre of the universe?

Learning Outcomes

Gravitational Field	Learning Outcomes Students should be able to:	Learning Experiences Students may have opportunities to:
Gravitational field	show an understanding of the concept of a gravitational field as an example of field of force and define the gravitational field strength at a point as the gravitational force exerted per unit mass placed at that point. recognise the analogy between certain qualitative and quantitative aspects of gravitational and electric fields.	7.1 Examine the representation used in gravitation Examine how field lines are useful as a representation of the gravitational field to help in visualising, communicating and deepening the understanding of concepts in gravitation¹. Discuss the possible limitations of field lines in explaining the various gravitation ideas and concepts as well as possible misconceptions that may arise. Discuss the representation of field lines at surface of the Earth². 7.2 Build a model for Newton’s law of gravitation using a simulation Develop a mathematical model for the force of gravitation between two masses using a simulation³. 7.3 Investigate the value of g through experiments Design, carry out and present different experiments⁴^,⁵ (e.g. electromagnetic induction, free fall, oscillations) to find the value of acceleration of free fall, g. 7.4 Explore Newton’s thought experiment Explore Newton’s thought experiment on a cannon ball fired at right angles to the Earth’s gravitational field to come to an explanation for orbital motion and escape velocity. The calculated velocity of the cannon ball launched at the top of a mountain (with a height that is negligible when compared to the Earth’s radius) is 7,902 ms⁻¹. This is much greater than the muzzle velocity of modern military cannons, which reach velocities of about 1,800 ms⁻¹. The result is that Newton's Cannon could work in theory, but there is no existing way to fire a cannon ball or any projectile at the velocity required to orbit the Earth. 7.5 Explore the use of satellite data in Singapore Explore how data from satellites is used in Singapore, making reference to the work of the Centre for Remote Imaging, Sensing and Processing (CRISP) and Changi Metrological Station. Examples of how the data is used by Singapore include the monitoring of the haze problem⁶^,⁷ and the prediction of the weather. Students can also compare the differences in the use of data from geostationary orbits satellites and polar orbits satellites for these purposes.
Gravitational force between point masses	recall and use Newton’s law of gravitation in the form $F = \frac{G M_{1} M_{2}}{r^{2}}$ .
Gravitational field of a point mass	derive, from Newton’s law of gravitation and the definition of gravitational field strength, the equation $g = \frac{GM}{r^{2}}$ for the gravitational field strength of a point mass. recall and apply the equation $g = \frac{GM}{r^{2}}$ for the gravitational field strength of a point mass to new situations or to solve related problems.
Gravitational field near to the surface of the Earth	show an understanding that near the surface of the Earth g is approximately constant and equal to the acceleration of free fall.
Gravitational potential	define the gravitational potential at a point as the work done per unit mass in bringing a small test mass from infinity to that point. solve problems using the equation $φ = - \frac{GM}{r}$ for the gravitational potential in the field of a point mass.
Circular orbits	analyse circular orbits in inverse square law fields by relating the gravitational force to the centripetal acceleration it causes. show an understanding of geostationary orbits and their application.

1 Two Mass Model with Gravity Field Vector. Retrieved from [http://iwant2study.org/ospsg/index.php/interactive-resources/physics/05-electricity-and-magnetism/01-efield/265-ejss-model-twopointcharges01].

2 Earth Field 2D Mode. Retrieved from [http://iwant2study.org/ospsg/index.php/interactive-resources/physics/02-newtonian-mechanics/08-gravity/55-gravity03-1]

3 Gravity Force Lab. Retrieved from [https://phet.colorado.edu/en/simulation/gravity-force-lab].

4 Acceleration Due to Gravity. Retrieved from [http://physics.wustl.edu/introphys/Phys117_118/Lab_Manual/Experiments/AG2011.pdf].

5 Measurement of g using an electronic timer. Retrieved from [http://www.nuffieldfoundation.org/practical-physics/measurement-g-using-electronic-timer].

6 ASMC, Regional Haze Situation. Retrieved from [http://asmc.asean.org/home/].

7 NEA, Haze updates. Retrieved from [http://www.haze.gov.sg/haze-updates].

7. Introduction

In the topics of Dynamics, Forces, etc, we have been dealing with weights of different objects. Weight is a name given to the force acting on the object due to gravity. In other words, weight is a gravitational force.

Gravitational force is a force that is evident in our everyday lives and plays a crucial role in many processes on Earth. For instance, the ocean tides are caused by the gravitational attraction of both the Moon and Sun on the Earth’s oceans.

7.0 Real World Physics

7.0.1 Tidal changes over one day

On Day 0, approximately twice a month, around new moon when the Sun, Moon, and Earth form a line (a condition known as syzygy), the tidal force due to the sun reinforces that due to the Moon

On Day 0, when the Sun, Moon, and Earth form a line (a condition known as syzygy), the tidal force due to the Sun reinforces that due to the Moon. Note the observer experiences high tide.

At t =6 hours later, note it is low tide around the person.

At t =6 hours later, note the observer experiences low tide.

At t =12 hours later, note it is high tide around the person.

At t =12 hours later, note the observer experiences high tide.

At t =18 hours later, note it is low tide around the person.

At t =18 hours later, note the observer experiences low tide.

At t =24hours later, note it is low tide around the person.

At t =24 hours later, note the observer experiences high tide.

So it can be explained why in approximately one day ( t = 0, 6,12,18 and 24 hours), the combined gravitational forces of the Moon and the Sun give rise to the tidal changes ( high - low - high - low and high respectively).

7.0.2 Tidal changes over one month

At the end of the lunar cycle on the Day 29, 12 hours, around new moon when the Sun, Moon, and Earth form a line (a condition known as syzygy), the tidal force due to the Sun reinforces that due to the Moon. So over 29.5 days, which is a complete lunar cycle, the sea level varies as shown with orange representing the effects of the gravity of Sun, grey representing effects of the Moon and blue representing the resultant sea level waveform. So, gravity physics helps provide a way to formulate an explanation for the formation of tidal changes on Earth.
so after 29.5 days, the complete lunar cycle, the sea level varies as shown with orange represents the effects of the gravity of Sun, grey represents effects of the Moon and blue is the resultant sea level waveform

so after 29.5 days, the complete lunar cycle, the sea level varies as shown with orange represents the effects of the gravity of Sun, grey represents effects of the Moon and blue is the resultant sea level waveform

7.0.3 Other phenomena

More visibly around us, the falling of objects when released is also caused by the gravitational pull of the Earth on all objects.

In terms of explaining for planetary motion, the same gravitational force is also responsible for keeping the Earth in its orbit around the Sun.

7.0.4 YouTube

How do tides work? https://youtu.be/5ohDG7RqQ9I
Reasons for the Seasons https://youtu.be/Pgq0LThW7QA
What Physics Teachers Get Wrong About Tides! | Space Time | PBS Digital Studios https://youtu.be/pwChk4S99i4