Motion in the Universe
6 marks · NormalThe planet Mars and one of its artificial satellites both move in orbits around different objects. The table below gives the average orbital radius and time period of Mars around the Sun, and of a satellite around Mars.
| Object | Orbits | Average Orbital Radius (km) | Time Period (days) |
|---|---|---|---|
| Mars | Sun | 227,900,000 | 687 |
| Satellite | Mars | 6,000 | 0.32 |
State the name of the force responsible for keeping both Mars and the satellite in their respective orbits.
Explain why the time period of orbit is much greater for Mars than for its satellite, even though both are in orbit due to the same force.
Calculate the orbital speed of the artificial satellite around Mars. Give your answer in km/s. Use the formula: speed = (2 ) / , where is the orbital radius and is the time period in seconds.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) Filled in table as shown in content block; all values as per table.
(b) Gravity
(c) Mars takes longer to orbit the Sun because its orbital radius is much greater than that of the satellite around Mars. Objects further from the mass they orbit move more slowly and have longer time periods due to weaker gravitational pull.
(d) 1.36 km/s
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · Table is completed correctly as per provided values.
B1 (b) · 1 mark · Correctly names gravity as the force for both orbits.
M1 (c) · 1 mark · Explains the time period difference in terms of larger/smaller orbital radius or distance from central mass.
A1 (c) · 1 mark · Links greater radius to weaker gravitational pull and increased orbital period.
M1 (d) · 1 mark · Substitutes orbital radius and time correctly into the orbital speed formula.
A1 (d) · 1 mark · Accurate calculation with correct conversion of time to seconds and appropriate units (km/s). (follow-through)
Worked solution
a) Table is as provided; student does not need to fill in any new data.
b) The force responsible is gravity.
c) Mars takes longer to orbit the Sun than the artificial satellite takes to orbit Mars, because Mars orbits much farther from the Sun, so gravity is weaker and the orbit is larger. The satellite orbits very close to Mars, so gravity is strong and the orbit is small, leading to a shorter time period.
d) Orbital speed = (2 ) / .
Orbital radius km
Time period = 0.32 days = 0.32 × 24 × 3600 = 27,648 s