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Initially a satellite of 100 kg is in a circular orbit of radius 1.5R_E. This satellite can be moved to a circular orbit of radius 3R_E by supplying α×10⁶ J of energy. The value of α is (take radius of earth R_E=6×10⁶ m and g=10 m/s²)

Asked in JEE Main 21st Jan 1st Shift 2026 · Changing the orbit

• (1) 100
• (2) 500
• (3) 1000
• (4) 150

Step-by-step solution

Why the other options are wrong

• (1) Off by ten, the usual result of writing R_E=6×10⁵ m or of dropping one power of ten while turning gR_E² into GM.
• (2) Follows from using 1/(1.5)-1/3 without the factor 1/2 in E=-(GMm)/(2r) and then halving only once, so the bracket becomes 1/3 instead of 1/6.
• (4) Reading the orbit radii as 1.5R_E and 2R_E does not land here either: that gives α=500, the option above. No single consistent slip produces 150; it is a filler distractor built out of the 1.5 in the starting radius.

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