A spacecraft of mass $1.0 \times 10^6$ kg is in orbit around the Sun at a radius of $1.1 \times 10^{11}$ m - AQA - A-Level Physics - Question 17 - 2018 - Paper 2
Question 17
A spacecraft of mass $1.0 \times 10^6$ kg is in orbit around the Sun at a radius of $1.1 \times 10^{11}$ m. The spacecraft moves into a new orbit of radius $2.5 \tim... show full transcript
Worked Solution & Example Answer:A spacecraft of mass $1.0 \times 10^6$ kg is in orbit around the Sun at a radius of $1.1 \times 10^{11}$ m - AQA - A-Level Physics - Question 17 - 2018 - Paper 2
Step 1
Calculate the initial gravitational potential energy
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Answer
The gravitational potential energy (U) is given by the formula:
U=−rGMm
Where:
G is the gravitational constant (approximately 6.674×10−11m3kg−1s−2)
M is the mass of the Sun (approximately 1.989×1030kg)
m is the mass of the spacecraft (1.0×106kg)
r is the distance from the center of the Sun to the spacecraft.
For the initial radius (r1=1.1×1011m):
U1=−1.1×1011(6.674×10−11)(1.989×1030)(1.0×106)
Step 2
Calculate the final gravitational potential energy
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Answer
For the final radius (r2=2.5×1011m):
U2=−2.5×1011(6.674×10−11)(1.989×1030)(1.0×106)
Step 3
Determine the change in gravitational potential energy
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Answer
The change in gravitational potential energy (ΔU) is calculated as:
ΔU=U2−U1
Substituting the values calculated from the previous steps will yield the total change.
