Gravity

Question 1

What is the total energy of a satellite equal to? Why is the total energy seen as negative? Show on paper

Answer 1

1) The sum of its GPE and its KE, total E = GPE + KE = GMm/2r - GMm/r = -GMm/2r
2) This occurs because the zero of gravitational potential is assigned at infinity

Question 2

Why do satellites burn up?

Answer 2

Satellites that are in a low Earth orbit (LEO) are affect by Earth’s atmosphere, over time sufficient air resistance is created to reduce the satellites speed causing it to be pulled towards Earth. As a consequence the total energy decreases, however the KE increases making the satellite speed up. The satellite heats up due to increasing friction as it spirals closer to Earth. Intense heat is generated causing it to burn up

Question 3

What is a synchronous orbit? What is synchronous orbit around the Earth called?

Answer 3

1) An orbit where the time period is equal to the rotational period of the planet being orbited
2) A geosynchronous orbit

Question 4

What are the features and uses of a low Earth polar orbit?

Answer 4

1) The plane of the polar orbit is 90° to the equatorial plane. The satellite is much closer to Earth than a geostationary orbit and travels at a much faster speed, completing several orbits in one day
2) Can scan Earth in a few days so suitable for: mapping and land features, monitoring ocean currents, tracking cloud coverage, monitoring the extent of polar ice caps, observing short term environmental changes (e.g. drifting oil spills), military surveillance

Question 5

What is the gravitational field strength at a point defined as? What is the equation for gravitational field strength?

Answer 5

1) The gravitational force per unit mass at that point

2) g = F/m

Question 6

How would you work out the orbital speed of a satellite orbiting Earth? What does this equation show? Derive equation on paper

Answer 6

1) Equate Newton’s equations of gravitational force with the equation for the centripetal force as this is provided by the gravitational force of the planet. Then rearrange for v
2) Satellites in lower orbits require a higher orbital speed

Question 7

What is Newtons law of universal gravitation? What is the equation?

Answer 7

1) Any two point masses attract each other with a force F that is directly proportional to the product of their masses m’m’’ and inversely proportional to the square of their separation r
2) F = (Gm’m’’)/r², where G is the gravitational constant

Question 8

What does a ‘point mass’ mean?

Answer 8

A spherically symmetrical object of uniform density who’s gravitational effect acts as if all its mass is concentrated at the centre

Question 9

What does the KE of a satellite moving with orbit radius r around Earth equal? Show on paper

Answer 9

1/2mv² where v is the satellites orbital speed. Equating the centripetal force equation to Newton’s law gives: mv²/r = GMm/r², therefore KE = 1/2mv² = GMm/2r

Question 10

How was Newton able to demonstrate mathematically the relationship between the acceleration caused by earths gravitational force and the distance from the earths centre on an object? What is the relationship?

Answer 10

1) By comparing the motion of a falling object at the earths surface and the motion of the moon falling towards earth
2) gravitational force is directly proportional to 1/(distance)²

Question 11

How can you prove that the time period squared (T²) is proportional to the radius of orbit cubed (r^3)? Prove on paper

Answer 11

By equating Newton’s equation for gravitational force to the equation for centripetal force, then substituting ω = 2π/T into the equation and rearranging for T

Question 12

What is the neutral point between two masses? E.g. The earth and the moon

Answer 12

Where the gravitational field strength of one mass is equal to the other. The position of the neutral point depends on the the mass difference between the two objects, with it being closer the the object with less mass

Question 13

What represents the gradient (sometimes referred to as the potential gradient) of a graph of gravitational potential vs distance? What are two ways the relationship between V and g be summarised?

Answer 13

1) ΔV/Δr = -g
2) Gravitational field strength g is equal to the ‘-gradient’ of the graph of gravitational potential vs distance OR potential difference ΔV is equal to the area between the curve and the distance axis of a gravitational field strength vs distance graph

Question 14

How do you get to the conclusion that the acceleration due to gravity is equal to the gravitational field strength?

Answer 14

By comparing F = ma and g = F/m

Question 15

What is the gravitational potential V at a point in a gravitational field? What are the units?

Answer 15

The work done (or gain in P.E.) per unit mass to move a mass from infinity (a point beyond the influence of the objects gravitational field) to that point. Units are J/kg

Question 16

What type of orbit does a communication satellite require and why? What is the name for this type of orbit?

Answer 16

A special type of geosynchronous orbit that orbits with a 24hr time period, orbits in the same direction as Earth and orbits in an equatorial plane. This is so that the receiving dishes can maintain continuous contact with the satellite while remaining in a fixed position pointing at the same spot
2) Known as a geostationary orbit

Question 17

How can the work done (energy required) to move a mass m from the earths surface to a height specified be found?

Answer 17

By working out the gravitational potential difference (ΔV) between these two values and then plugging into the equation: ΔW = mΔV

Question 18

What is an objects escape velocity? What is the velocity required to for a mass m to completely escape the gravitational field of planet of mass M and radius R? Show on paper

Answer 18

1) The speed at which it needs to be travelling away from an astronomical body in order to break free from the gravitational field without the use of any further propulsion
2) The energy required is equal to the work done (ΔW) in moving mass m from the planets surface to a point where the planet’s gravitational field has no effect (infinity): ΔW = mΔV = mGM/R, if the energy required to do this work is provided by the objects original KE, then 1/2mv² = mGM/R and v = √(2GM/R)

Question 19

What does the gravitational potential energy of a satellite moving with orbit radius r around Earth equal? Show on paper

Answer 19

The gravitational potential at distance r from the Earth’s centre multiplied by the satellites mass m, GPE = mV = (m)(-GM/r) =
-GMm/r

Question 20

What is gravitational potential energy?

Answer 20

The energy an object has because of its position in a gravitational field

Question 21

What is an equipotential surface? Work

Answer 21

The area around an object (e.g. Earth) where the gravitational potential is the same. No work is done as a satellite moves in its orbit along an equipotential surface, work required to move one from an inner equipotential surface to an outer one