M5 topic 3 motion in a gravatational field

Question 1

What is Newton’s law of universal gravitation equation

Answer 1

F= GMm/r²

Question 2

what does each symbol in Newton’s law of universal gravitation equation mean, and what units is each measured in

Answer 2

F = the gravitational force (newtons(N))
M = the mass  of object 1 (kg)
m = the mass of object 2 (kg)
r = the distance between the centres of objects 1 and 2 (m)
G = the gravitational constant (6.67 x 10⁻¹¹ Nm²kg⁻²)

Question 3

what is the Gravitational Field Strength equation

Answer 3

g=GM/r²

Question 4

what does each symbol in Gravitational Field Strength equation and what units is each measured in

Answer 4

g = the gravitational field strength (Newtons per kilogram (Nkg⁻¹))
M = the mass of an object in the field (kg)
G = the gravitational constant (6.67 x 10⁻¹¹ Nm²kg⁻²)
r = the distance from the centre to the object in the field

Question 5

what is Einstein’s concept of Gravitational Attraction (2)

Answer 5

• Massive objects curve spacetime, making gravitational wells
• Other massive objects affected by this curvature experience an attractive force

Question 6

list the types of orbits (3)

Answer 6

• LEO (low Earth Orbit)
• MEO (Mid-Earth orbit)
• GEO (geostationary orbit

Question 7

List the characteristics of a LEO (low Earth orbit) orbit (altitude, Orbital period, Application(3))

Answer 7

Altitude: 100-1000 km
Orbital period: 60-90 mins (250 km altitude)
Applications: Hubble Space telescope, Earth observation, Weather monitoring

Question 8

List the characteristics of a GEO (low Earth orbit) orbit (altitude, Orbital period, Application(3))

Answer 8

Altitude: 35800km
Orbital period: 23hr 56mins
Applications: Communication, mass media, weather monitoring

Question 9

What is the “orbital speed of a satellite” equation

Answer 9

v = 2π/r = √(GM/r)

Question 10

What does each symbol mean in the orbital speed of a satellite equation and what unit is it measured in

Answer 10

v = Orbital speed of satellite (m/s)
G = gravitational constant (6.67 x 10⁻¹¹ N m²kg⁻²)
M = mass of the Earth (6.0 x 10²⁴kg)
r = radius of the circular orbit (m)

Question 11

What are kepler’s law of Planetary motion (3)

Answer 11

1st law: the planets follow a elliptical orbits with the sun at one focus
2nd law: planets sweep the same amount of area in equal amount of times
3rd law: The cube of the orbital radius of a planet is proportional to the square of its orbital period

Question 12

what is the equation of kepler 3rd law

Answer 12

r³/T² =GM/4π²

Question 13

what does each symbol in the kepler’s 3rd law equation represent

Answer 13

r= radius of orbit (m)
T= period of orbit (s)
G = the gravitational constant (6.67 x 10⁻¹¹ N m²kg⁻²)
M = mass of the Earth (6.0 x 10²⁴kg)

Question 14

how is gravitational potential energy using the gravitational constant calculated

Answer 14

U = - GMm/r

Question 15

what does each symbol mean in the gravitational potential energy equation (using G) and what units are they measured in

Answer 15

U = gravitational potential energy (newtons)
G = the gravitational constant (6.67 x 10⁻¹¹ N m²kg⁻²)
M = mass of the bigger object (kg)
m = mass of the smaller object (kg
r = the distance between both objects (m)

Question 16

what determines an object’s gravitational potential energy (2)

Answer 16

• how big the gravitational well is (the more denser the object the bigger the well)
• and the position the object is in the gravitational well

Question 17

how is escape velocity derived from the gravitational potential equation (show reasoning and working)

Answer 17

• to escape, a projectile’s kinetic energy must be equal the gravitational potential energy
• so the kinetic and gravitational potential energy are equal (K=U , 1/2mv² = GMm/r, then solve for v)

Question 18

what is the escape velocity equation

Answer 18

vₑₛ𝒸ₐₚₑ = √(2GM/r)

Question 19

what does each symbol in the escape velocity equation mean and what unit is it measured in

Answer 19

vₑₛ𝒸ₐₚₑ = escape velocity
G= the gravitational constant (6.67 x 10⁻¹¹ N m²kg⁻²)
M= mass of object
r= distance away from the surface of the earth

Question 20

what is the equation for the kinetic energy of a satellite

Answer 20

K= GMm/2r (half of the magnitude of gravitational potential energy (but positive))

Question 21

what does each symbol in the equation for the kinetic energy of a satellite mean

Answer 21

K= kinetic energy
G= the gravitational constant (6.67 x 10⁻¹¹ N m²kg⁻²)
M= mass of the bigger object
m= mass of the satelite
r = distance of the satellite from the bigger object

Question 22

what is the total energy of an object equal to

Answer 22

Eₜₒₜₐₗ= U + K = - GMm/2r