Dawson 203-SNA-DW tutoring
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Send the chapter you’re studying in 203-SNA-DW and a question you’ve tried. We’ll confirm whether we can help before you book.
Optional course listed in the catalogue. It may not run every term. Ask us whether we can tutor you in it.
Prepare for later in the course
After the orbital-radius check below, extend the model when gravitation is in your announced chapters. This is not an early-midterm checklist. Two examples and four circular-orbit problems. Follow your section’s current instructions.
Use the centre-to-centre radius in a circular orbit
Dawson’s description of 203-SNA-DW includes universal gravitation and orbital mechanics. This original check develops only that mechanics topic. The catalogue description does not confirm a particular term, section or assessment.
In a hypothetical model, a planet with a spherically symmetric mass distribution has radius R = 6.0 × 10⁶ m and gravitational parameter μ = GM = 3.2 × 10¹⁴ m³/s². Here G is the gravitational constant and M is the planet’s mass; their product μ is supplied. A satellite of mass m = 200 kg follows a circular orbit at altitude h = 2.0 × 10⁶ m above the surface. Treat the planet as fixed and the satellite as a particle of negligible mass compared with the planet. Gravity is the only force; ignore the atmosphere, thrust and other bodies.
Find the orbital radius r, the satellite’s speed v and the gravitational force magnitude . Before calculating, predict whether using h as the radius would make your speed too large or too small.
Show a hint
The force law uses distance from the planet’s centre. Draw R and h on the same radial line. Gravity supplies the inward acceleration; a separate “centripetal force” arrow is not another interaction.
Show the worked solution
1. Identify the radius and the force
The radius is r = R + h = 8.0 × 10⁶ m. Draw one force on the satellite: gravity toward the planet’s centre. The velocity is tangent to the circle. Its speed is constant, but its direction changes, so its acceleration is not zero.
2. Connect gravity to the required inward acceleration
Newton’s law gives = mμ/r². Uniform circular motion requires inward acceleration v²/r. Therefore
The satellite mass cancels because both sides contain the same positive mass m. This cancellation assumes the stated fixed-planet approximation; it does not mean the gravitational force is independent of the satellite’s mass.
3. Calculate and check the units
Since μ/r has units m²/s², its square root is a speed. The gravitational acceleration is μ/r² = 5.0 m/s², giving = 200 × 5.0 = 1000 N. Independently, v²/r = 5.0 m/s² before rounding.
4. Diagnose the radius error
Using h = 2.0 × 10⁶ m would give about 12.6 km/s, twice the correct speed in this model. The radius entered would be four times too small. Altitude starts at the surface; r starts at the centre. Also, this circular speed is not the escape speed and does not describe every possible orbit at that distance.
Retry: change the altitude, not the planet
For the same planet and satellite, use a new circular-orbit altitude h = 10.0 × 10⁶ m. Find the new radius, speed and gravitational force. Predict their changes before substituting numbers. Would doubling m change the required circular speed?
Check the new orbit
The new radius is 16.0 × 10⁶ m, twice the original radius. Thus and . Gravity varies as 1/r², so its acceleration falls to 1.25 m/s² and its force on this 200 kg satellite falls to 250 N.
Doubling m doubles the gravitational force and the required inward force at a given speed. Their equality still gives the same circular speed, within the fixed-planet approximation. Doubling altitude alone would not double r because the planet’s radius must still be added.
Use your sketch to find the first error
Bring a labelled radius/altitude sketch and your radial equation. A tutor can check where each distance begins, whether gravity has been counted once, and why the satellite’s mass cancels. Then change only the altitude and explain the predicted speed and force ratios before doing a fresh calculation.
Review the inward-axis and real-force method. That resource’s string, friction and contact examples supply the method; the gravitational model is worked out here. Use μ/r² for this orbit’s acceleration; the resource’s 9.8 m/s² convention belongs to its own near-surface examples. Use its explanation of changing velocity direction if constant speed and acceleration seem contradictory.
The scope reference is Dawson’s official physics course list. Use your current outline for the other astronomy topics. Send your chapter and attempt to confirm tutoring coverage before booking.
Related subject areas
Choose the area that matches the chapter you’re studying.
Common difficulties
- Turning the situation into a model
- Using vectors, signs, and units consistently
- Selecting the relevant physical principle
How tutoring can help
Lessons follow your course materials and focus on what you want help with. Your tutor adapts to your needs and pace, explaining difficult ideas patiently, step by step. There’s time to ask questions, revisit unclear steps and practise together to build understanding and confidence.
Exam preparation for 203-SNA-DW
Choose a permitted practice question from your current review list and try it without its solution. Mark the first step you cannot explain. After reviewing that step, redo the question and explain why your method applies.
Use your section’s outline to choose the chapters to review. We work through permitted practice and comparable problems, without completing graded assignments or exams on your behalf.
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